94 lines
2.2 KiB
Mathematica
94 lines
2.2 KiB
Mathematica
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%----------------------------------------------------------------
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% PURPOSE
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% Analysis of a plate.
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% unit mm N MPa
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%----------------------------------------------------------------
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clear all;clc;
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%----- Topology -------------------------------------------------
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%square plate with n element each side
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n_length=100;
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m_width=20;
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num=0;
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for j=1:m_width
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for i=1:n_length
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num=num+1;
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Enode(num,:)=[num (j-1)*(n_length+1)+i (j-1)*(n_length+1)+i+1 (j)*(n_length+1)+i+1 (j)*(n_length+1)+i];
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ex(num,:)=[(i-1)*5 i*5 i*5 (i-1)*5];%unit mm
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ey(num,:)=[(j-1)*5 (j-1)*5 j*5 j*5];
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if i*5>=0 && i*5<200
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t(num)=0.5+(3-0.5)/200*i*5;
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elseif i*5>=200 && i*5<300
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t(num)=3;
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elseif i*5>=300 && i*5<=500
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t(num)=0.5+(3-0.5)/200*(500-i*5);
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end
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end
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end
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% Enode=[1 1 2 5 4;
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% 2 2 3 6 5;
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% 3 5 6 9 8;
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% 4 4 5 8 7];
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ndof=3;
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Edof=caldof(Enode,ndof);
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% ex=[0 1 1 0;
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% 1 2 2 1;
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% 1 2 2 1;
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% 0 1 1 0];
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% ey=[0 0 1 1;
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% 0 0 1 1;
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% 1 1 2 2;
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% 1 1 2 2];
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%----- Element stiffness ----------------------------------------
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E=2.1*10^5; %2.1e5MPa
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v=0.3;
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D=hooke(E,v);
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% t=2;
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ep=[t];
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nie=size(Enode,1);
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for i=1:nie
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Ke(:,:,i)=platre(ex(i,:),ey(i,:),ep(i),D);
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end
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%----- Assemble Ke into K ---------------------------------------
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K=zeros(max(max(Edof))); K=assem(Edof,K,Ke);
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%----- load vector f and boundary conditions bc -----------------
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f=zeros(max(max(Edof)),1); f(3184)=-400;
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num=0;
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for i=0:20
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num=num+1;
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boundary_node(num)=(i)*101+1;
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num=num+1;
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boundary_node(num)=(i+1)*101;
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end
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for i=1:length(boundary_node)
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bc((i-1)*3+1,:)=[3*(boundary_node(i)-1)+1 0];
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bc((i-1)*3+2,:)=[3*(boundary_node(i)-1)+2 0];
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bc((i-1)*3+3,:)=[3*(boundary_node(i)-1)+3 0];
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end
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%----- Solve the system of equations and compute reactions ------
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[a]=solveq(K,f,bc);
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%----- Postprocess ----------------------------------------------
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Ed=extract(Edof,a);
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num=0;
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for i=1:21
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for j=1:101
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num=num+1;
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x(i,j)=(j-1)*5;
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y(i,j)=(i-1)*5;
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z(i,j)=abs(a((num-1)*3+1));
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end
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end
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surf(x,y,z)
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xlabel('length(mm)');
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ylabel('width(mm)');
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zlabel('displacement(mm)');
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%------------------------ end -----------------------------------
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