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.
[1]
Ahmed K. Noor,et al.
Preconditioned conjugate gradient technique for the analysis of symmetric anisotropic structures
,
1987
.
[2]
David Bushnell.
Analysis of buckling and vibration of ring-stiffened, segmented shells of revolution
,
1970
.
[3]
J. L. Sanders,et al.
NONLINEAR THEORIES FOR THIN SHELLS
,
1963
.
[4]
Joseph Padovan,et al.
Complex numerical integration procedure for static loading of anisotropic shells of revolution
,
1974
.
[5]
A. Greenbaum.
Comparison of splittings used with the conjugate gradient algorithm
,
1979
.
[6]
Richard B. Nelson,et al.
Simplified calculation of eigenvector derivatives
,
1976
.
[7]
Bernard Budiansky,et al.
Notes on nonlinear shell theory.
,
1968
.
[8]
G. A. Cohen,et al.
FASOR—A second generation shell of revolution code
,
1979
.
[9]
Ahmed K. Noor,et al.
Vibration analysis of laminated anisotropic shells of revolution
,
1987
.
[10]
Ahmed K. Noor,et al.
Analysis of Laminated Anisotropic Shells of Revolution
,
1987
.