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A Chebyshev collocation multidomain method to solve the Reissner–Mindlin equations for the transient response of an anisotropic plate subjected to impact
Author(s) -
Kjellmert Bo
Publication year - 1997
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/(sici)1097-0207(19971030)40:20<3689::aid-nme233>3.0.co;2-e
Subject(s) - collocation (remote sensing) , mathematics , discretization , collocation method , orthogonal collocation , mathematical analysis , chebyshev polynomials , chebyshev filter , jacobian matrix and determinant , geometry , differential equation , computer science , ordinary differential equation , machine learning
The transient response of an anisotropic rectangular plate subjected to impact is described through a Chebyshev collocation multidomain discretization of the Reissner–Mindlin plate equations. The trapezoidal rule is used for time‐integration. The spatial collocation derivative operators are represented by matrices, and the subdomains are patched by natural and essential conditions. At each time level the resulting governing matrix equation is reduced by two consecutive block Gaussian eliminations, so that an equation for the variables at the subdomain corners has to be solved. Back‐substitution gives the variables at all other collocation points. The time history as represented by computed contour plots has been compared with analytical results and with photos produced by holographic interferometry. The agreements are satisfactory. © 1997 John Wiley & Sons, Ltd.