SetAttributes[{a, b, q}, Constant];
eqn = {Laplacian[w[x, y], {x, y}] == v[x, y],
Laplacian[v[x, y], {x, y}] == 7};
bcs = {w[0, y] == 0, w[x, 20] == 0, w[10, y] == 0, w[x, 0] == 0,
Derivative[1, 0][w][0, y] == 0, v[x, 20] == 0,
Derivative[1, 0][w][10, y] == 0, v[x, 0] == 0};
ufun = NDSolveValue[{eqn, bcs}, w, {x, 0, 10}, {y, 0, 20}]
NDSolveValue::fembdnl: The dependent variable in (w^(1,0))[0,y]==0 in the boundary condition DirichletCondition[(w^(1,0))[0,y]==0,x==0.] needs to be linear.
怎么搞成线性的啊

Neumann边界条件用NeumannValue指定，而且你这个自然的可以不指定。
然后就是你Dirichlet边界条件和Neumann的冲突。

SetAttributes[{a, b, q}, Constant];也没有你想象中的那种作用，请不要想当然。
然后，对于双调和方程，NDSolve目前没有完备的支持，很多时候求解需要费点功夫，参看
《2D inhomogeneous biharmonic equation》
https://mathematica.stackexchange.com/q/135893/1871
《2D inhomogeneous biharmonic equation with wedged edge》
mathematica.stackexchange.com/q/155820/1871

恩 我在做板的非线性弯曲 不用Nsolve自己编程序呗 找个方法学