The Thin Plate Problem with clamped or simply supported boundary is considered. The current research is devoted to construction of approximated solution of the Thin Shell Problem in the case, when initial planar domain is described by quadrilateral mesh without any special regularity assumptions.

C1 (G1)-smooth solution is found by FEM, based on quartic or quintic Bezier representation of patches. Boundary of domaincan be also interpolated by G1-smooth curve.

Left: Initial planar mesh for the Thin Plate Problem.
Right: Error distribution of the numerical computation of surface with clamped boundary under uniform load.

Resulting smooth surface.