<< MATLAB Codes for Finite Element Analysis - Solids and Structures (Ferreira) >> 笔记
chapter 01 matlab basic
略
第二章: 离散系统
笔记、例题
Matlab代码
- problem1.m
% MATLAB codes for Finite Element Analysis
% Problem 1: 3 springs problem
% clear memory
clear ;
% ? define vars
P=10; % N
ki=[1;1;1;1];
% elementNodes: connections at elements
elementNodes=[1 2;
2 3;
2 4];
% numberElements: number of Elements
numberElements=size(elementNodes,1);
% numberNodes: number of nodes
numberNodes=4;
% for structure:
% displacements: displacement vector N x 1
% force : force vector N x 1
% stiffness: stiffness matrix N x N
displacements=zeros(numberNodes,1); %#ok<PREALL>
force=zeros(numberNodes,1);
stiffness=zeros(numberNodes);
% applied load at node 2
force(2)=P;
% computation of the system stiffness matrix
for e=1:numberElements
% elementDof: element degrees of freedom (Dof)
elementDof=elementNodes(e,:) ;
stiffness(elementDof,elementDof)=...
stiffness(elementDof,elementDof)+ki(e)*[1 -1;-1 1];
end
% boundary conditions and solution
% prescribed dofs
prescribedDof=[1;3;4];
% free Dof : activeDof
% setdiff() 函数-->求两个数组的差集
% C = setdiff(A,B) 返回 A 中存在但 B 中不存在的数据,不包含重复项.C 是有序的.
activeDof=setdiff((1:numberNodes)',prescribedDof);
% solution
% !KU=F --> U=K\F
displacements=stiffness(activeDof,activeDof)\force(activeDof);
% positioning all displacements
displacements1=zeros(numberNodes,1);
displacements1(activeDof)=displacements;
% output displacements/reactions
outputDisplacementsReactions(displacements1,stiffness,numberNodes,prescribedDof)
- outputDisplacementsReactions.m
function outputDisplacementsReactions(displacements,stiffness,GDof,prescribedDof)
% output of displacements and reactions in
% tabular form
% GDof: total number of degrees of freedom of the problem
% displacements
disp('Displacements')
%displacements=displacements1;
jj=1:GDof; % format
[jj' displacements]
% reactions
F=stiffness*displacements;
reactions=F(prescribedDof);
disp('reactions')
[prescribedDof reactions]
end