vibração em navíos
DESCRIPTION
Descobrindo a vibração em navíos.TRANSCRIPT
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Universidade Federal do Rio de JaneiroEngenharia Naval e OcenicaCurso de VibraoProf. Severino Fonseca da Silva Neto, D.Sc
Mdulo - Anlise Dinmica Linear - Vibrao Livre de Prtico Plano
MateriaisMaterial de numerao nmMdulo de elasticidade E(nm)Coeficiente de Poisson Mi(nm)Massa especfica Ro(nm)Coeficiente de Dilatao Linear Alfa(nm)
Propriedades GeomtricasPropriedade de numerao nprea da seo transversal A(np)Momento de Inrcia Iz(np)
NsNs de numerao nnodeCoordenadas X(nn), Y(nn)Numerao global de graus de liberdade: horizontal NGLx(nn), vertical NGLy(nn), rotao NGLrz(nn)
Elemento finito de prtico plano (viga no plano X-Y)Elemento de numerao nelMaterial Nm(nel)Propriedade Np(nel)N inicial Nini(nel)N final Nfin(nel)
Dados de Entrada: Materiais, Propriedades Geomtricas, Coordenadas e GLs dos Ns
restart:
with (linalg):
E(1):=200E9:
Ro(1):=7860:
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A(1):=1.11:Iz(1):=24.3:
X(1):=0:Y(1):=0:NGLx(1):=1:NGLy(1):=2:NGLrz(1):=3:
X(2):=3.75:Y(2):=0:NGLx(2):=4:NGLy(2):=5:NGLrz(2):=6:
X(3):=7.5:Y(3):=0:NGLx(3):=7:NGLy(3):=8:NGLrz(3):=9:
X(4):=11.25:Y(4):=0:NGLx(4):=10:NGLy(4):=11:NGLrz(4):=12:
X(5):=15:Y(5):=0:NGLx(5):=13:NGLy(5):=14:NGLrz(5):=15:
X(6):=18.75:Y(6):=0:NGLx(6):=16:NGLy(6):=17:
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NGLrz(6):=18:
X(7):=22.5:Y(7):=0:NGLx(7):=19:NGLy(7):=20:NGLrz(7):=21:
X(8):=26.25:Y(8):=0:NGLx(8):=22:NGLy(8):=23:NGLrz(8):=24:
X(9):=30:Y(9):=0:NGLx(9):=25:NGLy(9):=26:NGLrz(9):=27:
X(10):=33.75:Y(10):=0:NGLx(10):=28:NGLy(10):=29:NGLrz(10):=30:
X(11):=37.5:Y(11):=0:NGLx(11):=31:NGLy(11):=32:NGLrz(11):=33:
X(12):=41.25:Y(12):=0:NGLx(12):=34:NGLy(12):=35:NGLrz(12):=36:
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X(13):=45:Y(13):=0:NGLx(13):=37:NGLy(13):=38:NGLrz(13):=39:
X(14):=48.75:Y(14):=0:NGLx(14):=40:NGLy(14):=41:NGLrz(14):=42:
X(15):=52.5:Y(15):=0:NGLx(15):=43:NGLy(15):=44:NGLrz(15):=45:
X(16):=56.25:Y(16):=0:NGLx(16):=46:NGLy(16):=47:NGLrz(16):=48:
X(17):=60:Y(17):=0:NGLx(17):=49:NGLy(17):=50:NGLrz(17):=51:
Matrizes de Rigidez dos Elementos nos Referenciais Locais e Global e Matriz Global
KG:=matrix(51,51,0):
Nel:=1:Nm(Nel):=1:
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Np(Nel):=1:Nini(Nel):=1:Nfin(Nel):=2:
L(Nel):=sqrt((X(Nfin(Nel))-X(Nini(Nel)))^2+(Y(Nfin(Nel))-Y(Nini(Nel)))^2):CosLocGlob:=(X(Nfin(Nel))-X(Nini(Nel)))/L(Nel):SenLocGlob:=-(Y(Nfin(Nel))-Y(Nini(Nel)))/L(Nel):
Kloc:=matrix([[E(Nm(Nel))*A(Np(Nel))/L(Nel),0,0,-E(Nm(Nel))*A(Np(Nel))/L(Nel),0,0],[0,12.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^3,6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2,0,-12.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^3,6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2],[0,6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2,4.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel),0,-6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2,2.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)],[-E(Nm(Nel))*A(Np(Nel))/L(Nel),0,0,E(Nm(Nel))*A(Np(Nel))/L(Nel),0,0],[0,-12.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^3,-6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2,0,12.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^3,-6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2],[0,6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2,2.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel),0,-6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2,4.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)]]):
Rot(Nel):=matrix([[CosLocGlob,SenLocGlob,0,0,0,0],[-SenLocGlob,CosLocGlob,0,0,0,0],[0,0,1.,0,0,0],[0,0,0,CosLocGlob,SenLocGlob,0],[0,0,0,-SenLocGlob,CosLocGlob,0],[0,0,0,0,0,1.]]):
Trot:=transpose(Rot(Nel)):
K(Nel):=evalm(Rot(Nel)&*Kloc&*Trot):
KG[NGLx(Nini(Nel)),NGLx(Nini(Nel))]:=KG[NGLx(Nini(Nel)),NGLx(Nini(Nel))]+K(Nel)[1,1]:KG[NGLx(Nini(Nel)),NGLy(Nini(Nel))]:=KG[NGLx(Nini(Nel)),NGLy(Nini(Nel))]+K(Nel)[1,2]:KG[NGLx(Nini(Nel)),NGLrz(Nini(Nel))]:=KG[NGLx(Nini(Nel)),NGLrz(Nini(Nel))]+K(Nel)[1,3]:KG[NGLx(Nini(Nel)),NGLx(Nfin(Nel))]:=KG[NGLx(Nini(Nel)),NGLx(Nfin(Nel))]+K(Nel)[1,4]:KG[NGLx(Nini(Nel)),NGLy(Nfin(Nel))]:=KG[NGLx(Nini(Nel)),NGLy
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(Nfin(Nel))]+K(Nel)[1,5]:KG[NGLx(Nini(Nel)),NGLrz(Nfin(Nel))]:=KG[NGLx(Nini(Nel)),NGLrz(Nfin(Nel))]+K(Nel)[1,6]:
KG[NGLy(Nini(Nel)),NGLx(Nini(Nel))]:=KG[NGLy(Nini(Nel)),NGLx(Nini(Nel))]+K(Nel)[2,1]:KG[NGLy(Nini(Nel)),NGLy(Nini(Nel))]:=KG[NGLy(Nini(Nel)),NGLy(Nini(Nel))]+K(Nel)[2,2]:KG[NGLy(Nini(Nel)),NGLrz(Nini(Nel))]:=KG[NGLy(Nini(Nel)),NGLrz(Nini(Nel))]+K(Nel)[2,3]:KG[NGLy(Nini(Nel)),NGLx(Nfin(Nel))]:=KG[NGLy(Nini(Nel)),NGLx(Nfin(Nel))]+K(Nel)[2,4]:KG[NGLy(Nini(Nel)),NGLy(Nfin(Nel))]:=KG[NGLy(Nini(Nel)),NGLy(Nfin(Nel))]+K(Nel)[2,5]:KG[NGLy(Nini(Nel)),NGLrz(Nfin(Nel))]:=KG[NGLy(Nini(Nel)),NGLrz(Nfin(Nel))]+K(Nel)[2,6]:
KG[NGLrz(Nini(Nel)),NGLx(Nini(Nel))]:=KG[NGLrz(Nini(Nel)),NGLx(Nini(Nel))]+K(Nel)[3,1]:KG[NGLrz(Nini(Nel)),NGLy(Nini(Nel))]:=KG[NGLrz(Nini(Nel)),NGLy(Nini(Nel))]+K(Nel)[3,2]:KG[NGLrz(Nini(Nel)),NGLrz(Nini(Nel))]:=KG[NGLrz(Nini(Nel)),NGLrz(Nini(Nel))]+K(Nel)[3,3]:KG[NGLrz(Nini(Nel)),NGLx(Nfin(Nel))]:=KG[NGLrz(Nini(Nel)),NGLx(Nfin(Nel))]+K(Nel)[3,4]:KG[NGLrz(Nini(Nel)),NGLy(Nfin(Nel))]:=KG[NGLrz(Nini(Nel)),NGLy(Nfin(Nel))]+K(Nel)[3,5]:KG[NGLrz(Nini(Nel)),NGLrz(Nfin(Nel))]:=KG[NGLrz(Nini(Nel)),NGLrz(Nfin(Nel))]+K(Nel)[3,6]:
KG[NGLx(Nfin(Nel)),NGLx(Nini(Nel))]:=KG[NGLx(Nfin(Nel)),NGLx(Nini(Nel))]+K(Nel)[4,1]:KG[NGLx(Nfin(Nel)),NGLy(Nini(Nel))]:=KG[NGLx(Nfin(Nel)),NGLy(Nini(Nel))]+K(Nel)[4,2]:KG[NGLx(Nfin(Nel)),NGLrz(Nini(Nel))]:=KG[NGLx(Nfin(Nel)),NGLrz(Nini(Nel))]+K(Nel)[4,3]:KG[NGLx(Nfin(Nel)),NGLx(Nfin(Nel))]:=KG[NGLx(Nfin(Nel)),NGLx(Nfin(Nel))]+K(Nel)[4,4]:KG[NGLx(Nfin(Nel)),NGLy(Nfin(Nel))]:=KG[NGLx(Nfin(Nel)),NGLy(Nfin(Nel))]+K(Nel)[4,5]:
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KG[NGLx(Nfin(Nel)),NGLrz(Nfin(Nel))]:=KG[NGLx(Nfin(Nel)),NGLrz(Nfin(Nel))]+K(Nel)[4,6]:
KG[NGLy(Nfin(Nel)),NGLx(Nini(Nel))]:=KG[NGLy(Nfin(Nel)),NGLx(Nini(Nel))]+K(Nel)[5,1]:KG[NGLy(Nfin(Nel)),NGLy(Nini(Nel))]:=KG[NGLy(Nfin(Nel)),NGLy(Nini(Nel))]+K(Nel)[5,2]:KG[NGLy(Nfin(Nel)),NGLrz(Nini(Nel))]:=KG[NGLy(Nfin(Nel)),NGLrz(Nini(Nel))]+K(Nel)[5,3]:KG[NGLy(Nfin(Nel)),NGLx(Nfin(Nel))]:=KG[NGLy(Nfin(Nel)),NGLx(Nfin(Nel))]+K(Nel)[5,4]:KG[NGLy(Nfin(Nel)),NGLy(Nfin(Nel))]:=KG[NGLy(Nfin(Nel)),NGLy(Nfin(Nel))]+K(Nel)[5,5]:KG[NGLy(Nfin(Nel)),NGLrz(Nfin(Nel))]:=KG[NGLy(Nfin(Nel)),NGLrz(Nfin(Nel))]+K(Nel)[5,6]:
KG[NGLrz(Nfin(Nel)),NGLx(Nini(Nel))]:=KG[NGLrz(Nfin(Nel)),NGLx(Nini(Nel))]+K(Nel)[6,1]:KG[NGLrz(Nfin(Nel)),NGLy(Nini(Nel))]:=KG[NGLrz(Nfin(Nel)),NGLy(Nini(Nel))]+K(Nel)[6,2]:KG[NGLrz(Nfin(Nel)),NGLrz(Nini(Nel))]:=KG[NGLrz(Nfin(Nel)),NGLrz(Nini(Nel))]+K(Nel)[6,3]:KG[NGLrz(Nfin(Nel)),NGLx(Nfin(Nel))]:=KG[NGLrz(Nfin(Nel)),NGLx(Nfin(Nel))]+K(Nel)[6,4]:KG[NGLrz(Nfin(Nel)),NGLy(Nfin(Nel))]:=KG[NGLrz(Nfin(Nel)),NGLy(Nfin(Nel))]+K(Nel)[6,5]:KG[NGLrz(Nfin(Nel)),NGLrz(Nfin(Nel))]:=KG[NGLrz(Nfin(Nel)),NGLrz(Nfin(Nel))]+K(Nel)[6,6]:
evalm(KG):
Nel:=2:Nm(Nel):=1:Np(Nel):=1:Nini(Nel):=2:Nfin(Nel):=3:
L(Nel):=sqrt((X(Nfin(Nel))-X(Nini(Nel)))^2+(Y(Nfin(Nel))-Y(Nini(Nel)))^2):
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CosLocGlob:=(X(Nfin(Nel))-X(Nini(Nel)))/L(Nel):SenLocGlob:=-(Y(Nfin(Nel))-Y(Nini(Nel)))/L(Nel):
Kloc:=matrix([[E(Nm(Nel))*A(Np(Nel))/L(Nel),0,0,-E(Nm(Nel))*A(Np(Nel))/L(Nel),0,0],[0,12.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^3,6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2,0,-12.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^3,6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2],[0,6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2,4.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel),0,-6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2,2.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)],[-E(Nm(Nel))*A(Np(Nel))/L(Nel),0,0,E(Nm(Nel))*A(Np(Nel))/L(Nel),0,0],[0,-12.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^3,-6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2,0,12.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^3,-6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2],[0,6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2,2.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel),0,-6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2,4.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)]]):
