FORMULATION FOR SYMMETRICALLY LAMINATED BEAM AND PLATE FINITE ELEMENTS WITH SHEAR DEFORMATION
Abstract
In this thesis, finite element formulations were developed for symmetrically laminated composite beams and plates for static and free vibration analyses. First, a formulation, an efficient solution procedure, a microcomputer program, and a graphics routine for a 12 d.o.f. anisotropic symmetrically laminated beam finite element including the effect of shear deformation was introduced. The emphasis of the formulation and solution procedure was for simplicity, efficiency, and easy implementation on microcomputers. The formulation, solution procedure, and the program have been evaluated by performing a systematic choice of examples; whenever possible, the present solutions were compared with alternative existing solutions. Second, an 18 d.o.f. triangular plate element in bending with anisotropic symmetrically laminated composite materials was formulated. To demonstrate and evaluate the present development, numerical computations on the static, free vibration, and buckling analyses of a series of anisotropic symmetrically laminated plate problems have been performed using a microcomputer. Further testing and evaluation of the previously formulated beam element for more cases were conducted and the results compared with those obtained using the present plate elements. The comparison indicated that both types of element formulations were sufficiently simple and accurate, and that the numerical methods were efficient for microcomputers. Finally, an approach was presented in the formulation of a 36 d.o.f. symmetrically laminated composite triangular plate element including the effect of shear deformation for free vibration analysis. The strain energy of plates can be expressed as the sum of the flexural and shear strain energies. The total displacement was expressed as the sum of the displacement due to bending and that due to shear deformation. Thus only the displacement due to bending appear in the flexural strain energy and the displacement due to shear deformation appear in the shear strain energy. Numerical results for natural frequencies for a range of different isotropic, orthotropic and anisotropic plates with various thickness-to-length ratios were obtained and compared with various alternative solutions available in the literature to demonstrate the valid range of applicability of this approach for the free vibration of plates with the effect of shear deformation.
Degree
Ph.D.
Subject Area
Aerospace materials
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