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A spectral method to solve the equations of linear elasticity for the transient response of a tube subjected to impact
Author(s) -
Kjellmert Bo
Publication year - 1999
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(19990720)45:8<1115::aid-nme623>3.0.co;2-j
Subject(s) - galerkin method , fourier transform , mathematics , elasticity (physics) , mathematical analysis , collocation method , finite element method , physics , differential equation , ordinary differential equation , thermodynamics
The transient response of a tube subjected to impact is described through Fourier–Galerkin and Chebyshev collocation multidomain discretizations of the equations of linear elasticity. The trapezoidal rule is used for time integration. For each Fourier mode 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 complex Fourier coefficients at the subdomain corners has to be solved. Back‐substitution gives the coefficients at all other collocation points. An inverse discrete Fourier transform generates, at optional time levels, the three components of the displacement field. Through this method the long‐term evolution of the field may be calculated, provided the impact time is long enough. The time history as represented by computed contour plots has been compared with photos produced by holographic interferometry. The agreements are satisfactory. Copyright © 1999 John Wiley & Sons, Ltd.