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                    Mathematica-Compatible Notebook

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Notebook[{
Cell["\<\
Internal force & tangent stiffness of  2-node, linearly elastic, CR \
space bar element moving in 3D \
\>", "Text",
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Cell["\<\
Internal force vector p = partial of element internal energy wrt \
node displacements\
\>", "Text",
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Cell[TextData[{
  "CRSpaceBar2InternalForce[ncoor0_,Em_,A0_,ue_,N0_,sm_,numer_]:=\n  \
Module[{X1,Y1,Z1,X2,Y2,Z2,LX,LY,LZ,LL0,L0,x1,y1,z1,x2,y2,z2,\n          \
Lx,Ly,Lz,LL,L,Lavg,d,EA,e,dedL,d2edL2,ND,h,p},\n  \
{{X1,Y1,Z1},{X2,Y2,Z2}}=ncoor0; {{uX1,uY1,uZ1},{uX2,uY2,uZ2}}=ue; \n  \
{LX,LY,LZ}={X2-X1,Y2-Y1,Z2-Z1}; LL0=LX^2+LY^2+LZ^2; L0=Sqrt[LL0];\n  \
{{x1,y1,z1},{x2,y2,z2}}=ncoor0+ue; \n  {Lx,Ly,Lz}={x2-x1,y2-y1,z2-z1}; \
LL=Lx^2+Ly^2+Lz^2; L=Sqrt[LL];\n  d=L-L0; Lavg=(L+L0)/2; e=Null;\n  If \
[sm==\"eE\", e=d/L0;        dedL=1/L0;      d2edL2=0];\n  If [sm==\"eG\", \
e=d*Lavg/L0^2; dedL=L/L0^2;    d2edL2=1/L0^2];\n  If [sm==\"eH\", \
e=Log[L/L0];   dedL=1/L;       d2edL2=-1/L^2]; \n  If [sm==\"eM\", e=d/Lavg;  \
    dedL=L0/Lavg^2; d2edL2=L0/Lavg^3]; \n  If \
[e==Null,Print[\"CRSpaceBar2Force: Illegal sm arg\"]; Return[Null]];\n  \
ND=N0+Em*A0*e;",
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  " h={-Lx,-Ly,-Lz,Lx,Ly,Lz}/L; \n  p=ND*L0*dedL*h; If [numer,p=N[p]]; \n  \
Return[p]]; \n",
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  StyleBox["ClearAll[\[Epsilon]];  ncoor0=N[{{0,0,0},{11,10,2}}]; \nEm=5000; \
A0=3; N0=10; numer=True;\nFor [i\[Epsilon]=1, i\[Epsilon]<=4, i\[Epsilon]++, \
\[Epsilon]={0,0.0001,0.01,0.1}[[i\[Epsilon]]];",
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  StyleBox["\n     For [ism=1,ism<=4,ism++,  \
sm={\"eE\",\"eG\",\"eH\",\"eM\"}[[ism]];\n     \
p=CRSpaceBar2InternalForce[ncoor0,Em,A0,ue,N0,sm,numer];\n     Print[\"sm: \
\",sm,\", \[Epsilon]=\",\[Epsilon],\",  p=\",p];\n    ]];",
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}], "Input",
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Cell["\<\
 Tangent stiffness matrix : partial of internal force vector wrt \
node displacements\
\>", "Text",
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Cell["(* To be done as part of Exercises 14.3 and 14.4 *)", "Input",
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00<0001804P000000]P2:?oQon82n@960dL5:0?l0080001804P000000]P2:001
0000I00000400`<300000BL?00400@00000000000000060801T1T00000000000
00000000000000000000000000000000\>"
]

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