Rot(Nel):=matrix([[CosLocGlob,SenLocGlob,0,0,0,0],[-SenLocGlob,CosLocGlob,0,0,0,0],[0,0,1.,0,0,0],[0,0,0,CosLocGlob,SenLocGlob,0],[0,0,0,-SenLocGlob,CosLocGlob,0],[0,0,0,0,0,1.]]):
Trot:=transpose(Rot(Nel)):
K(Nel):=evalm(Rot(Nel)&*Kloc&*Trot):
KG[NGLx(Nini(Nel)),NGLx(Nini(Nel))]:=KG[NGLx(Nini(Nel)),NGLx(Nini(Nel))]+K(Nel)[1,1]:KG[NGLx(Nini(Nel)),NGLy(Nini(Nel))]:=KG[NGLx(Nini(Nel)),NGLy(Nini(Nel))]+K(Nel)[1,2]:KG[NGLx(Nini(Nel)),NGLrz(Nini(Nel))]:=KG[NGLx(Nini(Nel)),NGLrz(Nini(Nel))]+K(Nel)[1,3]:KG[NGLx(Nini(Nel)),NGLx(Nfin(Nel))]:=KG[NGLx(Nini(Nel)),NGLx(Nfin(Nel))]+K(Nel)[1,4]:KG[NGLx(Nini(Nel)),NGLy(Nfin(Nel))]:=KG[NGLx(Nini(Nel)),NGLy(Nfin(Nel))]+K(Nel)[1,5]:KG[NGLx(Nini(Nel)),NGLrz(Nfin(Nel))]:=KG[NGLx(Nini(Nel)),NGLrz(Nfin(Nel))]+K(Nel)[1,6]:
KG[NGLy(Nini(Nel)),NGLx(Nini(Nel))]:=KG[NGLy(Nini(Nel)),NGLx(Nini(Nel))]+K(Nel)[2,1]:
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KG[NGLy(Nini(Nel)),NGLy(Nini(Nel))]:=KG[NGLy(Nini(Nel)),NGLy(Nini(Nel))]+K(Nel)[2,2]:KG[NGLy(Nini(Nel)),NGLrz(Nini(Nel))]:=KG[NGLy(Nini(Nel)),NGLrz(Nini(Nel))]+K(Nel)[2,3]:KG[NGLy(Nini(Nel)),NGLx(Nfin(Nel))]:=KG[NGLy(Nini(Nel)),NGLx(Nfin(Nel))]+K(Nel)[2,4]:KG[NGLy(Nini(Nel)),NGLy(Nfin(Nel))]:=KG[NGLy(Nini(Nel)),NGLy(Nfin(Nel))]+K(Nel)[2,5]:KG[NGLy(Nini(Nel)),NGLrz(Nfin(Nel))]:=KG[NGLy(Nini(Nel)),NGLrz(Nfin(Nel))]+K(Nel)[2,6]:
KG[NGLrz(Nini(Nel)),NGLx(Nini(Nel))]:=KG[NGLrz(Nini(Nel)),NGLx(Nini(Nel))]+K(Nel)[3,1]:KG[NGLrz(Nini(Nel)),NGLy(Nini(Nel))]:=KG[NGLrz(Nini(Nel)),NGLy(Nini(Nel))]+K(Nel)[3,2]:KG[NGLrz(Nini(Nel)),NGLrz(Nini(Nel))]:=KG[NGLrz(Nini(Nel)),NGLrz(Nini(Nel))]+K(Nel)[3,3]:KG[NGLrz(Nini(Nel)),NGLx(Nfin(Nel))]:=KG[NGLrz(Nini(Nel)),NGLx(Nfin(Nel))]+K(Nel)[3,4]:KG[NGLrz(Nini(Nel)),NGLy(Nfin(Nel))]:=KG[NGLrz(Nini(Nel)),NGLy(Nfin(Nel))]+K(Nel)[3,5]:KG[NGLrz(Nini(Nel)),NGLrz(Nfin(Nel))]:=KG[NGLrz(Nini(Nel)),NGLrz(Nfin(Nel))]+K(Nel)[3,6]:
KG[NGLx(Nfin(Nel)),NGLx(Nini(Nel))]:=KG[NGLx(Nfin(Nel)),NGLx(Nini(Nel))]+K(Nel)[4,1]:KG[NGLx(Nfin(Nel)),NGLy(Nini(Nel))]:=KG[NGLx(Nfin(Nel)),NGLy(Nini(Nel))]+K(Nel)[4,2]:KG[NGLx(Nfin(Nel)),NGLrz(Nini(Nel))]:=KG[NGLx(Nfin(Nel)),NGLrz(Nini(Nel))]+K(Nel)[4,3]:KG[NGLx(Nfin(Nel)),NGLx(Nfin(Nel))]:=KG[NGLx(Nfin(Nel)),NGLx(Nfin(Nel))]+K(Nel)[4,4]:KG[NGLx(Nfin(Nel)),NGLy(Nfin(Nel))]:=KG[NGLx(Nfin(Nel)),NGLy(Nfin(Nel))]+K(Nel)[4,5]:KG[NGLx(Nfin(Nel)),NGLrz(Nfin(Nel))]:=KG[NGLx(Nfin(Nel)),NGLrz(Nfin(Nel))]+K(Nel)[4,6]:
KG[NGLy(Nfin(Nel)),NGLx(Nini(Nel))]:=KG[NGLy(Nfin(Nel)),NGLx(Nini(Nel))]+K(Nel)[5,1]:KG[NGLy(Nfin(Nel)),NGLy(Nini(Nel))]:=KG[NGLy(Nfin(Nel)),NGLy
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(Nini(Nel))]+K(Nel)[5,2]:KG[NGLy(Nfin(Nel)),NGLrz(Nini(Nel))]:=KG[NGLy(Nfin(Nel)),NGLrz(Nini(Nel))]+K(Nel)[5,3]:KG[NGLy(Nfin(Nel)),NGLx(Nfin(Nel))]:=KG[NGLy(Nfin(Nel)),NGLx(Nfin(Nel))]+K(Nel)[5,4]:KG[NGLy(Nfin(Nel)),NGLy(Nfin(Nel))]:=KG[NGLy(Nfin(Nel)),NGLy(Nfin(Nel))]+K(Nel)[5,5]:KG[NGLy(Nfin(Nel)),NGLrz(Nfin(Nel))]:=KG[NGLy(Nfin(Nel)),NGLrz(Nfin(Nel))]+K(Nel)[5,6]:
KG[NGLrz(Nfin(Nel)),NGLx(Nini(Nel))]:=KG[NGLrz(Nfin(Nel)),NGLx(Nini(Nel))]+K(Nel)[6,1]:KG[NGLrz(Nfin(Nel)),NGLy(Nini(Nel))]:=KG[NGLrz(Nfin(Nel)),NGLy(Nini(Nel))]+K(Nel)[6,2]:KG[NGLrz(Nfin(Nel)),NGLrz(Nini(Nel))]:=KG[NGLrz(Nfin(Nel)),NGLrz(Nini(Nel))]+K(Nel)[6,3]:KG[NGLrz(Nfin(Nel)),NGLx(Nfin(Nel))]:=KG[NGLrz(Nfin(Nel)),NGLx(Nfin(Nel))]+K(Nel)[6,4]:KG[NGLrz(Nfin(Nel)),NGLy(Nfin(Nel))]:=KG[NGLrz(Nfin(Nel)),NGLy(Nfin(Nel))]+K(Nel)[6,5]:KG[NGLrz(Nfin(Nel)),NGLrz(Nfin(Nel))]:=KG[NGLrz(Nfin(Nel)),NGLrz(Nfin(Nel))]+K(Nel)[6,6]:
evalm(KG):
Nel:=3:Nm(Nel):=1:Np(Nel):=1:Nini(Nel):=3:Nfin(Nel):=4:
L(Nel):=sqrt((X(Nfin(Nel))-X(Nini(Nel)))^2+(Y(Nfin(Nel))-Y(Nini(Nel)))^2):CosLocGlob:=(X(Nfin(Nel))-X(Nini(Nel)))/L(Nel):SenLocGlob:=-(Y(Nfin(Nel))-Y(Nini(Nel)))/L(Nel):
Kloc:=matrix([[E(Nm(Nel))*A(Np(Nel))/L(Nel),0,0,-E(Nm(Nel))*A(Np(Nel))/L(Nel),0,0],[0,12.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^3,6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2,0,-12.*E(Nm(Nel))*Iz(Np(Nel))
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/L(Nel)^3,6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2],[0,6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2,4.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel),0,-6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2,2.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)],[-E(Nm(Nel))*A(Np(Nel))/L(Nel),0,0,E(Nm(Nel))*A(Np(Nel))/L(Nel),0,0],[0,-12.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^3,-6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2,0,12.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^3,-6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2],[0,6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2,2.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel),0,-6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2,4.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)]]):
Rot(Nel):=matrix([[CosLocGlob,SenLocGlob,0,0,0,0],[-SenLocGlob,CosLocGlob,0,0,0,0],[0,0,1.,0,0,0],[0,0,0,CosLocGlob,SenLocGlob,0],[0,0,0,-SenLocGlob,CosLocGlob,0],[0,0,0,0,0,1.]]):
Trot:=transpose(Rot(Nel)):
K(Nel):=evalm(Rot(Nel)&*Kloc&*Trot):
KG[NGLx(Nini(Nel)),NGLx(Nini(Nel))]:=KG[NGLx(Nini(Nel)),NGLx(Nini(Nel))]+K(Nel)[1,1]:KG[NGLx(Nini(Nel)),NGLy(Nini(Nel))]:=KG[NGLx(Nini(Nel)),NGLy(Nini(Nel))]+K(Nel)[1,2]:KG[NGLx(Nini(Nel)),NGLrz(Nini(Nel))]:=KG[NGLx(Nini(Nel)),NGLrz(Nini(Nel))]+K(Nel)[1,3]:KG[NGLx(Nini(Nel)),NGLx(Nfin(Nel))]:=KG[NGLx(Nini(Nel)),NGLx(Nfin(Nel))]+K(Nel)[1,4]:KG[NGLx(Nini(Nel)),NGLy(Nfin(Nel))]:=KG[NGLx(Nini(Nel)),NGLy(Nfin(Nel))]+K(Nel)[1,5]:KG[NGLx(Nini(Nel)),NGLrz(Nfin(Nel))]:=KG[NGLx(Nini(Nel)),NGLrz(Nfin(Nel))]+K(Nel)[1,6]:
KG[NGLy(Nini(Nel)),NGLx(Nini(Nel))]:=KG[NGLy(Nini(Nel)),NGLx(Nini(Nel))]+K(Nel)[2,1]:KG[NGLy(Nini(Nel)),NGLy(Nini(Nel))]:=KG[NGLy(Nini(Nel)),NGLy(Nini(Nel))]+K(Nel)[2,2]:KG[NGLy(Nini(Nel)),NGLrz(Nini(Nel))]:=KG[NGLy(Nini(Nel)),NGLrz(Nini(Nel))]+K(Nel)[2,3]:KG[NGLy(Nini(Nel)),NGLx(Nfin(Nel))]:=KG[NGLy(Nini(Nel)),NGLx(Nfin(Nel))]+K(Nel)[2,4]:
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KG[NGLy(Nini(Nel)),NGLy(Nfin(Nel))]:=KG[NGLy(Nini(Nel)),NGLy(Nfin(Nel))]+K(Nel)[2,5]:KG[NGLy(Nini(Nel)),NGLrz(Nfin(Nel))]:=KG[NGLy(Nini(Nel)),NGLrz(Nfin(Nel))]+K(Nel)[2,6]:
KG[NGLrz(Nini(Nel)),NGLx(Nini(Nel))]:=KG[NGLrz(Nini(Nel)),NGLx(Nini(Nel))]+K(Nel)[3,1]:KG[NGLrz(Nini(Nel)),NGLy(Nini(Nel))]:=KG[NGLrz(Nini(Nel)),NGLy(Nini(Nel))]+K(Nel)[3,2]:KG[NGLrz(Nini(Nel)),NGLrz(Nini(Nel))]:=KG[NGLrz(Nini(Nel)),NGLrz(Nini(Nel))]+K(Nel)[3,3]:KG[NGLrz(Nini(Nel)),NGLx(Nfin(Nel))]:=KG[NGLrz(Nini(Nel)),NGLx(Nfin(Nel))]+K(Nel)[3,4]:KG[NGLrz(Nini(Nel)),NGLy(Nfin(Nel))]:=KG[NGLrz(Nini(Nel)),NGLy(Nfin(Nel))]+K(Nel)[3,5]:KG[NGLrz(Nini(Nel)),NGLrz(Nfin(Nel))]:=KG[NGLrz(Nini(Nel)),NGLrz(Nfin(Nel))]+K(Nel)[3,6]:
KG[NGLx(Nfin(Nel)),NGLx(Nini(Nel))]:=KG[NGLx(Nfin(Nel)),NGLx(Nini(Nel))]+K(Nel)[4,1]:KG[NGLx(Nfin(Nel)),NGLy(Nini(Nel))]:=KG[NGLx(Nfin(Nel)),NGLy(Nini(Nel))]+K(Nel)[4,2]:KG[NGLx(Nfin(Nel)),NGLrz(Nini(Nel))]:=KG[NGLx(Nfin(Nel)),NGLrz(Nini(Nel))]+K(Nel)[4,3]:KG[NGLx(Nfin(Nel)),NGLx(Nfin(Nel))]:=KG[NGLx(Nfin(Nel)),NGLx(Nfin(Nel))]+K(Nel)[4,4]:KG[NGLx(Nfin(Nel)),NGLy(Nfin(Nel))]:=KG[NGLx(Nfin(Nel)),NGLy(Nfin(Nel))]+K(Nel)[4,5]:KG[NGLx(Nfin(Nel)),NGLrz(Nfin(Nel))]:=KG[NGLx(Nfin(Nel)),NGLrz(Nfin(Nel))]+K(Nel)[4,6]:
KG[NGLy(Nfin(Nel)),NGLx(Nini(Nel))]:=KG[NGLy(Nfin(Nel)),NGLx(Nini(Nel))]+K(Nel)[5,1]:KG[NGLy(Nfin(Nel)),NGLy(Nini(Nel))]:=KG[NGLy(Nfin(Nel)),NGLy(Nini(Nel))]+K(Nel)[5,2]:KG[NGLy(Nfin(Nel)),NGLrz(Nini(Nel))]:=KG[NGLy(Nfin(Nel)),NGLrz(Nini(Nel))]+K(Nel)[5,3]:KG[NGLy(Nfin(Nel)),NGLx(Nfin(Nel))]:=KG[NGLy(Nfin(Nel)),NGLx(Nfin(Nel))]+K(Nel)[5,4]:KG[NGLy(Nfin(Nel)),NGLy(Nfin(Nel))]:=KG[NGLy(Nfin(Nel)),NGLy
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(Nfin(Nel))]+K(Nel)[5,5]:KG[NGLy(Nfin(Nel)),NGLrz(Nfin(Nel))]:=KG[NGLy(Nfin(Nel)),NGLrz(Nfin(Nel))]+K(Nel)[5,6]:
KG[NGLrz(Nfin(Nel)),NGLx(Nini(Nel))]:=KG[NGLrz(Nfin(Nel)),NGLx(Nini(Nel))]+K(Nel)[6,1]:KG[NGLrz(Nfin(Nel)),NGLy(Nini(Nel))]:=KG[NGLrz(Nfin(Nel)),NGLy(Nini(Nel))]+K(Nel)[6,2]:KG[NGLrz(Nfin(Nel)),NGLrz(Nini(Nel))]:=KG[NGLrz(Nfin(Nel)),NGLrz(Nini(Nel))]+K(Nel)[6,3]:KG[NGLrz(Nfin(Nel)),NGLx(Nfin(Nel))]:=KG[NGLrz(Nfin(Nel)),NGLx(Nfin(Nel))]+K(Nel)[6,4]:KG[NGLrz(Nfin(Nel)),NGLy(Nfin(Nel))]:=KG[NGLrz(Nfin(Nel)),NGLy(Nfin(Nel))]+K(Nel)[6,5]:KG[NGLrz(Nfin(Nel)),NGLrz(Nfin(Nel))]:=KG[NGLrz(Nfin(Nel)),NGLrz(Nfin(Nel))]+K(Nel)[6,6]:
