Interpolation polynomial -- 2

I need a polynomial of ( x,y) based on 2D Pascal triangle to describe a column vector of Ritz approximation functions that satisfy the boundary conditions of the problem. problem is thin plate (submitted to classical laminate theory) of width b and length l and thickness t with its X axis coinside with its length and Y axis coinside with its width. boundary conditions are : 1- for the side of Y= 0 ....... hinged support 2- for the side of Y = b ........ fixed support 3- for the side of X=0 .......... fixed support 4- for the side of X= l ........... free side i.e u_o (x,y,t)= {a_1 (x,y)}^T {q_1 (t)} v_o (x,y,t)= {a_2 (x,y)}^T {q_2 (t)} w_o (x,y,t)= {a_3 (x,y)}^T {q_3 (t)} i need a_i(x,y) where i =1,2,3 and u(x,y,z,t)= u_0 (x,y,t)-z (∂w_o (x,y,t))/∂x v(x,y,z,t)= v_0 (x,y,t)-z (∂w_o (x,y,t))/∂y w(x,y,z,t)= w_0 (x,y,t) I need not more than 4 terms for each of u,v and w it has to fulfil the initial 10 modes of the shown plate in the modal analysis compared to numerical Ansys solution for the same problem i will set milestone (half the budget) at which the work is handed over , then after check of the validity of model the rest of budget will be released