Hermitian numerical manifold method for large deflection of irregular Föppl-von Kármán plates

Abstract

We proposed the Hermitian manifold numerical method (HNMM) fitted for finite strain analysis of thin plates with irregular domains. The large deflection of elastic thin plates is generally characterized by Föppl-von Kármán (FvK) equations, coupled with nonlinear fourth-order partial differential equations. The corresponding primal variational formulation requires the solution function to be globally C1 continuous but piecewise C2 continuous (namely H2 regular). Hermitian numerical manifold method (HNMM) can easily construct an approximation to solutions that satisfy the H2 regular requirements with structured meshes. Furthermore, those classical plate elements in finite element history can be embedded in the framework of HNMM and be more flexible and adaptable to solve plates with irregular domains. Thus, HNMM is formulated based on the Föppl-von Kármán (FvK) model using the dual cover system and a triplet attributes group on the physical patches. The numerical results demonstrate the accuracy of HNMM in large deflection of Föppl-von Kármán plate with complex domain shape.