evalm(KG):
Nel:=4:Nm(Nel):=1:Np(Nel):=1:Nini(Nel):=4:Nfin(Nel):=5:
L(Nel):=sqrt((X(Nfin(Nel))-X(Nini(Nel)))^2+(Y(Nfin(Nel))-Y(Nini(Nel)))^2):CosLocGlob:=(X(Nfin(Nel))-X(Nini(Nel)))/L(Nel):SenLocGlob:=-(Y(Nfin(Nel))-Y(Nini(Nel)))/L(Nel):
Kloc:=matrix([[E(Nm(Nel))*A(Np(Nel))/L(Nel),0,0,-E(Nm(Nel))*A(Np(Nel))/L(Nel),0,0],[0,12.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^3,6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2,0,-12.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^3,6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2],[0,6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2,4.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel),0,-6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2,2.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)],[-E(Nm(Nel))*A(Np(Nel))/L(Nel),0,0,E(Nm(Nel))*A(Np(Nel))/L(Nel),0,0],[0,-12.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^3,-6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2,0,12.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^3,-6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2],[0,6.*E(Nm(Nel))*Iz(Np
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(Nel))/L(Nel)^2,2.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel),0,-6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2,4.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)]]):
Rot(Nel):=matrix([[CosLocGlob,SenLocGlob,0,0,0,0],[-SenLocGlob,CosLocGlob,0,0,0,0],[0,0,1.,0,0,0],[0,0,0,CosLocGlob,SenLocGlob,0],[0,0,0,-SenLocGlob,CosLocGlob,0],[0,0,0,0,0,1.]]):
Trot:=transpose(Rot(Nel)):
K(Nel):=evalm(Rot(Nel)&*Kloc&*Trot):
KG[NGLx(Nini(Nel)),NGLx(Nini(Nel))]:=KG[NGLx(Nini(Nel)),NGLx(Nini(Nel))]+K(Nel)[1,1]:KG[NGLx(Nini(Nel)),NGLy(Nini(Nel))]:=KG[NGLx(Nini(Nel)),NGLy(Nini(Nel))]+K(Nel)[1,2]:KG[NGLx(Nini(Nel)),NGLrz(Nini(Nel))]:=KG[NGLx(Nini(Nel)),NGLrz(Nini(Nel))]+K(Nel)[1,3]:KG[NGLx(Nini(Nel)),NGLx(Nfin(Nel))]:=KG[NGLx(Nini(Nel)),NGLx(Nfin(Nel))]+K(Nel)[1,4]:KG[NGLx(Nini(Nel)),NGLy(Nfin(Nel))]:=KG[NGLx(Nini(Nel)),NGLy(Nfin(Nel))]+K(Nel)[1,5]:KG[NGLx(Nini(Nel)),NGLrz(Nfin(Nel))]:=KG[NGLx(Nini(Nel)),NGLrz(Nfin(Nel))]+K(Nel)[1,6]:
KG[NGLy(Nini(Nel)),NGLx(Nini(Nel))]:=KG[NGLy(Nini(Nel)),NGLx(Nini(Nel))]+K(Nel)[2,1]:KG[NGLy(Nini(Nel)),NGLy(Nini(Nel))]:=KG[NGLy(Nini(Nel)),NGLy(Nini(Nel))]+K(Nel)[2,2]:KG[NGLy(Nini(Nel)),NGLrz(Nini(Nel))]:=KG[NGLy(Nini(Nel)),NGLrz(Nini(Nel))]+K(Nel)[2,3]:KG[NGLy(Nini(Nel)),NGLx(Nfin(Nel))]:=KG[NGLy(Nini(Nel)),NGLx(Nfin(Nel))]+K(Nel)[2,4]:KG[NGLy(Nini(Nel)),NGLy(Nfin(Nel))]:=KG[NGLy(Nini(Nel)),NGLy(Nfin(Nel))]+K(Nel)[2,5]:KG[NGLy(Nini(Nel)),NGLrz(Nfin(Nel))]:=KG[NGLy(Nini(Nel)),NGLrz(Nfin(Nel))]+K(Nel)[2,6]:
KG[NGLrz(Nini(Nel)),NGLx(Nini(Nel))]:=KG[NGLrz(Nini(Nel)),NGLx(Nini(Nel))]+K(Nel)[3,1]:
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KG[NGLrz(Nini(Nel)),NGLy(Nini(Nel))]:=KG[NGLrz(Nini(Nel)),NGLy(Nini(Nel))]+K(Nel)[3,2]:KG[NGLrz(Nini(Nel)),NGLrz(Nini(Nel))]:=KG[NGLrz(Nini(Nel)),NGLrz(Nini(Nel))]+K(Nel)[3,3]:KG[NGLrz(Nini(Nel)),NGLx(Nfin(Nel))]:=KG[NGLrz(Nini(Nel)),NGLx(Nfin(Nel))]+K(Nel)[3,4]:KG[NGLrz(Nini(Nel)),NGLy(Nfin(Nel))]:=KG[NGLrz(Nini(Nel)),NGLy(Nfin(Nel))]+K(Nel)[3,5]:KG[NGLrz(Nini(Nel)),NGLrz(Nfin(Nel))]:=KG[NGLrz(Nini(Nel)),NGLrz(Nfin(Nel))]+K(Nel)[3,6]:
KG[NGLx(Nfin(Nel)),NGLx(Nini(Nel))]:=KG[NGLx(Nfin(Nel)),NGLx(Nini(Nel))]+K(Nel)[4,1]:KG[NGLx(Nfin(Nel)),NGLy(Nini(Nel))]:=KG[NGLx(Nfin(Nel)),NGLy(Nini(Nel))]+K(Nel)[4,2]:KG[NGLx(Nfin(Nel)),NGLrz(Nini(Nel))]:=KG[NGLx(Nfin(Nel)),NGLrz(Nini(Nel))]+K(Nel)[4,3]:KG[NGLx(Nfin(Nel)),NGLx(Nfin(Nel))]:=KG[NGLx(Nfin(Nel)),NGLx(Nfin(Nel))]+K(Nel)[4,4]:KG[NGLx(Nfin(Nel)),NGLy(Nfin(Nel))]:=KG[NGLx(Nfin(Nel)),NGLy(Nfin(Nel))]+K(Nel)[4,5]:KG[NGLx(Nfin(Nel)),NGLrz(Nfin(Nel))]:=KG[NGLx(Nfin(Nel)),NGLrz(Nfin(Nel))]+K(Nel)[4,6]:
KG[NGLy(Nfin(Nel)),NGLx(Nini(Nel))]:=KG[NGLy(Nfin(Nel)),NGLx(Nini(Nel))]+K(Nel)[5,1]:KG[NGLy(Nfin(Nel)),NGLy(Nini(Nel))]:=KG[NGLy(Nfin(Nel)),NGLy(Nini(Nel))]+K(Nel)[5,2]:KG[NGLy(Nfin(Nel)),NGLrz(Nini(Nel))]:=KG[NGLy(Nfin(Nel)),NGLrz(Nini(Nel))]+K(Nel)[5,3]:KG[NGLy(Nfin(Nel)),NGLx(Nfin(Nel))]:=KG[NGLy(Nfin(Nel)),NGLx(Nfin(Nel))]+K(Nel)[5,4]:KG[NGLy(Nfin(Nel)),NGLy(Nfin(Nel))]:=KG[NGLy(Nfin(Nel)),NGLy(Nfin(Nel))]+K(Nel)[5,5]:KG[NGLy(Nfin(Nel)),NGLrz(Nfin(Nel))]:=KG[NGLy(Nfin(Nel)),NGLrz(Nfin(Nel))]+K(Nel)[5,6]:
KG[NGLrz(Nfin(Nel)),NGLx(Nini(Nel))]:=KG[NGLrz(Nfin(Nel)),NGLx(Nini(Nel))]+K(Nel)[6,1]:KG[NGLrz(Nfin(Nel)),NGLy(Nini(Nel))]:=KG[NGLrz(Nfin(Nel)),NGLy
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(Nini(Nel))]+K(Nel)[6,2]:KG[NGLrz(Nfin(Nel)),NGLrz(Nini(Nel))]:=KG[NGLrz(Nfin(Nel)),NGLrz(Nini(Nel))]+K(Nel)[6,3]:KG[NGLrz(Nfin(Nel)),NGLx(Nfin(Nel))]:=KG[NGLrz(Nfin(Nel)),NGLx(Nfin(Nel))]+K(Nel)[6,4]:KG[NGLrz(Nfin(Nel)),NGLy(Nfin(Nel))]:=KG[NGLrz(Nfin(Nel)),NGLy(Nfin(Nel))]+K(Nel)[6,5]:KG[NGLrz(Nfin(Nel)),NGLrz(Nfin(Nel))]:=KG[NGLrz(Nfin(Nel)),NGLrz(Nfin(Nel))]+K(Nel)[6,6]:
evalm(KG):
Nel:=5:Nm(Nel):=1:Np(Nel):=1:Nini(Nel):=5:Nfin(Nel):=6:
L(Nel):=sqrt((X(Nfin(Nel))-X(Nini(Nel)))^2+(Y(Nfin(Nel))-Y(Nini(Nel)))^2):CosLocGlob:=(X(Nfin(Nel))-X(Nini(Nel)))/L(Nel):SenLocGlob:=-(Y(Nfin(Nel))-Y(Nini(Nel)))/L(Nel):
Kloc:=matrix([[E(Nm(Nel))*A(Np(Nel))/L(Nel),0,0,-E(Nm(Nel))*A(Np(Nel))/L(Nel),0,0],[0,12.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^3,6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2,0,-12.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^3,6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2],[0,6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2,4.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel),0,-6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2,2.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)],[-E(Nm(Nel))*A(Np(Nel))/L(Nel),0,0,E(Nm(Nel))*A(Np(Nel))/L(Nel),0,0],[0,-12.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^3,-6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2,0,12.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^3,-6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2],[0,6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2,2.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel),0,-6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2,4.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)]]):
Rot(Nel):=matrix([[CosLocGlob,SenLocGlob,0,0,0,0],[-SenLocGlob,CosLocGlob,0,0,0,0],[0,0,1.,0,0,0],[0,0,0,CosLocGlob,SenLocGlob,0],[0,0,0,-SenLocGlob,CosLocGlob,0],[0,0,0,0,0,1.]])
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:
Trot:=transpose(Rot(Nel)):
K(Nel):=evalm(Rot(Nel)&*Kloc&*Trot):
KG[NGLx(Nini(Nel)),NGLx(Nini(Nel))]:=KG[NGLx(Nini(Nel)),NGLx(Nini(Nel))]+K(Nel)[1,1]:KG[NGLx(Nini(Nel)),NGLy(Nini(Nel))]:=KG[NGLx(Nini(Nel)),NGLy(Nini(Nel))]+K(Nel)[1,2]:KG[NGLx(Nini(Nel)),NGLrz(Nini(Nel))]:=KG[NGLx(Nini(Nel)),NGLrz(Nini(Nel))]+K(Nel)[1,3]:KG[NGLx(Nini(Nel)),NGLx(Nfin(Nel))]:=KG[NGLx(Nini(Nel)),NGLx(Nfin(Nel))]+K(Nel)[1,4]:KG[NGLx(Nini(Nel)),NGLy(Nfin(Nel))]:=KG[NGLx(Nini(Nel)),NGLy(Nfin(Nel))]+K(Nel)[1,5]:KG[NGLx(Nini(Nel)),NGLrz(Nfin(Nel))]:=KG[NGLx(Nini(Nel)),NGLrz(Nfin(Nel))]+K(Nel)[1,6]:
KG[NGLy(Nini(Nel)),NGLx(Nini(Nel))]:=KG[NGLy(Nini(Nel)),NGLx(Nini(Nel))]+K(Nel)[2,1]:KG[NGLy(Nini(Nel)),NGLy(Nini(Nel))]:=KG[NGLy(Nini(Nel)),NGLy(Nini(Nel))]+K(Nel)[2,2]:KG[NGLy(Nini(Nel)),NGLrz(Nini(Nel))]:=KG[NGLy(Nini(Nel)),NGLrz(Nini(Nel))]+K(Nel)[2,3]:KG[NGLy(Nini(Nel)),NGLx(Nfin(Nel))]:=KG[NGLy(Nini(Nel)),NGLx(Nfin(Nel))]+K(Nel)[2,4]:KG[NGLy(Nini(Nel)),NGLy(Nfin(Nel))]:=KG[NGLy(Nini(Nel)),NGLy(Nfin(Nel))]+K(Nel)[2,5]:KG[NGLy(Nini(Nel)),NGLrz(Nfin(Nel))]:=KG[NGLy(Nini(Nel)),NGLrz(Nfin(Nel))]+K(Nel)[2,6]:
KG[NGLrz(Nini(Nel)),NGLx(Nini(Nel))]:=KG[NGLrz(Nini(Nel)),NGLx(Nini(Nel))]+K(Nel)[3,1]:KG[NGLrz(Nini(Nel)),NGLy(Nini(Nel))]:=KG[NGLrz(Nini(Nel)),NGLy(Nini(Nel))]+K(Nel)[3,2]:KG[NGLrz(Nini(Nel)),NGLrz(Nini(Nel))]:=KG[NGLrz(Nini(Nel)),NGLrz(Nini(Nel))]+K(Nel)[3,3]:KG[NGLrz(Nini(Nel)),NGLx(Nfin(Nel))]:=KG[NGLrz(Nini(Nel)),NGLx(Nfin(Nel))]+K(Nel)[3,4]:
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KG[NGLrz(Nini(Nel)),NGLy(Nfin(Nel))]:=KG[NGLrz(Nini(Nel)),NGLy(Nfin(Nel))]+K(Nel)[3,5]:KG[NGLrz(Nini(Nel)),NGLrz(Nfin(Nel))]:=KG[NGLrz(Nini(Nel)),NGLrz(Nfin(Nel))]+K(Nel)[3,6]:
