Geometric Nonlinear Analysis of Structures with Qualified External Stiffness Matrix
Date Issued
2011
Date
2011
Author(s)
Cheng, Min-Chung
Abstract
A geometrically nonlinear analysis can be basically decomposed into two phases: the predictor phase and corrector phase. How to calculate the member forces for each incremental step in the corrector phase is a critical issue, as it controls the accuracy of the solution. In many previous works, the member forces are obtained by a well-known method based on the natural deformations. In calculating the natural deformations, the axial displacement of each element is modified as an approximation of the real axial extensions. This method is effective in the analysis of structures with beam elements, but it cannot be readily applied to other types of elements for which the natural deformations are difficult to define. On the other hand, in some previous studies, the concept of external stiffness matrix has also been used to eliminate the influence of rigid body motions in calculating the member forces. This concept has the advantage that the natural displacements need not be directly computed, but in comparison with the former method, it is not accurate enough, which may lead to slow convergence for some problems. Therefore, the objective of this thesis is to improve the external stiffness matrix method and to extend its practicability by deriving physically qualified external stiffness matrices.Based on various natural and rigid body modes presented previously for the two-dimensional and three-dimensional beams, along with the properties of the external stiffness matrix, this thesis will first derive qualified external stiffness matrices, which will then be modified through incorporation of the moments induced by the rotation of the beam in the three-dimensional space. Next, the formula for calculating the member forces incorporating the concept of external stiffness matrix will be derived. Finally, through the numerical verifications, it is demonstrated that the member force formula presented herein is feasible and can be generally used in the geometrically nonlinear analysis of structures.
Subjects
geometrically nonlinear analysis
natural deformations
external stiffness matrix
rigid body motions
corrector
Type
thesis
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