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# Project2 Help - MATERIAL MATRIX IN MATLAB...

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1 MATERIAL MATRIX IN MATLAB C=hooke(ptype,E,v) ------------------------------------------- PURPOSE Calculate the material matrix for a linear elastic and isotropic material. INPUT: ptype=1: plane stress 2: plane strain 3: axisymmetry 4: three dimensional E : Young's modulus v : Poisson's const. OUTPUT: C : material matrix -------------------------------------------

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2 MATLAB PROGRAM FOR CST ELEMENT Ke=plante(ex,ey,ep,C) [Ke,fe]=plante(ex,ey,ep,C,eq) ------------------------------------------------------- PURPOSE Calculate the stiffness matrix for a triangular plane stress or plane strain element. INPUT: ex = [x1 x2 x3] element coordinates ey = [y1 y2 y3] ep = [ptype h ] ptype: analysis type h: thickness C constitutive matrix eq = [bx; bx: body force x-dir by] by: body force y-dir OUTPUT: Ke : element stiffness matrix (6 x 6) fe : equivalent nodal forces (6 x 1) -------------------------------------------------------
3 MATLAB PROGRAM FOR CST ELEMENT [es,et]=plants(ex,ey,ep,C,ed) -------------------------------------------------------- PURPOSE Calculate element normal and shear stress for a triangular plane stress or plane strain element. INPUT: ex = [x1 x2 x3] element coordinates ey = [y1 y2 y3] ep = [ptype h ] ptype: analysis type h: thickness C constitutive matrix ed =[u1 u2 . ..u6 element displ. vector ...... ] one row for each element OUTPUT: es = [sigx sigy [sigz] tauxy element stress ...... ] matrix one row for each elem. et = [epsx epsy [epsz] gamxy element strain ...... ] matrix one row for each elem. --------------------------------------------------------

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4 EXAMPLE 8.1 (MATLAB) Edof=[1 1 2 3 4 5 6; 2 1 2 5 6 7 8]; ex = [0 10 10;0 10 0]; ey = [0 5 15;0 15 20]; ep = [1 0.1]; E = 3e7; nu = 0.3; D = hooke(1, E, nu); Ke1 = plante(ex(1,:), ey(1,:), ep, D); Ke2 = plante(ex(2,:), ey(2,:), ep, D); K=zeros(8); F=zeros(8,1); F(4)=-50000;F(5)=50000; K=assem(Edof(1,:),K,Ke1); K=assem(Edof(2,:),K,Ke2); bc=[1 0;2 0;7 0;8 0]; U=solveq(K,F,bc); ed = extract(Edof,U); [es, et]=plants(ex,ey,ep,D,ed); plcontour2(ex,ey,es(:,1),ed,100)
5 PLCONTOUR2.M function plcontour2(Ex,Ey,Es,Ed,scale) % % Plot the stress contour for 2-D triangular or quadrilateral elements % Input: % Ex = [x1 x2 x3 (x4);. ..] Element nodal x-coordinates matrix % Ey = [y1 y2 y3 (y4);. ..] Element nodal y-coordinates matrix % Es = [s1;. ..] Element stress values. Single value per element % figure;

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Project2 Help - MATERIAL MATRIX IN MATLAB...

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