KG[NGLx(Nfin(Nel)),NGLx(Nini(Nel))]:=KG[NGLx(Nfin(Nel)),NGLx(Nini(Nel))]+K(Nel)[4,1]:KG[NGLx(Nfin(Nel)),NGLy(Nini(Nel))]:=KG[NGLx(Nfin(Nel)),NGLy(Nini(Nel))]+K(Nel)[4,2]:KG[NGLx(Nfin(Nel)),NGLrz(Nini(Nel))]:=KG[NGLx(Nfin(Nel)),NGLrz(Nini(Nel))]+K(Nel)[4,3]:KG[NGLx(Nfin(Nel)),NGLx(Nfin(Nel))]:=KG[NGLx(Nfin(Nel)),NGLx(Nfin(Nel))]+K(Nel)[4,4]:KG[NGLx(Nfin(Nel)),NGLy(Nfin(Nel))]:=KG[NGLx(Nfin(Nel)),NGLy(Nfin(Nel))]+K(Nel)[4,5]:KG[NGLx(Nfin(Nel)),NGLrz(Nfin(Nel))]:=KG[NGLx(Nfin(Nel)),NGLrz(Nfin(Nel))]+K(Nel)[4,6]:
KG[NGLy(Nfin(Nel)),NGLx(Nini(Nel))]:=KG[NGLy(Nfin(Nel)),NGLx(Nini(Nel))]+K(Nel)[5,1]:KG[NGLy(Nfin(Nel)),NGLy(Nini(Nel))]:=KG[NGLy(Nfin(Nel)),NGLy(Nini(Nel))]+K(Nel)[5,2]:KG[NGLy(Nfin(Nel)),NGLrz(Nini(Nel))]:=KG[NGLy(Nfin(Nel)),NGLrz(Nini(Nel))]+K(Nel)[5,3]:KG[NGLy(Nfin(Nel)),NGLx(Nfin(Nel))]:=KG[NGLy(Nfin(Nel)),NGLx(Nfin(Nel))]+K(Nel)[5,4]:KG[NGLy(Nfin(Nel)),NGLy(Nfin(Nel))]:=KG[NGLy(Nfin(Nel)),NGLy(Nfin(Nel))]+K(Nel)[5,5]:KG[NGLy(Nfin(Nel)),NGLrz(Nfin(Nel))]:=KG[NGLy(Nfin(Nel)),NGLrz(Nfin(Nel))]+K(Nel)[5,6]:
KG[NGLrz(Nfin(Nel)),NGLx(Nini(Nel))]:=KG[NGLrz(Nfin(Nel)),NGLx(Nini(Nel))]+K(Nel)[6,1]:KG[NGLrz(Nfin(Nel)),NGLy(Nini(Nel))]:=KG[NGLrz(Nfin(Nel)),NGLy(Nini(Nel))]+K(Nel)[6,2]:KG[NGLrz(Nfin(Nel)),NGLrz(Nini(Nel))]:=KG[NGLrz(Nfin(Nel)),NGLrz(Nini(Nel))]+K(Nel)[6,3]:KG[NGLrz(Nfin(Nel)),NGLx(Nfin(Nel))]:=KG[NGLrz(Nfin(Nel)),NGLx(Nfin(Nel))]+K(Nel)[6,4]:KG[NGLrz(Nfin(Nel)),NGLy(Nfin(Nel))]:=KG[NGLrz(Nfin(Nel)),NGLy
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(Nfin(Nel))]+K(Nel)[6,5]:KG[NGLrz(Nfin(Nel)),NGLrz(Nfin(Nel))]:=KG[NGLrz(Nfin(Nel)),NGLrz(Nfin(Nel))]+K(Nel)[6,6]:
evalm(KG):
Nel:=6:Nm(Nel):=1:Np(Nel):=1:Nini(Nel):=6:Nfin(Nel):=7:
L(Nel):=sqrt((X(Nfin(Nel))-X(Nini(Nel)))^2+(Y(Nfin(Nel))-Y(Nini(Nel)))^2):CosLocGlob:=(X(Nfin(Nel))-X(Nini(Nel)))/L(Nel):SenLocGlob:=-(Y(Nfin(Nel))-Y(Nini(Nel)))/L(Nel):
Kloc:=matrix([[E(Nm(Nel))*A(Np(Nel))/L(Nel),0,0,-E(Nm(Nel))*A(Np(Nel))/L(Nel),0,0],[0,12.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^3,6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2,0,-12.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^3,6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2],[0,6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2,4.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel),0,-6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2,2.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)],[-E(Nm(Nel))*A(Np(Nel))/L(Nel),0,0,E(Nm(Nel))*A(Np(Nel))/L(Nel),0,0],[0,-12.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^3,-6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2,0,12.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^3,-6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2],[0,6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2,2.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel),0,-6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2,4.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)]]):
Rot(Nel):=matrix([[CosLocGlob,SenLocGlob,0,0,0,0],[-SenLocGlob,CosLocGlob,0,0,0,0],[0,0,1.,0,0,0],[0,0,0,CosLocGlob,SenLocGlob,0],[0,0,0,-SenLocGlob,CosLocGlob,0],[0,0,0,0,0,1.]]):
Trot:=transpose(Rot(Nel)):
K(Nel):=evalm(Rot(Nel)&*Kloc&*Trot):
KG[NGLx(Nini(Nel)),NGLx(Nini(Nel))]:=KG[NGLx(Nini(Nel)),NGLx
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(Nini(Nel))]+K(Nel)[1,1]:KG[NGLx(Nini(Nel)),NGLy(Nini(Nel))]:=KG[NGLx(Nini(Nel)),NGLy(Nini(Nel))]+K(Nel)[1,2]:KG[NGLx(Nini(Nel)),NGLrz(Nini(Nel))]:=KG[NGLx(Nini(Nel)),NGLrz(Nini(Nel))]+K(Nel)[1,3]:KG[NGLx(Nini(Nel)),NGLx(Nfin(Nel))]:=KG[NGLx(Nini(Nel)),NGLx(Nfin(Nel))]+K(Nel)[1,4]:KG[NGLx(Nini(Nel)),NGLy(Nfin(Nel))]:=KG[NGLx(Nini(Nel)),NGLy(Nfin(Nel))]+K(Nel)[1,5]:KG[NGLx(Nini(Nel)),NGLrz(Nfin(Nel))]:=KG[NGLx(Nini(Nel)),NGLrz(Nfin(Nel))]+K(Nel)[1,6]:
KG[NGLy(Nini(Nel)),NGLx(Nini(Nel))]:=KG[NGLy(Nini(Nel)),NGLx(Nini(Nel))]+K(Nel)[2,1]:KG[NGLy(Nini(Nel)),NGLy(Nini(Nel))]:=KG[NGLy(Nini(Nel)),NGLy(Nini(Nel))]+K(Nel)[2,2]:KG[NGLy(Nini(Nel)),NGLrz(Nini(Nel))]:=KG[NGLy(Nini(Nel)),NGLrz(Nini(Nel))]+K(Nel)[2,3]:KG[NGLy(Nini(Nel)),NGLx(Nfin(Nel))]:=KG[NGLy(Nini(Nel)),NGLx(Nfin(Nel))]+K(Nel)[2,4]:KG[NGLy(Nini(Nel)),NGLy(Nfin(Nel))]:=KG[NGLy(Nini(Nel)),NGLy(Nfin(Nel))]+K(Nel)[2,5]:KG[NGLy(Nini(Nel)),NGLrz(Nfin(Nel))]:=KG[NGLy(Nini(Nel)),NGLrz(Nfin(Nel))]+K(Nel)[2,6]:
KG[NGLrz(Nini(Nel)),NGLx(Nini(Nel))]:=KG[NGLrz(Nini(Nel)),NGLx(Nini(Nel))]+K(Nel)[3,1]:KG[NGLrz(Nini(Nel)),NGLy(Nini(Nel))]:=KG[NGLrz(Nini(Nel)),NGLy(Nini(Nel))]+K(Nel)[3,2]:KG[NGLrz(Nini(Nel)),NGLrz(Nini(Nel))]:=KG[NGLrz(Nini(Nel)),NGLrz(Nini(Nel))]+K(Nel)[3,3]:KG[NGLrz(Nini(Nel)),NGLx(Nfin(Nel))]:=KG[NGLrz(Nini(Nel)),NGLx(Nfin(Nel))]+K(Nel)[3,4]:KG[NGLrz(Nini(Nel)),NGLy(Nfin(Nel))]:=KG[NGLrz(Nini(Nel)),NGLy(Nfin(Nel))]+K(Nel)[3,5]:KG[NGLrz(Nini(Nel)),NGLrz(Nfin(Nel))]:=KG[NGLrz(Nini(Nel)),NGLrz(Nfin(Nel))]+K(Nel)[3,6]:
KG[NGLx(Nfin(Nel)),NGLx(Nini(Nel))]:=KG[NGLx(Nfin(Nel)),NGLx(Nini(Nel))]+K(Nel)[4,1]:
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KG[NGLx(Nfin(Nel)),NGLy(Nini(Nel))]:=KG[NGLx(Nfin(Nel)),NGLy(Nini(Nel))]+K(Nel)[4,2]:KG[NGLx(Nfin(Nel)),NGLrz(Nini(Nel))]:=KG[NGLx(Nfin(Nel)),NGLrz(Nini(Nel))]+K(Nel)[4,3]:KG[NGLx(Nfin(Nel)),NGLx(Nfin(Nel))]:=KG[NGLx(Nfin(Nel)),NGLx(Nfin(Nel))]+K(Nel)[4,4]:KG[NGLx(Nfin(Nel)),NGLy(Nfin(Nel))]:=KG[NGLx(Nfin(Nel)),NGLy(Nfin(Nel))]+K(Nel)[4,5]:KG[NGLx(Nfin(Nel)),NGLrz(Nfin(Nel))]:=KG[NGLx(Nfin(Nel)),NGLrz(Nfin(Nel))]+K(Nel)[4,6]:
KG[NGLy(Nfin(Nel)),NGLx(Nini(Nel))]:=KG[NGLy(Nfin(Nel)),NGLx(Nini(Nel))]+K(Nel)[5,1]:KG[NGLy(Nfin(Nel)),NGLy(Nini(Nel))]:=KG[NGLy(Nfin(Nel)),NGLy(Nini(Nel))]+K(Nel)[5,2]:KG[NGLy(Nfin(Nel)),NGLrz(Nini(Nel))]:=KG[NGLy(Nfin(Nel)),NGLrz(Nini(Nel))]+K(Nel)[5,3]:KG[NGLy(Nfin(Nel)),NGLx(Nfin(Nel))]:=KG[NGLy(Nfin(Nel)),NGLx(Nfin(Nel))]+K(Nel)[5,4]:KG[NGLy(Nfin(Nel)),NGLy(Nfin(Nel))]:=KG[NGLy(Nfin(Nel)),NGLy(Nfin(Nel))]+K(Nel)[5,5]:KG[NGLy(Nfin(Nel)),NGLrz(Nfin(Nel))]:=KG[NGLy(Nfin(Nel)),NGLrz(Nfin(Nel))]+K(Nel)[5,6]:
KG[NGLrz(Nfin(Nel)),NGLx(Nini(Nel))]:=KG[NGLrz(Nfin(Nel)),NGLx(Nini(Nel))]+K(Nel)[6,1]:KG[NGLrz(Nfin(Nel)),NGLy(Nini(Nel))]:=KG[NGLrz(Nfin(Nel)),NGLy(Nini(Nel))]+K(Nel)[6,2]:KG[NGLrz(Nfin(Nel)),NGLrz(Nini(Nel))]:=KG[NGLrz(Nfin(Nel)),NGLrz(Nini(Nel))]+K(Nel)[6,3]:KG[NGLrz(Nfin(Nel)),NGLx(Nfin(Nel))]:=KG[NGLrz(Nfin(Nel)),NGLx(Nfin(Nel))]+K(Nel)[6,4]:KG[NGLrz(Nfin(Nel)),NGLy(Nfin(Nel))]:=KG[NGLrz(Nfin(Nel)),NGLy(Nfin(Nel))]+K(Nel)[6,5]:KG[NGLrz(Nfin(Nel)),NGLrz(Nfin(Nel))]:=KG[NGLrz(Nfin(Nel)),NGLrz(Nfin(Nel))]+K(Nel)[6,6]:
evalm(KG):
Nel:=7:
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Nm(Nel):=1:Np(Nel):=1:Nini(Nel):=7:Nfin(Nel):=8:
L(Nel):=sqrt((X(Nfin(Nel))-X(Nini(Nel)))^2+(Y(Nfin(Nel))-Y(Nini(Nel)))^2):CosLocGlob:=(X(Nfin(Nel))-X(Nini(Nel)))/L(Nel):SenLocGlob:=-(Y(Nfin(Nel))-Y(Nini(Nel)))/L(Nel):
Kloc:=matrix([[E(Nm(Nel))*A(Np(Nel))/L(Nel),0,0,-E(Nm(Nel))*A(Np(Nel))/L(Nel),0,0],[0,12.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^3,6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2,0,-12.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^3,6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2],[0,6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2,4.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel),0,-6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2,2.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)],[-E(Nm(Nel))*A(Np(Nel))/L(Nel),0,0,E(Nm(Nel))*A(Np(Nel))/L(Nel),0,0],[0,-12.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^3,-6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2,0,12.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^3,-6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2],[0,6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2,2.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel),0,-6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2,4.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)]]):
Rot(Nel):=matrix([[CosLocGlob,SenLocGlob,0,0,0,0],[-SenLocGlob,CosLocGlob,0,0,0,0],[0,0,1.,0,0,0],[0,0,0,CosLocGlob,SenLocGlob,0],[0,0,0,-SenLocGlob,CosLocGlob,0],[0,0,0,0,0,1.]]):
Trot:=transpose(Rot(Nel)):
K(Nel):=evalm(Rot(Nel)&*Kloc&*Trot):
KG[NGLx(Nini(Nel)),NGLx(Nini(Nel))]:=KG[NGLx(Nini(Nel)),NGLx(Nini(Nel))]+K(Nel)[1,1]:KG[NGLx(Nini(Nel)),NGLy(Nini(Nel))]:=KG[NGLx(Nini(Nel)),NGLy(Nini(Nel))]+K(Nel)[1,2]:KG[NGLx(Nini(Nel)),NGLrz(Nini(Nel))]:=KG[NGLx(Nini(Nel)),NGLrz(Nini(Nel))]+K(Nel)[1,3]:KG[NGLx(Nini(Nel)),NGLx(Nfin(Nel))]:=KG[NGLx(Nini(Nel)),NGLx(Nfin(Nel))]+K(Nel)[1,4]:
