To plot the shear stress distribution in a laminated beam using the stress equilibrium equation and finite element method (FEM), you can follow these steps:
% Define geometry and material properties
length = 1; % length of the beam
height = 0.1; % height of the beam
num_elements = 10; % number of finite elements
E = 1e9; % Young's modulus
nu = 0.3; % Poisson's ratio
% Discretize the beam into finite elements
element_length = length / num_elements;
x = linspace(0, length, num_elements+1);
% Apply boundary conditions
displacements = zeros(num_elements+1, 1);
displacements(1) = 0; % fixed support at one end
displacements(end) = 0; % fixed support at the other end
% Solve the system of equations using FEM
% (code to assemble and solve the stiffness matrix and load vector)
% Calculate shear stresses at each element
shear_stresses = zeros(num_elements, 1);
for i = 1:num_elements
% calculate shear stress using stress equilibrium equation
end
% Plot shear stress distribution
figure;
plot(x(1:end-1), shear_stresses);
xlabel('Position along beam');
ylabel('Shear stress');
title('Shear Stress Distribution in Laminated Beam');
This code assumes that you have already implemented the FEM solver to obtain the displacements. You would need to fill in the missing parts specific to your implementation.
