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Thread Subject:
4th-order PDEs with PDE toolbox

Subject: 4th-order PDEs with PDE toolbox

From: Chris H

Date: 4 Dec, 2010 10:20:20

Message: 1 of 4

Hi there,

I want to solve the biharmonic equation

nabla^4 f = 0

in two dimensions for complicated domain shapes requiring finite elements, with Neumann and/or Dirichlet boundary conditions for f. Can the PDE toolbox achieve this goal, e.g., in the Structural Mechanics mode?

The PDE toolbox can definitely handle the relevant linear elasticity problem in which one is looking for the strain fields. However, what I am actually after is the function f. Is it possible to use the standard algorithms implemented in the PDE toolbox to this end, focusing purely on the biharmonic equation and forgetting about any context in linear elasticity theory?

Thanks!

Subject: 4th-order PDEs with PDE toolbox

From: Steffen

Date: 31 May, 2011 13:17:04

Message: 2 of 4

"Chris H" wrote in message <idd4l4$io1$1@fred.mathworks.com>...
> Hi there,
>
> I want to solve the biharmonic equation
>
> nabla^4 f = 0
>
> in two dimensions for complicated domain shapes requiring finite elements, with Neumann and/or Dirichlet boundary conditions for f. Can the PDE toolbox achieve this goal, e.g., in the Structural Mechanics mode?
>
> The PDE toolbox can definitely handle the relevant linear elasticity problem in which one is looking for the strain fields. However, what I am actually after is the function f. Is it possible to use the standard algorithms implemented in the PDE toolbox to this end, focusing purely on the biharmonic equation and forgetting about any context in linear elasticity theory?
>
> Thanks!

did you find a way to achieve this?

Subject: 4th-order PDEs with PDE toolbox

From: Eric

Date: 30 Jan, 2012 13:46:10

Message: 3 of 4

Is it the equation for membrane or shell deformation ? Could you detail the context and what you intend to do ?
Eric

"Chris H" wrote in message <idd4l4$io1$1@fred.mathworks.com>...
> Hi there,
>
> I want to solve the biharmonic equation
>
> nabla^4 f = 0
>
> in two dimensions for complicated domain shapes requiring finite elements, with Neumann and/or Dirichlet boundary conditions for f. Can the PDE toolbox achieve this goal, e.g., in the Structural Mechanics mode?
>
> The PDE toolbox can definitely handle the relevant linear elasticity problem in which one is looking for the strain fields. However, what I am actually after is the function f. Is it possible to use the standard algorithms implemented in the PDE toolbox to this end, focusing purely on the biharmonic equation and forgetting about any context in linear elasticity theory?
>
> Thanks!

Subject: 4th-order PDEs with PDE toolbox

From: Bill Greene

Date: 6 Feb, 2012 19:26:10

Message: 4 of 4

Hi Chris,

>
> I want to solve the biharmonic equation
>
> nabla^4 f = 0
>

Yes, this can be done with PDE Toolbox.
The main trick is that you have to replace
your 4'th order PDE with two 2'nd order
PDEs that PDE Toolbox can handle.
Then you have to translate the 4'th
order boundary conditions into 2'nd
order ones; this is not straightforward,
in general.

I have recently created a simple of example
for a clamped, square plate with a pressure load
that might be helpful to you. See this link:
http://www.mathworks.com/matlabcentral/fileexchange/34870

Regards,

Bill

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