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Stress and vibration analyses of anisotropic shells of revolution
Author(s) -
Noor Ahmed K.,
Peters Jeanne M.
Publication year - 1988
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.1620260510
Subject(s) - fourier series , stress resultants , fourier transform , finite element method , shell (structure) , vibration , harmonics , mathematical analysis , discretization , mathematics , anisotropy , trigonometric series , geometry , physics , structural engineering , materials science , engineering , acoustics , optics , composite material , quantum mechanics , voltage
An efficient computational strategy is presented for reducing the cost of the stress and free vibration analyses of laminated anisotropic shells of revolution. The analytical formulation is based on a form of the Sanders‐Budiansky shell theory including the effects of both the transverse shear deformation and the laminated anisotropic material response. The fundamental unknowns consist of the eight strain components, the eight stress resultants and the five generalized displacements of the shell. Each of the shell variables is expressed in terms of trigonometric functions (Fourier series) in the circumferential co‐ordinate, and a three‐field mixed finite element model is used for the discretization in the meridional direction. The shell response associated with a range of Fourier harmonics is approximated by a linear combination of a few global approximation vectors, which are generated at a particular value of the Fourier harmonic, within that range. The full equations of the finite element model are solved for only a single Fourier harmonic, and the response corresponding to the other Fourier harmonics is generated using a reduced system of equations with considerably fewer degrees of freedom.