matalb平面 4 节点四边形单元的单元刚度矩阵、单元组装、单元应力的计算 程序。
时间: 2023-05-29 17:02:36 浏览: 59
以下是matlab平面4节点四边形单元的单元刚度矩阵、单元组装、单元应力的计算程序:
% 定义节点坐标
x1 = 0; y1 = 0;
x2 = 2; y2 = 0;
x3 = 2; y3 = 1;
x4 = 0; y4 = 1;
% 定义材料属性
E = 2e11; % 弹性模量
nu = 0.3; % 泊松比
% 计算单元刚度矩阵
C1 = E/(1-nu^2)*[1, nu, 0;
nu, 1, 0;
0, 0, (1-nu)/2];
Ke = (1/2)*abs((x2-x1)*(y3-y4)-(x3-x4)*(y2-y1))*C1*[1 -1 1 -1;
-1 1 -1 1;
1 -1 1 -1;
-1 1 -1 1];
% 定义节点编号
IEN = [1 2 3 4];
% 构造全局刚度矩阵
K = zeros(8,8);
for i = 1:4
for j = 1:4
K(IEN(i),IEN(j)) = K(IEN(i),IEN(j)) + Ke(i,j);
end
end
% 定义边界条件
BC = [1 2 7 8];
% 构造载荷向量
F = zeros(8,1);
F(6) = -1000;
% 将边界条件应用到全局刚度矩阵和载荷向量中
K_reduced = K;
F_reduced = F;
K_reduced(BC,:) = [];
K_reduced(:,BC) = [];
F_reduced(BC,:) = [];
% 求解未知位移
U_reduced = K_reduced\F_reduced;
U = zeros(8,1);
U(~BC) = U_reduced;
% 根据位移计算单元应力
ex = (1/2*(-U(1)+U(2)+U(3)-U(4)))/(x2-x1);
ey = (1/2*(-U(1)-U(2)+U(3)+U(4)))/(y3-y1);
ez = 0;
G = E/(2*(1+nu));
exy = G*(1/2*(-U(2)+U(1)-U(4)+U(3)))/(x2-x1)/(y3-y1);
sigma = [ex exy; exy ey]