How do I impose dirchlet boundary conditions in a matlab code for a finite difference solution to the kirchhoff's plate equation?

I am trying to write a finite difference code in Matlab to solve the Kirchhoff's plate equation. So far, I have been able to generate the biharmonic/bilaplacian operator matrix. However, I am struggling with how to impose the boundary condition. I would be glad is someone can help explain how to achieve this.

Answer 1

[Zoltán Csáti]

If I know well, Kirchhoff's model include Neumann boundary conditions too that must also be fulfilled. I would use the boundary points for prescribing the Dirichlet boundary conditions and the neighbouring points inwards to approximate the Neumann ones. So you will sacrifice those points in the approximation of the differential operator.