The analysis of isotropic and laminated rectangular plates including geometrical non-linearity using the P-version finite element method
The analysis of isotropic and laminated rectangular plates including geometrical non-linearity using the P-version finite element method
The 3-D equilibrium equations are used to determine the transverse shear stresses of laminated composite plates which are first analysed using a commercial FE package (ANSYS) based on the first-order shear deformation theory (FSDT). The results are compared with 3-D exact elasticity solutions. The application of the 3-D equilibrium equations to FEM produces very good transverse shear stress prediction for thin and medium thick (h/a≤0.1) symmetrically laminated plates. A two-phase procedure is combined with the FEM using re-analysis, in which limited ability of the method in improving the accuracy of the transverse shear stress prediction has been found.
A new hierarchical finite element method (HFEM) is developed for laminated composite rectangular plates including geometrical non-linearity. The application of very high order polynomials as displacement functions makes it possible to model a whole rectangular plate as only one element(super-element). The difficulty in integrating the very high order polynomials needed to form the stiffness and mass matrices, is overcome by applying symbolic manipulation which yields the exact values of the integration. The von Karman geometrically nonlinear strain-displacement relationships are used. The transverse shear stresses are neglected for thin plates. In-plane displacements are included in the model.
The HFEM is applied to linear free and forced vibration analysis, and to static geometrically non-linear analysis of isotropic and laminated rectangular plates. Very good numerical properties (convergence, stability, numerical efficiency et al) have been shown. In the application of the HFEM to geometrically nonlinear free vibration analysis of isotropic and laminated rectangular plates, the harmonic balance method is employed. The influence of in-plane displacements on static and dynamic nonlinear behaviour of rectangular plates is studied. The applicability of Berger's hypothesis to isotropic and laminated rectangular plates is discussed.
University of Southampton
1993
Han, Wanmin
(1993)
The analysis of isotropic and laminated rectangular plates including geometrical non-linearity using the P-version finite element method.
University of Southampton, Doctoral Thesis.
Record type:
Thesis
(Doctoral)
Abstract
The 3-D equilibrium equations are used to determine the transverse shear stresses of laminated composite plates which are first analysed using a commercial FE package (ANSYS) based on the first-order shear deformation theory (FSDT). The results are compared with 3-D exact elasticity solutions. The application of the 3-D equilibrium equations to FEM produces very good transverse shear stress prediction for thin and medium thick (h/a≤0.1) symmetrically laminated plates. A two-phase procedure is combined with the FEM using re-analysis, in which limited ability of the method in improving the accuracy of the transverse shear stress prediction has been found.
A new hierarchical finite element method (HFEM) is developed for laminated composite rectangular plates including geometrical non-linearity. The application of very high order polynomials as displacement functions makes it possible to model a whole rectangular plate as only one element(super-element). The difficulty in integrating the very high order polynomials needed to form the stiffness and mass matrices, is overcome by applying symbolic manipulation which yields the exact values of the integration. The von Karman geometrically nonlinear strain-displacement relationships are used. The transverse shear stresses are neglected for thin plates. In-plane displacements are included in the model.
The HFEM is applied to linear free and forced vibration analysis, and to static geometrically non-linear analysis of isotropic and laminated rectangular plates. Very good numerical properties (convergence, stability, numerical efficiency et al) have been shown. In the application of the HFEM to geometrically nonlinear free vibration analysis of isotropic and laminated rectangular plates, the harmonic balance method is employed. The influence of in-plane displacements on static and dynamic nonlinear behaviour of rectangular plates is studied. The applicability of Berger's hypothesis to isotropic and laminated rectangular plates is discussed.
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Published date: 1993
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Local EPrints ID: 462405
URI: http://eprints.soton.ac.uk/id/eprint/462405
PURE UUID: 35a16fed-1675-4229-a29e-1966fcc98967
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Date deposited: 04 Jul 2022 19:07
Last modified: 04 Jul 2022 19:07
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Author:
Wanmin Han
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