## How to include in-plane displacements in the PDE solver?

### Henry1993x (view profile)

on 3 May 2016
Latest activity Commented on by Henry1993x

### Henry1993x (view profile)

on 6 May 2016
Hi there,
There is an example available for calculating the deflection w of a uniformly loaded, isotropic plate using the PDE solver (not the pdetool):
The boundary conditions are expressed as:
k = 1e7; % spring stiffness
bOuter = applyBoundaryCondition(pdem,'Edge',(1:4), 'g', [0 0], 'q', [0 0; k 0]);
So I wonder,
1. How can plane stresses sigma_x and sigma_y be calculated?
2. How can in-plane displacements (perpendicular to w) be included as boundary conditions in the formulation of the problem?
Also, the solution to the elliptical PDE:
res = solvepde(pdem);
outputs something like:
res =
StationaryResults with properties:
NodalSolution: [100x2 double]
Mesh: [1x1 FEMesh]
I assume that XGradient and YGradient are the dw/dx and dw/dy respectively. My other question is then, how can the second derivative d2w/dx2 and d2w/dy2 can be estimated?
Thanks!

Vaibhav Awale

### Vaibhav Awale (view profile)

님의 답변 6 May 2016

Hi Henry,
I will try to answer the questions that I know.
1) You can refer to this example . PDE app is used in this case to find plane stress and strain. However, you can do it using PDE toolbox command line approach as well.
2) I am not sure what you mean by in plane displacement at boundary.
3) Looking at the way the problem is formulated, res.NodalSolution consists of solution to [u1, u2] where u1 = w u2 = \Delta^2 w = v