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Nonlinear static and dynamic analysis of circular plates and shallow spherical shells using the collocation method
Author(s) -
Nath Y.,
Dumir P. C.,
Bhatiaf R. S.
Publication year - 1985
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620210314
Subject(s) - collocation (remote sensing) , discretization , nonlinear system , buckling , mathematics , polynomial , chebyshev polynomials , orthogonal collocation , mathematical analysis , collocation method , geometry , structural engineering , engineering , computer science , physics , ordinary differential equation , quantum mechanics , machine learning , differential equation
The present work investigates the efficacy and applicability of interior global orthogonal point collocation method to the axisymmetric nonlinear analysis of elastic circular plates and shallow spherical shells subjected to uniformly distributed transverse load. Spacewise discretisation has been carried out using a polynomial expansion with the zeros of a Chebyshev polynomial as collocation points. Timewise integration has been carried out with Newmark k ‐β scheme corresponding to average acceleration method. The static response and snap‐through buckling results, as well as, the dynamic response and dynamic buckling results under a uniformly distributed step load have been obtained and found to agree closely with the available results.