Hey Daeho,
It is possible to calculate stress from deformation data in MATLAB without the PDE toolbox. The calculation of stress from deformation depends on stress, strain, and deformation in the material.
Since you mentioned that you have calculated the deformatoin, the next step would be to calculate the stress and strain.
- From the deformation data, you can calculate the strain. For small deformations, strain can often be approximated as the gradient of the displacement field.
- With the strain, you can then use the material's constitutive model to calculate stress. For a linear elastic material, this is generally done using Hooke's law.
This following example code snippet assumes you have a simple model and you're working with linear elasticity. Please adjust the parameters according to your requirements:
% Calculate D, the elasticity matrix for plane stress
E = 210e9; % Example for steel, in Pascals
nu = 0.3; % Typical for steel
D = E / (1 - nu^2) * [1, nu, 0; nu, 1, 0; 0, 0, (1 - nu) / 2];
% For each element, calculate strain and then stress
for elem = 1:size(elementNodes, 1)
% Extract nodal coordinates and displacements for the current element
nodes = elementNodes(elem, :);
elemCoords = nodeCoordinates(nodes, :);
elemD = deformation(nodes, :);
% Calculate strain for the element - simplified, depends on element type
% This step is highly dependent on your element type and mesh
% For example, for a 2D triangular element:
% B = ... % Calculate the strain-displacement matrix B
% strain = B * elemD(:);
% Calculate stress
stress = D * strain;
% Store or process the stress as needed
% ...
end
Here, E is the Young's modulus, nu is the Poisson's ratio, deformation is a matrix of nodal displacements obtained from your analysis, elementNodes is a matrix defining nodes for each element, nodeCoordinates is a matrix defining the x, y coordinates of each node.
