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

R. M. Kirby, Z. Yosibash*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

31 Scopus citations


The von-Kármán non-linear, dynamic, partial differential system over rectangular domains is solved by the Chebyshev-collocation method in space and the implicit Newmark-β time marching scheme in time. In the Newmark-β 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-Kármán system, demonstrating that it is justified. A comparison of our steady-state von-Kármán 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.

Original languageEnglish
Pages (from-to)575-599
Number of pages25
JournalComputer Methods in Applied Mechanics and Engineering
Issue number6-8
StatePublished - 13 Feb 2004
Externally publishedYes


FundersFunder number
Air Force Office of Scientific ResearchF49620-01-1-0035


    • Modeling errors
    • Pseudo-spectral methods
    • von-Kármán plate model


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