轴向加载阶梯轴的MATLAB分析

Question

我有一个阶梯轴，根据所附的图像。可作为输入参数的下列信息：

123e3N/mm^2.

• Cross-sectional杨氏模量400mm

• Cross-sectional面积300 is ^2为400mm

• Cross-sectional面积400 is^2，长度为250 is

• 轴向力200 on轴向作用于轴上，轴向截面面积为300 is×2

时，载荷位于轴的一端200 is处。

我需要在MATALB中进行有限元分析。请帮助我编写MATLAB代码。

​

Answer 1

%% Clearing workspace

clc
clear
close all

%% Element specifications 

ne = 3; % Number of elements 
nne = 2; % Number of nodes per element 
nn = ne*(nne - 1) + 1; % total number of nodes
ndof = 1; % Number of degress of freedom per node 
sg = nn*ndof; % size of global stiffness matrix 
se = nne*ndof; % size of elemental stiffness matrix 
KG = zeros(sg,sg); % Global stiffness matrix 
Ke = zeros(se,se); % Elemental Stiffness MAtrix 
Fe = zeros(se,1); % Elemental Force Vector 
FG = zeros(sg,1); % Global Force Vector

%% Geometrical parameters

E = 123e3*ones(1,ne); % Young's Modulus in N/mm^2
P = 200e3; % Force in N
F = P;

A = ones(1,ne) ; % Area of cross-section 
A(1)=300; % Area of cross-section of 1st element in mm^2
A(2)=300; % Area of cross-section of 2nd element in mm^2
A(3)=400; % Area of cross-section of 3rd element in mm^2

L = ones(1,ne); % Length of elements in mm
L(1)=200; % Length of 1st element in mm
L(2)=200; % Length of 2nd element in mm
L(3)=250; % Length of 3rd element in mm

%% Assembly of Global Stiffness Matrix

for i = 1:ne
    Ke = (A(i)*E(i)/L(i))*[1 -1;-1 1]; % Element Stiffness Matrix
    for j = 1:se
        for k = 1:se
            KG(i + j - 1, i + k - 1) = KG(i + j - 1, i + k - 1) + Ke(j,k);
        end
    end
end

%% Concentrated Load Vector at end

FG(2,1) = F; % Defining location of concentrated load

%% Application of boundary conditions

KGS = KG;
cdof = [1 4]; % specify fixed degree of freedom number
Lcdof = length(cdof);
for a = 1:Lcdof
    KGS(cdof(a),:) = 0;
    KGS(:,cdof(a)) = 1;
    FG(cdof(a),1) = 0;
end
FGL = length(FG); 
for b = 1:FGL
    if(b > length(FG))
        elseif(FG(b)<0)
            FG(b) = [];
    end
end

%% Solving for displacement

U = linsolve(KGS,FG) 
U1=KGS\FG 

%% Calculation of Reaction Forces 

FR = KG*U1