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KG[NGLx(Nini(Nel)),NGLy(Nfin(Nel))]:=KG[NGLx(Nini(Nel)),NGLy(Nfin(Nel))]+K(Nel)[1,5]:KG[NGLx(Nini(Nel)),NGLrz(Nfin(Nel))]:=KG[NGLx(Nini(Nel)),NGLrz(Nfin(Nel))]+K(Nel)[1,6]:
KG[NGLy(Nini(Nel)),NGLx(Nini(Nel))]:=KG[NGLy(Nini(Nel)),NGLx(Nini(Nel))]+K(Nel)[2,1]:KG[NGLy(Nini(Nel)),NGLy(Nini(Nel))]:=KG[NGLy(Nini(Nel)),NGLy(Nini(Nel))]+K(Nel)[2,2]:KG[NGLy(Nini(Nel)),NGLrz(Nini(Nel))]:=KG[NGLy(Nini(Nel)),NGLrz(Nini(Nel))]+K(Nel)[2,3]:KG[NGLy(Nini(Nel)),NGLx(Nfin(Nel))]:=KG[NGLy(Nini(Nel)),NGLx(Nfin(Nel))]+K(Nel)[2,4]:KG[NGLy(Nini(Nel)),NGLy(Nfin(Nel))]:=KG[NGLy(Nini(Nel)),NGLy(Nfin(Nel))]+K(Nel)[2,5]:KG[NGLy(Nini(Nel)),NGLrz(Nfin(Nel))]:=KG[NGLy(Nini(Nel)),NGLrz(Nfin(Nel))]+K(Nel)[2,6]:
KG[NGLrz(Nini(Nel)),NGLx(Nini(Nel))]:=KG[NGLrz(Nini(Nel)),NGLx(Nini(Nel))]+K(Nel)[3,1]:KG[NGLrz(Nini(Nel)),NGLy(Nini(Nel))]:=KG[NGLrz(Nini(Nel)),NGLy(Nini(Nel))]+K(Nel)[3,2]:KG[NGLrz(Nini(Nel)),NGLrz(Nini(Nel))]:=KG[NGLrz(Nini(Nel)),NGLrz(Nini(Nel))]+K(Nel)[3,3]:KG[NGLrz(Nini(Nel)),NGLx(Nfin(Nel))]:=KG[NGLrz(Nini(Nel)),NGLx(Nfin(Nel))]+K(Nel)[3,4]:KG[NGLrz(Nini(Nel)),NGLy(Nfin(Nel))]:=KG[NGLrz(Nini(Nel)),NGLy(Nfin(Nel))]+K(Nel)[3,5]:KG[NGLrz(Nini(Nel)),NGLrz(Nfin(Nel))]:=KG[NGLrz(Nini(Nel)),NGLrz(Nfin(Nel))]+K(Nel)[3,6]:
KG[NGLx(Nfin(Nel)),NGLx(Nini(Nel))]:=KG[NGLx(Nfin(Nel)),NGLx(Nini(Nel))]+K(Nel)[4,1]:KG[NGLx(Nfin(Nel)),NGLy(Nini(Nel))]:=KG[NGLx(Nfin(Nel)),NGLy(Nini(Nel))]+K(Nel)[4,2]:KG[NGLx(Nfin(Nel)),NGLrz(Nini(Nel))]:=KG[NGLx(Nfin(Nel)),NGLrz(Nini(Nel))]+K(Nel)[4,3]:KG[NGLx(Nfin(Nel)),NGLx(Nfin(Nel))]:=KG[NGLx(Nfin(Nel)),NGLx(Nfin(Nel))]+K(Nel)[4,4]:KG[NGLx(Nfin(Nel)),NGLy(Nfin(Nel))]:=KG[NGLx(Nfin(Nel)),NGLy
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(Nfin(Nel))]+K(Nel)[4,5]:KG[NGLx(Nfin(Nel)),NGLrz(Nfin(Nel))]:=KG[NGLx(Nfin(Nel)),NGLrz(Nfin(Nel))]+K(Nel)[4,6]:
KG[NGLy(Nfin(Nel)),NGLx(Nini(Nel))]:=KG[NGLy(Nfin(Nel)),NGLx(Nini(Nel))]+K(Nel)[5,1]:KG[NGLy(Nfin(Nel)),NGLy(Nini(Nel))]:=KG[NGLy(Nfin(Nel)),NGLy(Nini(Nel))]+K(Nel)[5,2]:KG[NGLy(Nfin(Nel)),NGLrz(Nini(Nel))]:=KG[NGLy(Nfin(Nel)),NGLrz(Nini(Nel))]+K(Nel)[5,3]:KG[NGLy(Nfin(Nel)),NGLx(Nfin(Nel))]:=KG[NGLy(Nfin(Nel)),NGLx(Nfin(Nel))]+K(Nel)[5,4]:KG[NGLy(Nfin(Nel)),NGLy(Nfin(Nel))]:=KG[NGLy(Nfin(Nel)),NGLy(Nfin(Nel))]+K(Nel)[5,5]:KG[NGLy(Nfin(Nel)),NGLrz(Nfin(Nel))]:=KG[NGLy(Nfin(Nel)),NGLrz(Nfin(Nel))]+K(Nel)[5,6]:
KG[NGLrz(Nfin(Nel)),NGLx(Nini(Nel))]:=KG[NGLrz(Nfin(Nel)),NGLx(Nini(Nel))]+K(Nel)[6,1]:KG[NGLrz(Nfin(Nel)),NGLy(Nini(Nel))]:=KG[NGLrz(Nfin(Nel)),NGLy(Nini(Nel))]+K(Nel)[6,2]:KG[NGLrz(Nfin(Nel)),NGLrz(Nini(Nel))]:=KG[NGLrz(Nfin(Nel)),NGLrz(Nini(Nel))]+K(Nel)[6,3]:KG[NGLrz(Nfin(Nel)),NGLx(Nfin(Nel))]:=KG[NGLrz(Nfin(Nel)),NGLx(Nfin(Nel))]+K(Nel)[6,4]:KG[NGLrz(Nfin(Nel)),NGLy(Nfin(Nel))]:=KG[NGLrz(Nfin(Nel)),NGLy(Nfin(Nel))]+K(Nel)[6,5]:KG[NGLrz(Nfin(Nel)),NGLrz(Nfin(Nel))]:=KG[NGLrz(Nfin(Nel)),NGLrz(Nfin(Nel))]+K(Nel)[6,6]:
evalm(KG):
Nel:=8:Nm(Nel):=1:Np(Nel):=1:Nini(Nel):=8:Nfin(Nel):=9:
L(Nel):=sqrt((X(Nfin(Nel))-X(Nini(Nel)))^2+(Y(Nfin(Nel))-Y(Nini
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(Nel)))^2):CosLocGlob:=(X(Nfin(Nel))-X(Nini(Nel)))/L(Nel):SenLocGlob:=-(Y(Nfin(Nel))-Y(Nini(Nel)))/L(Nel):
Kloc:=matrix([[E(Nm(Nel))*A(Np(Nel))/L(Nel),0,0,-E(Nm(Nel))*A(Np(Nel))/L(Nel),0,0],[0,12.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^3,6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2,0,-12.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^3,6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2],[0,6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2,4.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel),0,-6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2,2.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)],[-E(Nm(Nel))*A(Np(Nel))/L(Nel),0,0,E(Nm(Nel))*A(Np(Nel))/L(Nel),0,0],[0,-12.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^3,-6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2,0,12.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^3,-6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2],[0,6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2,2.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel),0,-6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2,4.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)]]):
Rot(Nel):=matrix([[CosLocGlob,SenLocGlob,0,0,0,0],[-SenLocGlob,CosLocGlob,0,0,0,0],[0,0,1.,0,0,0],[0,0,0,CosLocGlob,SenLocGlob,0],[0,0,0,-SenLocGlob,CosLocGlob,0],[0,0,0,0,0,1.]]):
Trot:=transpose(Rot(Nel)):
K(Nel):=evalm(Rot(Nel)&*Kloc&*Trot):
KG[NGLx(Nini(Nel)),NGLx(Nini(Nel))]:=KG[NGLx(Nini(Nel)),NGLx(Nini(Nel))]+K(Nel)[1,1]:KG[NGLx(Nini(Nel)),NGLy(Nini(Nel))]:=KG[NGLx(Nini(Nel)),NGLy(Nini(Nel))]+K(Nel)[1,2]:KG[NGLx(Nini(Nel)),NGLrz(Nini(Nel))]:=KG[NGLx(Nini(Nel)),NGLrz(Nini(Nel))]+K(Nel)[1,3]:KG[NGLx(Nini(Nel)),NGLx(Nfin(Nel))]:=KG[NGLx(Nini(Nel)),NGLx(Nfin(Nel))]+K(Nel)[1,4]:KG[NGLx(Nini(Nel)),NGLy(Nfin(Nel))]:=KG[NGLx(Nini(Nel)),NGLy(Nfin(Nel))]+K(Nel)[1,5]:KG[NGLx(Nini(Nel)),NGLrz(Nfin(Nel))]:=KG[NGLx(Nini(Nel)),NGLrz(Nfin(Nel))]+K(Nel)[1,6]:
KG[NGLy(Nini(Nel)),NGLx(Nini(Nel))]:=KG[NGLy(Nini(Nel)),NGLx
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(Nini(Nel))]+K(Nel)[2,1]:KG[NGLy(Nini(Nel)),NGLy(Nini(Nel))]:=KG[NGLy(Nini(Nel)),NGLy(Nini(Nel))]+K(Nel)[2,2]:KG[NGLy(Nini(Nel)),NGLrz(Nini(Nel))]:=KG[NGLy(Nini(Nel)),NGLrz(Nini(Nel))]+K(Nel)[2,3]:KG[NGLy(Nini(Nel)),NGLx(Nfin(Nel))]:=KG[NGLy(Nini(Nel)),NGLx(Nfin(Nel))]+K(Nel)[2,4]:KG[NGLy(Nini(Nel)),NGLy(Nfin(Nel))]:=KG[NGLy(Nini(Nel)),NGLy(Nfin(Nel))]+K(Nel)[2,5]:KG[NGLy(Nini(Nel)),NGLrz(Nfin(Nel))]:=KG[NGLy(Nini(Nel)),NGLrz(Nfin(Nel))]+K(Nel)[2,6]:
KG[NGLrz(Nini(Nel)),NGLx(Nini(Nel))]:=KG[NGLrz(Nini(Nel)),NGLx(Nini(Nel))]+K(Nel)[3,1]:KG[NGLrz(Nini(Nel)),NGLy(Nini(Nel))]:=KG[NGLrz(Nini(Nel)),NGLy(Nini(Nel))]+K(Nel)[3,2]:KG[NGLrz(Nini(Nel)),NGLrz(Nini(Nel))]:=KG[NGLrz(Nini(Nel)),NGLrz(Nini(Nel))]+K(Nel)[3,3]:KG[NGLrz(Nini(Nel)),NGLx(Nfin(Nel))]:=KG[NGLrz(Nini(Nel)),NGLx(Nfin(Nel))]+K(Nel)[3,4]:KG[NGLrz(Nini(Nel)),NGLy(Nfin(Nel))]:=KG[NGLrz(Nini(Nel)),NGLy(Nfin(Nel))]+K(Nel)[3,5]:KG[NGLrz(Nini(Nel)),NGLrz(Nfin(Nel))]:=KG[NGLrz(Nini(Nel)),NGLrz(Nfin(Nel))]+K(Nel)[3,6]:
KG[NGLx(Nfin(Nel)),NGLx(Nini(Nel))]:=KG[NGLx(Nfin(Nel)),NGLx(Nini(Nel))]+K(Nel)[4,1]:KG[NGLx(Nfin(Nel)),NGLy(Nini(Nel))]:=KG[NGLx(Nfin(Nel)),NGLy(Nini(Nel))]+K(Nel)[4,2]:KG[NGLx(Nfin(Nel)),NGLrz(Nini(Nel))]:=KG[NGLx(Nfin(Nel)),NGLrz(Nini(Nel))]+K(Nel)[4,3]:KG[NGLx(Nfin(Nel)),NGLx(Nfin(Nel))]:=KG[NGLx(Nfin(Nel)),NGLx(Nfin(Nel))]+K(Nel)[4,4]:KG[NGLx(Nfin(Nel)),NGLy(Nfin(Nel))]:=KG[NGLx(Nfin(Nel)),NGLy(Nfin(Nel))]+K(Nel)[4,5]:KG[NGLx(Nfin(Nel)),NGLrz(Nfin(Nel))]:=KG[NGLx(Nfin(Nel)),NGLrz(Nfin(Nel))]+K(Nel)[4,6]:
KG[NGLy(Nfin(Nel)),NGLx(Nini(Nel))]:=KG[NGLy(Nfin(Nel)),NGLx(Nini(Nel))]+K(Nel)[5,1]:
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KG[NGLy(Nfin(Nel)),NGLy(Nini(Nel))]:=KG[NGLy(Nfin(Nel)),NGLy(Nini(Nel))]+K(Nel)[5,2]:KG[NGLy(Nfin(Nel)),NGLrz(Nini(Nel))]:=KG[NGLy(Nfin(Nel)),NGLrz(Nini(Nel))]+K(Nel)[5,3]:KG[NGLy(Nfin(Nel)),NGLx(Nfin(Nel))]:=KG[NGLy(Nfin(Nel)),NGLx(Nfin(Nel))]+K(Nel)[5,4]:KG[NGLy(Nfin(Nel)),NGLy(Nfin(Nel))]:=KG[NGLy(Nfin(Nel)),NGLy(Nfin(Nel))]+K(Nel)[5,5]:KG[NGLy(Nfin(Nel)),NGLrz(Nfin(Nel))]:=KG[NGLy(Nfin(Nel)),NGLrz(Nfin(Nel))]+K(Nel)[5,6]:
KG[NGLrz(Nfin(Nel)),NGLx(Nini(Nel))]:=KG[NGLrz(Nfin(Nel)),NGLx(Nini(Nel))]+K(Nel)[6,1]:KG[NGLrz(Nfin(Nel)),NGLy(Nini(Nel))]:=KG[NGLrz(Nfin(Nel)),NGLy(Nini(Nel))]+K(Nel)[6,2]:KG[NGLrz(Nfin(Nel)),NGLrz(Nini(Nel))]:=KG[NGLrz(Nfin(Nel)),NGLrz(Nini(Nel))]+K(Nel)[6,3]:KG[NGLrz(Nfin(Nel)),NGLx(Nfin(Nel))]:=KG[NGLrz(Nfin(Nel)),NGLx(Nfin(Nel))]+K(Nel)[6,4]:KG[NGLrz(Nfin(Nel)),NGLy(Nfin(Nel))]:=KG[NGLrz(Nfin(Nel)),NGLy(Nfin(Nel))]+K(Nel)[6,5]:KG[NGLrz(Nfin(Nel)),NGLrz(Nfin(Nel))]:=KG[NGLrz(Nfin(Nel)),NGLrz(Nfin(Nel))]+K(Nel)[6,6]:
evalm(KG):
Nel:=9:Nm(Nel):=1:Np(Nel):=1:Nini(Nel):=9:Nfin(Nel):=10:
L(Nel):=sqrt((X(Nfin(Nel))-X(Nini(Nel)))^2+(Y(Nfin(Nel))-Y(Nini(Nel)))^2):CosLocGlob:=(X(Nfin(Nel))-X(Nini(Nel)))/L(Nel):SenLocGlob:=-(Y(Nfin(Nel))-Y(Nini(Nel)))/L(Nel):
Kloc:=matrix([[E(Nm(Nel))*A(Np(Nel))/L(Nel),0,0,-E(Nm(Nel))*A(Np(Nel))/L(Nel),0,0],[0,12.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^3,6.
