| Summary: | 碩士 === 國立中興大學 === 機械工程學系所 === 104 === The objective of this thesis is to formulate a nonlinear finite element model for analysis of frame made up of composite laminated beams which have circular cross sections. In this model the nonlinear strain-displacement relations of beam are considered. To solve the nonlinear finite element equations, two numerical methods are adopted. One is Newton- Raphson method, which is used to solve the lateral deformation as well as the postbuckling deformation of the frame; the other is eigenvector iteration method, which is used specifically for the postbuckling analysis.
In this model, the beam is allowed to have axial and lateral flexural displacement, as well as the transverse shear and torsion deformation. To derive the finite element model of the frame structure, first, the element’s stiffness matrix, geometric stiffness matrix, and tangential stiffness matrix of beam are obtained. Then, the coordinate transformation matrices are used to transform the above element’s matrices, which are defined in the local coordinates of beam, to the ones referring to the global reference coordinates. These matrices are assembled to yield the finite element equilibrium equations of the frame structure. The equations are then used to investigate the nonlinear displacement responses of the frame structure by employing the two numerical methods mentioned.
In the numerical examples, planar and space frames made of isotropic as well as composite materials are treated. The buckling loads and modes, and the lateral and postbuckling displacements of frames are studied. First, the buckling load and buckling modes of the frame made of isotropic materials are analyzed and compared with those obtained from ANSYS. The differences in buckling loads of the first ten bucking modes between them are less than 7.2 percent and the corresponding mode shapes look quite similar. In the nonlinear analyses, the displacements of isotropic steel frames and two types of composite material frames which consist of laminated beams having different stacking angles are compared. The results indicate that the stacking angles have a significant influence on the nonlinear displacement responses. The steel frames are found to have the highest nonlinear stiffness characteristics, while for complex material frames whose bars having stacking angles [〖90〗^°/〖45〗^°/〖-45〗^°/0_6^°/〖90〗^°] have stronger geometrically nonlinear characteristics than those of [0_10^o] which may be caused by the coupling of nonlinear displacement variables due to the lamination angles. Finally, the two numerical methods used in the post- buckling displacement analyses are found in good agreement if the frame subjected to only axial loads will not have significant lateral displacements. If significant lateral displacements do occur when the frame is subjected only to axial load, the Newton-Raphson method is a better choice of the two.
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