[ D_{11} \frac{\partial^4 w}{\partial x^4} + 2(D_{12}+2D_{66}) \frac{\partial^4 w}{\partial x^2 \partial y^2} + D_{22} \frac{\partial^4 w}{\partial y^4} = q(x,y) ]
Similarly for ( \partial^4 w/\partial y^4 ) and mixed derivative: Composite Plate Bending Analysis With Matlab Code
Boundary conditions (simply supported): [ w = 0,\quad M_{xx}=0 \Rightarrow \frac{\partial^2 w}{\partial x^2}=0 \text{ on } x=0,a ] (same for y-direction) a ] (same for y-direction)