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*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2,0,-12.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^3,6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2],[0,6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2,4.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel),0,-6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2,2.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)],[-E(Nm(Nel))*A(Np(Nel))/L(Nel),0,0,E(Nm(Nel))*A(Np(Nel))/L(Nel),0,0],[0,-12.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^3,-6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2,0,12.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^3,-6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2],[0,6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2,2.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel),0,-6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2,4.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)]]):
Rot(Nel):=matrix([[CosLocGlob,SenLocGlob,0,0,0,0],[-SenLocGlob,CosLocGlob,0,0,0,0],[0,0,1.,0,0,0],[0,0,0,CosLocGlob,SenLocGlob,0],[0,0,0,-SenLocGlob,CosLocGlob,0],[0,0,0,0,0,1.]]):
Trot:=transpose(Rot(Nel)):
K(Nel):=evalm(Rot(Nel)&*Kloc&*Trot):
KG[NGLx(Nini(Nel)),NGLx(Nini(Nel))]:=KG[NGLx(Nini(Nel)),NGLx(Nini(Nel))]+K(Nel)[1,1]:KG[NGLx(Nini(Nel)),NGLy(Nini(Nel))]:=KG[NGLx(Nini(Nel)),NGLy(Nini(Nel))]+K(Nel)[1,2]:KG[NGLx(Nini(Nel)),NGLrz(Nini(Nel))]:=KG[NGLx(Nini(Nel)),NGLrz(Nini(Nel))]+K(Nel)[1,3]:KG[NGLx(Nini(Nel)),NGLx(Nfin(Nel))]:=KG[NGLx(Nini(Nel)),NGLx(Nfin(Nel))]+K(Nel)[1,4]:KG[NGLx(Nini(Nel)),NGLy(Nfin(Nel))]:=KG[NGLx(Nini(Nel)),NGLy(Nfin(Nel))]+K(Nel)[1,5]:KG[NGLx(Nini(Nel)),NGLrz(Nfin(Nel))]:=KG[NGLx(Nini(Nel)),NGLrz(Nfin(Nel))]+K(Nel)[1,6]:
KG[NGLy(Nini(Nel)),NGLx(Nini(Nel))]:=KG[NGLy(Nini(Nel)),NGLx(Nini(Nel))]+K(Nel)[2,1]:KG[NGLy(Nini(Nel)),NGLy(Nini(Nel))]:=KG[NGLy(Nini(Nel)),NGLy(Nini(Nel))]+K(Nel)[2,2]:KG[NGLy(Nini(Nel)),NGLrz(Nini(Nel))]:=KG[NGLy(Nini(Nel)),NGLrz(Nini(Nel))]+K(Nel)[2,3]:KG[NGLy(Nini(Nel)),NGLx(Nfin(Nel))]:=KG[NGLy(Nini(Nel)),NGLx
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(Nfin(Nel))]+K(Nel)[2,4]:KG[NGLy(Nini(Nel)),NGLy(Nfin(Nel))]:=KG[NGLy(Nini(Nel)),NGLy(Nfin(Nel))]+K(Nel)[2,5]:KG[NGLy(Nini(Nel)),NGLrz(Nfin(Nel))]:=KG[NGLy(Nini(Nel)),NGLrz(Nfin(Nel))]+K(Nel)[2,6]:
KG[NGLrz(Nini(Nel)),NGLx(Nini(Nel))]:=KG[NGLrz(Nini(Nel)),NGLx(Nini(Nel))]+K(Nel)[3,1]:KG[NGLrz(Nini(Nel)),NGLy(Nini(Nel))]:=KG[NGLrz(Nini(Nel)),NGLy(Nini(Nel))]+K(Nel)[3,2]:KG[NGLrz(Nini(Nel)),NGLrz(Nini(Nel))]:=KG[NGLrz(Nini(Nel)),NGLrz(Nini(Nel))]+K(Nel)[3,3]:KG[NGLrz(Nini(Nel)),NGLx(Nfin(Nel))]:=KG[NGLrz(Nini(Nel)),NGLx(Nfin(Nel))]+K(Nel)[3,4]:KG[NGLrz(Nini(Nel)),NGLy(Nfin(Nel))]:=KG[NGLrz(Nini(Nel)),NGLy(Nfin(Nel))]+K(Nel)[3,5]:KG[NGLrz(Nini(Nel)),NGLrz(Nfin(Nel))]:=KG[NGLrz(Nini(Nel)),NGLrz(Nfin(Nel))]+K(Nel)[3,6]:
KG[NGLx(Nfin(Nel)),NGLx(Nini(Nel))]:=KG[NGLx(Nfin(Nel)),NGLx(Nini(Nel))]+K(Nel)[4,1]:KG[NGLx(Nfin(Nel)),NGLy(Nini(Nel))]:=KG[NGLx(Nfin(Nel)),NGLy(Nini(Nel))]+K(Nel)[4,2]:KG[NGLx(Nfin(Nel)),NGLrz(Nini(Nel))]:=KG[NGLx(Nfin(Nel)),NGLrz(Nini(Nel))]+K(Nel)[4,3]:KG[NGLx(Nfin(Nel)),NGLx(Nfin(Nel))]:=KG[NGLx(Nfin(Nel)),NGLx(Nfin(Nel))]+K(Nel)[4,4]:KG[NGLx(Nfin(Nel)),NGLy(Nfin(Nel))]:=KG[NGLx(Nfin(Nel)),NGLy(Nfin(Nel))]+K(Nel)[4,5]:KG[NGLx(Nfin(Nel)),NGLrz(Nfin(Nel))]:=KG[NGLx(Nfin(Nel)),NGLrz(Nfin(Nel))]+K(Nel)[4,6]:
KG[NGLy(Nfin(Nel)),NGLx(Nini(Nel))]:=KG[NGLy(Nfin(Nel)),NGLx(Nini(Nel))]+K(Nel)[5,1]:KG[NGLy(Nfin(Nel)),NGLy(Nini(Nel))]:=KG[NGLy(Nfin(Nel)),NGLy(Nini(Nel))]+K(Nel)[5,2]:KG[NGLy(Nfin(Nel)),NGLrz(Nini(Nel))]:=KG[NGLy(Nfin(Nel)),NGLrz(Nini(Nel))]+K(Nel)[5,3]:KG[NGLy(Nfin(Nel)),NGLx(Nfin(Nel))]:=KG[NGLy(Nfin(Nel)),NGLx(Nfin(Nel))]+K(Nel)[5,4]:
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KG[NGLy(Nfin(Nel)),NGLy(Nfin(Nel))]:=KG[NGLy(Nfin(Nel)),NGLy(Nfin(Nel))]+K(Nel)[5,5]:KG[NGLy(Nfin(Nel)),NGLrz(Nfin(Nel))]:=KG[NGLy(Nfin(Nel)),NGLrz(Nfin(Nel))]+K(Nel)[5,6]:
KG[NGLrz(Nfin(Nel)),NGLx(Nini(Nel))]:=KG[NGLrz(Nfin(Nel)),NGLx(Nini(Nel))]+K(Nel)[6,1]:KG[NGLrz(Nfin(Nel)),NGLy(Nini(Nel))]:=KG[NGLrz(Nfin(Nel)),NGLy(Nini(Nel))]+K(Nel)[6,2]:KG[NGLrz(Nfin(Nel)),NGLrz(Nini(Nel))]:=KG[NGLrz(Nfin(Nel)),NGLrz(Nini(Nel))]+K(Nel)[6,3]:KG[NGLrz(Nfin(Nel)),NGLx(Nfin(Nel))]:=KG[NGLrz(Nfin(Nel)),NGLx(Nfin(Nel))]+K(Nel)[6,4]:KG[NGLrz(Nfin(Nel)),NGLy(Nfin(Nel))]:=KG[NGLrz(Nfin(Nel)),NGLy(Nfin(Nel))]+K(Nel)[6,5]:KG[NGLrz(Nfin(Nel)),NGLrz(Nfin(Nel))]:=KG[NGLrz(Nfin(Nel)),NGLrz(Nfin(Nel))]+K(Nel)[6,6]:
evalm(KG):
Nel:=10:Nm(Nel):=1:Np(Nel):=1:Nini(Nel):=10:Nfin(Nel):=11:
L(Nel):=sqrt((X(Nfin(Nel))-X(Nini(Nel)))^2+(Y(Nfin(Nel))-Y(Nini(Nel)))^2):CosLocGlob:=(X(Nfin(Nel))-X(Nini(Nel)))/L(Nel):SenLocGlob:=-(Y(Nfin(Nel))-Y(Nini(Nel)))/L(Nel):
Kloc:=matrix([[E(Nm(Nel))*A(Np(Nel))/L(Nel),0,0,-E(Nm(Nel))*A(Np(Nel))/L(Nel),0,0],[0,12.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^3,6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2,0,-12.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^3,6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2],[0,6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2,4.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel),0,-6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2,2.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)],[-E(Nm(Nel))*A(Np(Nel))/L(Nel),0,0,E(Nm(Nel))*A(Np(Nel))/L(Nel),0,0],[0,-12.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^3,-6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2,0,12.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)
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^3,-6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2],[0,6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2,2.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel),0,-6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2,4.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)]]):
Rot(Nel):=matrix([[CosLocGlob,SenLocGlob,0,0,0,0],[-SenLocGlob,CosLocGlob,0,0,0,0],[0,0,1.,0,0,0],[0,0,0,CosLocGlob,SenLocGlob,0],[0,0,0,-SenLocGlob,CosLocGlob,0],[0,0,0,0,0,1.]]):
Trot:=transpose(Rot(Nel)):
K(Nel):=evalm(Rot(Nel)&*Kloc&*Trot):
KG[NGLx(Nini(Nel)),NGLx(Nini(Nel))]:=KG[NGLx(Nini(Nel)),NGLx(Nini(Nel))]+K(Nel)[1,1]:KG[NGLx(Nini(Nel)),NGLy(Nini(Nel))]:=KG[NGLx(Nini(Nel)),NGLy(Nini(Nel))]+K(Nel)[1,2]:KG[NGLx(Nini(Nel)),NGLrz(Nini(Nel))]:=KG[NGLx(Nini(Nel)),NGLrz(Nini(Nel))]+K(Nel)[1,3]:KG[NGLx(Nini(Nel)),NGLx(Nfin(Nel))]:=KG[NGLx(Nini(Nel)),NGLx(Nfin(Nel))]+K(Nel)[1,4]:KG[NGLx(Nini(Nel)),NGLy(Nfin(Nel))]:=KG[NGLx(Nini(Nel)),NGLy(Nfin(Nel))]+K(Nel)[1,5]:KG[NGLx(Nini(Nel)),NGLrz(Nfin(Nel))]:=KG[NGLx(Nini(Nel)),NGLrz(Nfin(Nel))]+K(Nel)[1,6]:
KG[NGLy(Nini(Nel)),NGLx(Nini(Nel))]:=KG[NGLy(Nini(Nel)),NGLx(Nini(Nel))]+K(Nel)[2,1]:KG[NGLy(Nini(Nel)),NGLy(Nini(Nel))]:=KG[NGLy(Nini(Nel)),NGLy(Nini(Nel))]+K(Nel)[2,2]:KG[NGLy(Nini(Nel)),NGLrz(Nini(Nel))]:=KG[NGLy(Nini(Nel)),NGLrz(Nini(Nel))]+K(Nel)[2,3]:KG[NGLy(Nini(Nel)),NGLx(Nfin(Nel))]:=KG[NGLy(Nini(Nel)),NGLx(Nfin(Nel))]+K(Nel)[2,4]:KG[NGLy(Nini(Nel)),NGLy(Nfin(Nel))]:=KG[NGLy(Nini(Nel)),NGLy(Nfin(Nel))]+K(Nel)[2,5]:KG[NGLy(Nini(Nel)),NGLrz(Nfin(Nel))]:=KG[NGLy(Nini(Nel)),NGLrz(Nfin(Nel))]+K(Nel)[2,6]:
KG[NGLrz(Nini(Nel)),NGLx(Nini(Nel))]:=KG[NGLrz(Nini(Nel)),NGLx
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(Nini(Nel))]+K(Nel)[3,1]:KG[NGLrz(Nini(Nel)),NGLy(Nini(Nel))]:=KG[NGLrz(Nini(Nel)),NGLy(Nini(Nel))]+K(Nel)[3,2]:KG[NGLrz(Nini(Nel)),NGLrz(Nini(Nel))]:=KG[NGLrz(Nini(Nel)),NGLrz(Nini(Nel))]+K(Nel)[3,3]:KG[NGLrz(Nini(Nel)),NGLx(Nfin(Nel))]:=KG[NGLrz(Nini(Nel)),NGLx(Nfin(Nel))]+K(Nel)[3,4]:KG[NGLrz(Nini(Nel)),NGLy(Nfin(Nel))]:=KG[NGLrz(Nini(Nel)),NGLy(Nfin(Nel))]+K(Nel)[3,5]:KG[NGLrz(Nini(Nel)),NGLrz(Nfin(Nel))]:=KG[NGLrz(Nini(Nel)),NGLrz(Nfin(Nel))]+K(Nel)[3,6]:
KG[NGLx(Nfin(Nel)),NGLx(Nini(Nel))]:=KG[NGLx(Nfin(Nel)),NGLx(Nini(Nel))]+K(Nel)[4,1]:KG[NGLx(Nfin(Nel)),NGLy(Nini(Nel))]:=KG[NGLx(Nfin(Nel)),NGLy(Nini(Nel))]+K(Nel)[4,2]:KG[NGLx(Nfin(Nel)),NGLrz(Nini(Nel))]:=KG[NGLx(Nfin(Nel)),NGLrz(Nini(Nel))]+K(Nel)[4,3]:KG[NGLx(Nfin(Nel)),NGLx(Nfin(Nel))]:=KG[NGLx(Nfin(Nel)),NGLx(Nfin(Nel))]+K(Nel)[4,4]:KG[NGLx(Nfin(Nel)),NGLy(Nfin(Nel))]:=KG[NGLx(Nfin(Nel)),NGLy(Nfin(Nel))]+K(Nel)[4,5]:KG[NGLx(Nfin(Nel)),NGLrz(Nfin(Nel))]:=KG[NGLx(Nfin(Nel)),NGLrz(Nfin(Nel))]+K(Nel)[4,6]:
KG[NGLy(Nfin(Nel)),NGLx(Nini(Nel))]:=KG[NGLy(Nfin(Nel)),NGLx(Nini(Nel))]+K(Nel)[5,1]:KG[NGLy(Nfin(Nel)),NGLy(Nini(Nel))]:=KG[NGLy(Nfin(Nel)),NGLy(Nini(Nel))]+K(Nel)[5,2]:KG[NGLy(Nfin(Nel)),NGLrz(Nini(Nel))]:=KG[NGLy(Nfin(Nel)),NGLrz(Nini(Nel))]+K(Nel)[5,3]:KG[NGLy(Nfin(Nel)),NGLx(Nfin(Nel))]:=KG[NGLy(Nfin(Nel)),NGLx(Nfin(Nel))]+K(Nel)[5,4]:KG[NGLy(Nfin(Nel)),NGLy(Nfin(Nel))]:=KG[NGLy(Nfin(Nel)),NGLy(Nfin(Nel))]+K(Nel)[5,5]:KG[NGLy(Nfin(Nel)),NGLrz(Nfin(Nel))]:=KG[NGLy(Nfin(Nel)),NGLrz(Nfin(Nel))]+K(Nel)[5,6]:
