TY - JOUR
T1 - Solution of von-Kármán dynamic non-linear plate equations using a pseudo-spectral method
AU - Kirby, R. M.
AU - Yosibash, Z.
N1 - Funding Information:
The second author gratefully acknowledges the support of this work by the Air Force Office of Scientific Research (Computational Mathematics Program) under grant number F49620-01-1-0035.
PY - 2004/2/13
Y1 - 2004/2/13
N2 - 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.
AB - 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.
KW - Modeling errors
KW - Pseudo-spectral methods
KW - von-Kármán plate model
UR - http://www.scopus.com/inward/record.url?scp=0442297717&partnerID=8YFLogxK
U2 - 10.1016/j.cma.2003.10.013
DO - 10.1016/j.cma.2003.10.013
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AN - SCOPUS:0442297717
SN - 0045-7825
VL - 193
SP - 575
EP - 599
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
IS - 6-8
ER -