Solution of von-Karman dynamic non-linear plate equations using a pseudo-spectral method

The von-Karman non-linear, dynamic, partial differential system over rectangular domains is solved by the Chebyshev-collocation method in space and the implicit Newmark-beta time marching scheme in time. In the Newmark-beta scheme, a non-linear fixed point iteration algorithm is employed. We monitor both temporal and spatial discretization errors based on derived analytical solutions, demonstrating highly accurate approximations. We also quantify the influence of a common modeling assumption which neglects the in-plane inertia terms in the full von-Karman system, demonstrating that it is justified. A comparison of our steady-state von-Karman solutions to previous results in the literature and to a three-dimensional high-order finite element analysis is performed, showing an excellent agreement. Other modeling assumptions such as neglecting in-plane quadratic terms in the strain expressions are also addressed. (C) 2003 Elsevier B.V. All rights reserved.