KG[NGLrz(Nfin(Nel)),NGLx(Nini(Nel))]:=KG[NGLrz(Nfin(Nel)),NGLx(Nini(Nel))]+K(Nel)[6,1]:
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KG[NGLrz(Nfin(Nel)),NGLy(Nini(Nel))]:=KG[NGLrz(Nfin(Nel)),NGLy(Nini(Nel))]+K(Nel)[6,2]:KG[NGLrz(Nfin(Nel)),NGLrz(Nini(Nel))]:=KG[NGLrz(Nfin(Nel)),NGLrz(Nini(Nel))]+K(Nel)[6,3]:KG[NGLrz(Nfin(Nel)),NGLx(Nfin(Nel))]:=KG[NGLrz(Nfin(Nel)),NGLx(Nfin(Nel))]+K(Nel)[6,4]:KG[NGLrz(Nfin(Nel)),NGLy(Nfin(Nel))]:=KG[NGLrz(Nfin(Nel)),NGLy(Nfin(Nel))]+K(Nel)[6,5]:KG[NGLrz(Nfin(Nel)),NGLrz(Nfin(Nel))]:=KG[NGLrz(Nfin(Nel)),NGLrz(Nfin(Nel))]+K(Nel)[6,6]:
evalm(KG):
Nel:=11:Nm(Nel):=1:Np(Nel):=1:Nini(Nel):=11:Nfin(Nel):=12:
L(Nel):=sqrt((X(Nfin(Nel))-X(Nini(Nel)))^2+(Y(Nfin(Nel))-Y(Nini(Nel)))^2):CosLocGlob:=(X(Nfin(Nel))-X(Nini(Nel)))/L(Nel):SenLocGlob:=-(Y(Nfin(Nel))-Y(Nini(Nel)))/L(Nel):
Kloc:=matrix([[E(Nm(Nel))*A(Np(Nel))/L(Nel),0,0,-E(Nm(Nel))*A(Np(Nel))/L(Nel),0,0],[0,12.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^3,6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2,0,-12.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^3,6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2],[0,6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2,4.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel),0,-6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2,2.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)],[-E(Nm(Nel))*A(Np(Nel))/L(Nel),0,0,E(Nm(Nel))*A(Np(Nel))/L(Nel),0,0],[0,-12.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^3,-6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2,0,12.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^3,-6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2],[0,6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2,2.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel),0,-6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2,4.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)]]):
Rot(Nel):=matrix([[CosLocGlob,SenLocGlob,0,0,0,0],[-SenLocGlob,CosLocGlob,0,0,0,0],[0,0,1.,0,0,0],[0,0,0,CosLocGlob,
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SenLocGlob,0],[0,0,0,-SenLocGlob,CosLocGlob,0],[0,0,0,0,0,1.]]):
Trot:=transpose(Rot(Nel)):
K(Nel):=evalm(Rot(Nel)&*Kloc&*Trot):
KG[NGLx(Nini(Nel)),NGLx(Nini(Nel))]:=KG[NGLx(Nini(Nel)),NGLx(Nini(Nel))]+K(Nel)[1,1]:KG[NGLx(Nini(Nel)),NGLy(Nini(Nel))]:=KG[NGLx(Nini(Nel)),NGLy(Nini(Nel))]+K(Nel)[1,2]:KG[NGLx(Nini(Nel)),NGLrz(Nini(Nel))]:=KG[NGLx(Nini(Nel)),NGLrz(Nini(Nel))]+K(Nel)[1,3]:KG[NGLx(Nini(Nel)),NGLx(Nfin(Nel))]:=KG[NGLx(Nini(Nel)),NGLx(Nfin(Nel))]+K(Nel)[1,4]:KG[NGLx(Nini(Nel)),NGLy(Nfin(Nel))]:=KG[NGLx(Nini(Nel)),NGLy(Nfin(Nel))]+K(Nel)[1,5]:KG[NGLx(Nini(Nel)),NGLrz(Nfin(Nel))]:=KG[NGLx(Nini(Nel)),NGLrz(Nfin(Nel))]+K(Nel)[1,6]:
KG[NGLy(Nini(Nel)),NGLx(Nini(Nel))]:=KG[NGLy(Nini(Nel)),NGLx(Nini(Nel))]+K(Nel)[2,1]:KG[NGLy(Nini(Nel)),NGLy(Nini(Nel))]:=KG[NGLy(Nini(Nel)),NGLy(Nini(Nel))]+K(Nel)[2,2]:KG[NGLy(Nini(Nel)),NGLrz(Nini(Nel))]:=KG[NGLy(Nini(Nel)),NGLrz(Nini(Nel))]+K(Nel)[2,3]:KG[NGLy(Nini(Nel)),NGLx(Nfin(Nel))]:=KG[NGLy(Nini(Nel)),NGLx(Nfin(Nel))]+K(Nel)[2,4]:KG[NGLy(Nini(Nel)),NGLy(Nfin(Nel))]:=KG[NGLy(Nini(Nel)),NGLy(Nfin(Nel))]+K(Nel)[2,5]:KG[NGLy(Nini(Nel)),NGLrz(Nfin(Nel))]:=KG[NGLy(Nini(Nel)),NGLrz(Nfin(Nel))]+K(Nel)[2,6]:
KG[NGLrz(Nini(Nel)),NGLx(Nini(Nel))]:=KG[NGLrz(Nini(Nel)),NGLx(Nini(Nel))]+K(Nel)[3,1]:KG[NGLrz(Nini(Nel)),NGLy(Nini(Nel))]:=KG[NGLrz(Nini(Nel)),NGLy(Nini(Nel))]+K(Nel)[3,2]:KG[NGLrz(Nini(Nel)),NGLrz(Nini(Nel))]:=KG[NGLrz(Nini(Nel)),NGLrz(Nini(Nel))]+K(Nel)[3,3]:KG[NGLrz(Nini(Nel)),NGLx(Nfin(Nel))]:=KG[NGLrz(Nini(Nel)),NGLx(Nfin(Nel))]+K(Nel)[3,4]:
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KG[NGLrz(Nini(Nel)),NGLy(Nfin(Nel))]:=KG[NGLrz(Nini(Nel)),NGLy(Nfin(Nel))]+K(Nel)[3,5]:KG[NGLrz(Nini(Nel)),NGLrz(Nfin(Nel))]:=KG[NGLrz(Nini(Nel)),NGLrz(Nfin(Nel))]+K(Nel)[3,6]:
KG[NGLx(Nfin(Nel)),NGLx(Nini(Nel))]:=KG[NGLx(Nfin(Nel)),NGLx(Nini(Nel))]+K(Nel)[4,1]:KG[NGLx(Nfin(Nel)),NGLy(Nini(Nel))]:=KG[NGLx(Nfin(Nel)),NGLy(Nini(Nel))]+K(Nel)[4,2]:KG[NGLx(Nfin(Nel)),NGLrz(Nini(Nel))]:=KG[NGLx(Nfin(Nel)),NGLrz(Nini(Nel))]+K(Nel)[4,3]:KG[NGLx(Nfin(Nel)),NGLx(Nfin(Nel))]:=KG[NGLx(Nfin(Nel)),NGLx(Nfin(Nel))]+K(Nel)[4,4]:KG[NGLx(Nfin(Nel)),NGLy(Nfin(Nel))]:=KG[NGLx(Nfin(Nel)),NGLy(Nfin(Nel))]+K(Nel)[4,5]:KG[NGLx(Nfin(Nel)),NGLrz(Nfin(Nel))]:=KG[NGLx(Nfin(Nel)),NGLrz(Nfin(Nel))]+K(Nel)[4,6]:
KG[NGLy(Nfin(Nel)),NGLx(Nini(Nel))]:=KG[NGLy(Nfin(Nel)),NGLx(Nini(Nel))]+K(Nel)[5,1]:KG[NGLy(Nfin(Nel)),NGLy(Nini(Nel))]:=KG[NGLy(Nfin(Nel)),NGLy(Nini(Nel))]+K(Nel)[5,2]:KG[NGLy(Nfin(Nel)),NGLrz(Nini(Nel))]:=KG[NGLy(Nfin(Nel)),NGLrz(Nini(Nel))]+K(Nel)[5,3]:KG[NGLy(Nfin(Nel)),NGLx(Nfin(Nel))]:=KG[NGLy(Nfin(Nel)),NGLx(Nfin(Nel))]+K(Nel)[5,4]:KG[NGLy(Nfin(Nel)),NGLy(Nfin(Nel))]:=KG[NGLy(Nfin(Nel)),NGLy(Nfin(Nel))]+K(Nel)[5,5]:KG[NGLy(Nfin(Nel)),NGLrz(Nfin(Nel))]:=KG[NGLy(Nfin(Nel)),NGLrz(Nfin(Nel))]+K(Nel)[5,6]:
KG[NGLrz(Nfin(Nel)),NGLx(Nini(Nel))]:=KG[NGLrz(Nfin(Nel)),NGLx(Nini(Nel))]+K(Nel)[6,1]:KG[NGLrz(Nfin(Nel)),NGLy(Nini(Nel))]:=KG[NGLrz(Nfin(Nel)),NGLy(Nini(Nel))]+K(Nel)[6,2]:KG[NGLrz(Nfin(Nel)),NGLrz(Nini(Nel))]:=KG[NGLrz(Nfin(Nel)),NGLrz(Nini(Nel))]+K(Nel)[6,3]:KG[NGLrz(Nfin(Nel)),NGLx(Nfin(Nel))]:=KG[NGLrz(Nfin(Nel)),NGLx(Nfin(Nel))]+K(Nel)[6,4]:KG[NGLrz(Nfin(Nel)),NGLy(Nfin(Nel))]:=KG[NGLrz(Nfin(Nel)),NGLy
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(Nfin(Nel))]+K(Nel)[6,5]:KG[NGLrz(Nfin(Nel)),NGLrz(Nfin(Nel))]:=KG[NGLrz(Nfin(Nel)),NGLrz(Nfin(Nel))]+K(Nel)[6,6]:
evalm(KG):
Nel:=12:Nm(Nel):=1:Np(Nel):=1:Nini(Nel):=12:Nfin(Nel):=13:
L(Nel):=sqrt((X(Nfin(Nel))-X(Nini(Nel)))^2+(Y(Nfin(Nel))-Y(Nini(Nel)))^2):CosLocGlob:=(X(Nfin(Nel))-X(Nini(Nel)))/L(Nel):SenLocGlob:=-(Y(Nfin(Nel))-Y(Nini(Nel)))/L(Nel):
Kloc:=matrix([[E(Nm(Nel))*A(Np(Nel))/L(Nel),0,0,-E(Nm(Nel))*A(Np(Nel))/L(Nel),0,0],[0,12.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^3,6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2,0,-12.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^3,6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2],[0,6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2,4.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel),0,-6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2,2.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)],[-E(Nm(Nel))*A(Np(Nel))/L(Nel),0,0,E(Nm(Nel))*A(Np(Nel))/L(Nel),0,0],[0,-12.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^3,-6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2,0,12.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^3,-6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2],[0,6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2,2.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel),0,-6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2,4.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)]]):
Rot(Nel):=matrix([[CosLocGlob,SenLocGlob,0,0,0,0],[-SenLocGlob,CosLocGlob,0,0,0,0],[0,0,1.,0,0,0],[0,0,0,CosLocGlob,SenLocGlob,0],[0,0,0,-SenLocGlob,CosLocGlob,0],[0,0,0,0,0,1.]]):
Trot:=transpose(Rot(Nel)):
K(Nel):=evalm(Rot(Nel)&*Kloc&*Trot):
KG[NGLx(Nini(Nel)),NGLx(Nini(Nel))]:=KG[NGLx(Nini(Nel)),NGLx
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(Nini(Nel))]+K(Nel)[1,1]:KG[NGLx(Nini(Nel)),NGLy(Nini(Nel))]:=KG[NGLx(Nini(Nel)),NGLy(Nini(Nel))]+K(Nel)[1,2]:KG[NGLx(Nini(Nel)),NGLrz(Nini(Nel))]:=KG[NGLx(Nini(Nel)),NGLrz(Nini(Nel))]+K(Nel)[1,3]:KG[NGLx(Nini(Nel)),NGLx(Nfin(Nel))]:=KG[NGLx(Nini(Nel)),NGLx(Nfin(Nel))]+K(Nel)[1,4]:KG[NGLx(Nini(Nel)),NGLy(Nfin(Nel))]:=KG[NGLx(Nini(Nel)),NGLy(Nfin(Nel))]+K(Nel)[1,5]:KG[NGLx(Nini(Nel)),NGLrz(Nfin(Nel))]:=KG[NGLx(Nini(Nel)),NGLrz(Nfin(Nel))]+K(Nel)[1,6]:
KG[NGLy(Nini(Nel)),NGLx(Nini(Nel))]:=KG[NGLy(Nini(Nel)),NGLx(Nini(Nel))]+K(Nel)[2,1]:KG[NGLy(Nini(Nel)),NGLy(Nini(Nel))]:=KG[NGLy(Nini(Nel)),NGLy(Nini(Nel))]+K(Nel)[2,2]:KG[NGLy(Nini(Nel)),NGLrz(Nini(Nel))]:=KG[NGLy(Nini(Nel)),NGLrz(Nini(Nel))]+K(Nel)[2,3]:KG[NGLy(Nini(Nel)),NGLx(Nfin(Nel))]:=KG[NGLy(Nini(Nel)),NGLx(Nfin(Nel))]+K(Nel)[2,4]:KG[NGLy(Nini(Nel)),NGLy(Nfin(Nel))]:=KG[NGLy(Nini(Nel)),NGLy(Nfin(Nel))]+K(Nel)[2,5]:KG[NGLy(Nini(Nel)),NGLrz(Nfin(Nel))]:=KG[NGLy(Nini(Nel)),NGLrz(Nfin(Nel))]+K(Nel)[2,6]:
KG[NGLrz(Nini(Nel)),NGLx(Nini(Nel))]:=KG[NGLrz(Nini(Nel)),NGLx(Nini(Nel))]+K(Nel)[3,1]:KG[NGLrz(Nini(Nel)),NGLy(Nini(Nel))]:=KG[NGLrz(Nini(Nel)),NGLy(Nini(Nel))]+K(Nel)[3,2]:KG[NGLrz(Nini(Nel)),NGLrz(Nini(Nel))]:=KG[NGLrz(Nini(Nel)),NGLrz(Nini(Nel))]+K(Nel)[3,3]:KG[NGLrz(Nini(Nel)),NGLx(Nfin(Nel))]:=KG[NGLrz(Nini(Nel)),NGLx(Nfin(Nel))]+K(Nel)[3,4]:KG[NGLrz(Nini(Nel)),NGLy(Nfin(Nel))]:=KG[NGLrz(Nini(Nel)),NGLy(Nfin(Nel))]+K(Nel)[3,5]:KG[NGLrz(Nini(Nel)),NGLrz(Nfin(Nel))]:=KG[NGLrz(Nini(Nel)),NGLrz(Nfin(Nel))]+K(Nel)[3,6]:
