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# 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 PDE app, 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.

Property NameProperty Value/DefaultDescription

tensor

ux|uy|vx|vy|exx|eyy|exy|sxx|syy|sxy|e1|
e2|s1|s2|
{von Mises}

Tensor expression

application

{ps}|pn

Plane stress|plane strain

nu

Scalar or string expression {0.3}

Poisson's ratio

The available tensor expressions are

• ux, which is $\frac{\partial u}{\partial x}$

• uy, which is $\frac{\partial u}{\partial y}$

• vx, which is $\frac{\partial v}{\partial x}$

• vy, which is $\frac{\partial v}{\partial y}$

• exx, the x-direction strain (εx)

• eyy, the y-direction strain (εy)

• exy, the shear strain (γxy)

• sxx, the x-direction stress (σx)

• syy, the y-direction stress (σy)

• sxy, the shear stress (τxy)

• 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

$\sqrt{{\sigma }_{1}^{2}+{\sigma }_{2}^{2}-{\sigma }_{1}{\sigma }_{2}}$

or for plane strain conditions

$\sqrt{\left({\sigma }_{1}^{2}+{\sigma }_{2}^{2}\right)\left({v}^{2}-v+1\right)+{\sigma }_{1}{\sigma }_{2}\left(2{v}^{2}-2v-1\right)}$

where $v$ is Poisson's ratio nu.

## 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);```