Partial Differential Equation Toolbox™

pdesmech - Calculate structural mechanics tensor functions

Syntax

ux=pdesmech(p,t,c,u,'PropertyName',PropertyValue,...)

Description

ux=pdesmech(p,t,c,u,p1,v1,...) returns a tensor expression evaluated at the center of each triangle. The tensor expressions are stresses and strains for structural mechanics applications with plane stress or plane strain conditions. pdesmech is intended to be used for postprocessing of a solution computed using the structural mechanics application modes of the pdetool GUI, after exporting the solution, the mesh, and the PDE coefficients to the MATLAB^® workspace. Poisson's ratio, nu, has to be supplied explicitly for calculations of shear stresses and strains, and for the von Mises effective stress in plane strain mode.

Valid property name/property value pairs include the following.

The available tensor expressions are

• 

• 

• 

• 

• exx, the x-direction strain (ε_x)

• eyy, the y-direction strain (ε_y)

• exy, the shear strain (γ_xy)

• sxx, the x-direction stress (σ_x)

• syy, the y-direction stress (σ_y)

• sxy, the shear stress (τ_xy)

• e1, the first principal strain (ε₁)

• e2, the second principal strain (ε₂)

• s1, the first principal stress (σ₁)

• s2, the second principal stress (σ₂)

• von Mises, the von Mises effective stress, for plane stress conditions

  

  or for plane strain conditions

  

Examples

Assuming that a problem has been solved using the application mode "Structural Mechanics, Plane Stress," discussed in Structural Mechanics — Plane Stress, and that the solution u, the mesh data p and t, and the PDE coefficient c all have been exported to the MATLAB workspace, the x-direction strain is computed as

sx=pdesmech(p,t,c,u,'tensor','sxx'); 

To compute the von Mises effective stress for a plane strain problem with Poisson's ratio equal to 0.3, type

mises=pdesmech(p,t,c,u,'tensor','von Mises',...
  'application','pn','nu',0.3);

pdesdp, pdesde, pdesdt

pdesurf