KG[NGLx(Nfin(Nel)),NGLx(Nini(Nel))]:=KG[NGLx(Nfin(Nel)),NGLx(Nini(Nel))]+K(Nel)[4,1]:
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KG[NGLx(Nfin(Nel)),NGLy(Nini(Nel))]:=KG[NGLx(Nfin(Nel)),NGLy(Nini(Nel))]+K(Nel)[4,2]:KG[NGLx(Nfin(Nel)),NGLrz(Nini(Nel))]:=KG[NGLx(Nfin(Nel)),NGLrz(Nini(Nel))]+K(Nel)[4,3]:KG[NGLx(Nfin(Nel)),NGLx(Nfin(Nel))]:=KG[NGLx(Nfin(Nel)),NGLx(Nfin(Nel))]+K(Nel)[4,4]:KG[NGLx(Nfin(Nel)),NGLy(Nfin(Nel))]:=KG[NGLx(Nfin(Nel)),NGLy(Nfin(Nel))]+K(Nel)[4,5]:KG[NGLx(Nfin(Nel)),NGLrz(Nfin(Nel))]:=KG[NGLx(Nfin(Nel)),NGLrz(Nfin(Nel))]+K(Nel)[4,6]:
KG[NGLy(Nfin(Nel)),NGLx(Nini(Nel))]:=KG[NGLy(Nfin(Nel)),NGLx(Nini(Nel))]+K(Nel)[5,1]:KG[NGLy(Nfin(Nel)),NGLy(Nini(Nel))]:=KG[NGLy(Nfin(Nel)),NGLy(Nini(Nel))]+K(Nel)[5,2]:KG[NGLy(Nfin(Nel)),NGLrz(Nini(Nel))]:=KG[NGLy(Nfin(Nel)),NGLrz(Nini(Nel))]+K(Nel)[5,3]:KG[NGLy(Nfin(Nel)),NGLx(Nfin(Nel))]:=KG[NGLy(Nfin(Nel)),NGLx(Nfin(Nel))]+K(Nel)[5,4]:KG[NGLy(Nfin(Nel)),NGLy(Nfin(Nel))]:=KG[NGLy(Nfin(Nel)),NGLy(Nfin(Nel))]+K(Nel)[5,5]:KG[NGLy(Nfin(Nel)),NGLrz(Nfin(Nel))]:=KG[NGLy(Nfin(Nel)),NGLrz(Nfin(Nel))]+K(Nel)[5,6]:
KG[NGLrz(Nfin(Nel)),NGLx(Nini(Nel))]:=KG[NGLrz(Nfin(Nel)),NGLx(Nini(Nel))]+K(Nel)[6,1]:KG[NGLrz(Nfin(Nel)),NGLy(Nini(Nel))]:=KG[NGLrz(Nfin(Nel)),NGLy(Nini(Nel))]+K(Nel)[6,2]:KG[NGLrz(Nfin(Nel)),NGLrz(Nini(Nel))]:=KG[NGLrz(Nfin(Nel)),NGLrz(Nini(Nel))]+K(Nel)[6,3]:KG[NGLrz(Nfin(Nel)),NGLx(Nfin(Nel))]:=KG[NGLrz(Nfin(Nel)),NGLx(Nfin(Nel))]+K(Nel)[6,4]:KG[NGLrz(Nfin(Nel)),NGLy(Nfin(Nel))]:=KG[NGLrz(Nfin(Nel)),NGLy(Nfin(Nel))]+K(Nel)[6,5]:KG[NGLrz(Nfin(Nel)),NGLrz(Nfin(Nel))]:=KG[NGLrz(Nfin(Nel)),NGLrz(Nfin(Nel))]+K(Nel)[6,6]:
evalm(KG):
Nel:=13:
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Nm(Nel):=1:Np(Nel):=1:Nini(Nel):=13:Nfin(Nel):=14:
L(Nel):=sqrt((X(Nfin(Nel))-X(Nini(Nel)))^2+(Y(Nfin(Nel))-Y(Nini(Nel)))^2):CosLocGlob:=(X(Nfin(Nel))-X(Nini(Nel)))/L(Nel):SenLocGlob:=-(Y(Nfin(Nel))-Y(Nini(Nel)))/L(Nel):
Kloc:=matrix([[E(Nm(Nel))*A(Np(Nel))/L(Nel),0,0,-E(Nm(Nel))*A(Np(Nel))/L(Nel),0,0],[0,12.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^3,6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2,0,-12.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^3,6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2],[0,6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2,4.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel),0,-6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2,2.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)],[-E(Nm(Nel))*A(Np(Nel))/L(Nel),0,0,E(Nm(Nel))*A(Np(Nel))/L(Nel),0,0],[0,-12.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^3,-6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2,0,12.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^3,-6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2],[0,6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2,2.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel),0,-6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2,4.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)]]):
Rot(Nel):=matrix([[CosLocGlob,SenLocGlob,0,0,0,0],[-SenLocGlob,CosLocGlob,0,0,0,0],[0,0,1.,0,0,0],[0,0,0,CosLocGlob,SenLocGlob,0],[0,0,0,-SenLocGlob,CosLocGlob,0],[0,0,0,0,0,1.]]):
Trot:=transpose(Rot(Nel)):
K(Nel):=evalm(Rot(Nel)&*Kloc&*Trot):
KG[NGLx(Nini(Nel)),NGLx(Nini(Nel))]:=KG[NGLx(Nini(Nel)),NGLx(Nini(Nel))]+K(Nel)[1,1]:KG[NGLx(Nini(Nel)),NGLy(Nini(Nel))]:=KG[NGLx(Nini(Nel)),NGLy(Nini(Nel))]+K(Nel)[1,2]:KG[NGLx(Nini(Nel)),NGLrz(Nini(Nel))]:=KG[NGLx(Nini(Nel)),NGLrz(Nini(Nel))]+K(Nel)[1,3]:KG[NGLx(Nini(Nel)),NGLx(Nfin(Nel))]:=KG[NGLx(Nini(Nel)),NGLx(Nfin(Nel))]+K(Nel)[1,4]:
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KG[NGLx(Nini(Nel)),NGLy(Nfin(Nel))]:=KG[NGLx(Nini(Nel)),NGLy(Nfin(Nel))]+K(Nel)[1,5]:KG[NGLx(Nini(Nel)),NGLrz(Nfin(Nel))]:=KG[NGLx(Nini(Nel)),NGLrz(Nfin(Nel))]+K(Nel)[1,6]:
KG[NGLy(Nini(Nel)),NGLx(Nini(Nel))]:=KG[NGLy(Nini(Nel)),NGLx(Nini(Nel))]+K(Nel)[2,1]:KG[NGLy(Nini(Nel)),NGLy(Nini(Nel))]:=KG[NGLy(Nini(Nel)),NGLy(Nini(Nel))]+K(Nel)[2,2]:KG[NGLy(Nini(Nel)),NGLrz(Nini(Nel))]:=KG[NGLy(Nini(Nel)),NGLrz(Nini(Nel))]+K(Nel)[2,3]:KG[NGLy(Nini(Nel)),NGLx(Nfin(Nel))]:=KG[NGLy(Nini(Nel)),NGLx(Nfin(Nel))]+K(Nel)[2,4]:KG[NGLy(Nini(Nel)),NGLy(Nfin(Nel))]:=KG[NGLy(Nini(Nel)),NGLy(Nfin(Nel))]+K(Nel)[2,5]:KG[NGLy(Nini(Nel)),NGLrz(Nfin(Nel))]:=KG[NGLy(Nini(Nel)),NGLrz(Nfin(Nel))]+K(Nel)[2,6]:
KG[NGLrz(Nini(Nel)),NGLx(Nini(Nel))]:=KG[NGLrz(Nini(Nel)),NGLx(Nini(Nel))]+K(Nel)[3,1]:KG[NGLrz(Nini(Nel)),NGLy(Nini(Nel))]:=KG[NGLrz(Nini(Nel)),NGLy(Nini(Nel))]+K(Nel)[3,2]:KG[NGLrz(Nini(Nel)),NGLrz(Nini(Nel))]:=KG[NGLrz(Nini(Nel)),NGLrz(Nini(Nel))]+K(Nel)[3,3]:KG[NGLrz(Nini(Nel)),NGLx(Nfin(Nel))]:=KG[NGLrz(Nini(Nel)),NGLx(Nfin(Nel))]+K(Nel)[3,4]:KG[NGLrz(Nini(Nel)),NGLy(Nfin(Nel))]:=KG[NGLrz(Nini(Nel)),NGLy(Nfin(Nel))]+K(Nel)[3,5]:KG[NGLrz(Nini(Nel)),NGLrz(Nfin(Nel))]:=KG[NGLrz(Nini(Nel)),NGLrz(Nfin(Nel))]+K(Nel)[3,6]:
KG[NGLx(Nfin(Nel)),NGLx(Nini(Nel))]:=KG[NGLx(Nfin(Nel)),NGLx(Nini(Nel))]+K(Nel)[4,1]:KG[NGLx(Nfin(Nel)),NGLy(Nini(Nel))]:=KG[NGLx(Nfin(Nel)),NGLy(Nini(Nel))]+K(Nel)[4,2]:KG[NGLx(Nfin(Nel)),NGLrz(Nini(Nel))]:=KG[NGLx(Nfin(Nel)),NGLrz(Nini(Nel))]+K(Nel)[4,3]:KG[NGLx(Nfin(Nel)),NGLx(Nfin(Nel))]:=KG[NGLx(Nfin(Nel)),NGLx(Nfin(Nel))]+K(Nel)[4,4]:KG[NGLx(Nfin(Nel)),NGLy(Nfin(Nel))]:=KG[NGLx(Nfin(Nel)),NGLy
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(Nfin(Nel))]+K(Nel)[4,5]:KG[NGLx(Nfin(Nel)),NGLrz(Nfin(Nel))]:=KG[NGLx(Nfin(Nel)),NGLrz(Nfin(Nel))]+K(Nel)[4,6]:
KG[NGLy(Nfin(Nel)),NGLx(Nini(Nel))]:=KG[NGLy(Nfin(Nel)),NGLx(Nini(Nel))]+K(Nel)[5,1]:KG[NGLy(Nfin(Nel)),NGLy(Nini(Nel))]:=KG[NGLy(Nfin(Nel)),NGLy(Nini(Nel))]+K(Nel)[5,2]:KG[NGLy(Nfin(Nel)),NGLrz(Nini(Nel))]:=KG[NGLy(Nfin(Nel)),NGLrz(Nini(Nel))]+K(Nel)[5,3]:KG[NGLy(Nfin(Nel)),NGLx(Nfin(Nel))]:=KG[NGLy(Nfin(Nel)),NGLx(Nfin(Nel))]+K(Nel)[5,4]:KG[NGLy(Nfin(Nel)),NGLy(Nfin(Nel))]:=KG[NGLy(Nfin(Nel)),NGLy(Nfin(Nel))]+K(Nel)[5,5]:KG[NGLy(Nfin(Nel)),NGLrz(Nfin(Nel))]:=KG[NGLy(Nfin(Nel)),NGLrz(Nfin(Nel))]+K(Nel)[5,6]:
KG[NGLrz(Nfin(Nel)),NGLx(Nini(Nel))]:=KG[NGLrz(Nfin(Nel)),NGLx(Nini(Nel))]+K(Nel)[6,1]:KG[NGLrz(Nfin(Nel)),NGLy(Nini(Nel))]:=KG[NGLrz(Nfin(Nel)),NGLy(Nini(Nel))]+K(Nel)[6,2]:KG[NGLrz(Nfin(Nel)),NGLrz(Nini(Nel))]:=KG[NGLrz(Nfin(Nel)),NGLrz(Nini(Nel))]+K(Nel)[6,3]:KG[NGLrz(Nfin(Nel)),NGLx(Nfin(Nel))]:=KG[NGLrz(Nfin(Nel)),NGLx(Nfin(Nel))]+K(Nel)[6,4]:KG[NGLrz(Nfin(Nel)),NGLy(Nfin(Nel))]:=KG[NGLrz(Nfin(Nel)),NGLy(Nfin(Nel))]+K(Nel)[6,5]:KG[NGLrz(Nfin(Nel)),NGLrz(Nfin(Nel))]:=KG[NGLrz(Nfin(Nel)),NGLrz(Nfin(Nel))]+K(Nel)[6,6]:
evalm(KG):
Nel:=14:Nm(Nel):=1:Np(Nel):=1:Nini(Nel):=14:Nfin(Nel):=15:
L(Nel):=sqrt((X(Nfin(Nel))-X(Nini(Nel)))^2+(Y(Nfin(Nel))-Y(Nini
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(Nel)))^2):CosLocGlob:=(X(Nfin(Nel))-X(Nini(Nel)))/L(Nel):SenLocGlob:=-(Y(Nfin(Nel))-Y(Nini(Nel)))/L(Nel):
Kloc:=matrix([[E(Nm(Nel))*A(Np(Nel))/L(Nel),0,0,-E(Nm(Nel))*A(Np(Nel))/L(Nel),0,0],[0,12.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^3,6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2,0,-12.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^3,6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2],[0,6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2,4.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel),0,-6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2,2.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)],[-E(Nm(Nel))*A(Np(Nel))/L(Nel),0,0,E(Nm(Nel))*A(Np(Nel))/L(Nel),0,0],[0,-12.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^3,-6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2,0,12.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^3,-6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2],[0,6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2,2.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel),0,-6.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)^2,4.*E(Nm(Nel))*Iz(Np(Nel))/L(Nel)]]):
Rot(Nel):=matrix([[CosLocGlob,SenLocGlob,0,0,0,0],[-SenLocGlob,CosLocGlob,0,0,0,0],[0,0,1.,0,0,0],[0,0,0,CosLocGlob,SenLocGlob,0],[0,0,0,-SenLocGlob,CosLocGlob,0],[0,0,0,0,0,1.]]):
Trot:=transpose(Rot(Nel)):
K(Nel):=evalm(Rot(Nel)&*Kloc&*Trot):
KG[NGLx(Nini(Nel)),NGLx(Nini(Nel))]:=KG[NGLx(Nini(Nel)),NGLx(Nini(Nel))]+K(Nel)[1,1]:KG[NGLx(Nini(Nel)),NGLy(Nini(Nel))]:=KG[NGLx(Nini(Nel)),NGLy(Nini(Nel))]+K(Nel)[1,2]:KG[NGLx(Nini(Nel)),NGLrz(Nini(Nel))]:=KG[NGLx(Nini(Nel)),NGLrz(Nini(Nel))]+K(Nel)[1,3]:KG[NGLx(Nini(Nel)),NGLx(Nfin(Nel))]:=KG[NGLx(Nini(Nel)),NGLx(Nfin(Nel))]+K(Nel)[1,4]:KG[NGLx(Nini(Nel)),NGLy(Nfin(Nel))]:=KG[NGLx(Nini(Nel)),NGLy(Nfin(Nel))]+K(Nel)[1,5]:KG[NGLx(Nini(Nel)),NGLrz(Nfin(Nel))]:=KG[NGLx(Nini(Nel)),NGLrz(Nfin(Nel))]+K(Nel)[1,6]:
KG[NGLy(Nini(Nel)),NGLx(Nini(Nel))]:=KG[NGLy(Nini(Nel)),NGLx
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