Create pde as structural dynamic problem

Hello all again:

I have a system of PDEs described as follows:

syms pres

syms u1(x,y,t) u2(x,y,t)

pdeeq = [-laplacian(u1,[x y])+u2; D*laplacian(u2,[x y])+ mass*diff(u1,t,t)-pres];

symcoeffs = pdeCoefficients(pdeeq,[u1,u2],'Symbolic',true);

c2=symcoeffs.c;

And as I need to apply Craig-Bampton reduction method, I was thinking whether it could be possible to define the model as model = createpde("structural","transient-plainstress");

REading the documentation, I think I have understood that the analysis of structural PDE follows the formulas o Linear elacticity : −∇·σ=f.

In that expression the laplacian is not used, so I guess I cannot express my problem in terms that will allow me to use the command: createpde("structural","transient-plainstress");

Is there any way of being able to use that command?

Thanks very much

Answer 1

[Raghav]

Hi Jorge,

The “createpde” function in MATLAB is primarily used for solving linear elasticity problems in the context of structural mechanics. The equation you have provided, which involves the Laplacian operator, does not directly fit into the framework of linear elasticity.

To use the “createpde” function with the "structural" option, you would need to express your problem in terms of the linear elasticity equation, which is of the form:

−∇·σ = f

This equation represents the balance of linear momentum, where σ is the stress tensor and f is the body force.

There are other alternative approaches you can consider for solving your system of PDEs like Finite Element Method.

Please refer to the below documentation:

https://www.mathworks.com/help/pde/ug/basics-of-the-finite-element-method.html

Hope it helps,

Best Regards,

Raghav Bansal

MathWorks Technical Support