AN EIGEN-FORCE METHOD FOR ANALYSIS OF PLANAR STRUCTURES

Abstract

In this thesis a new computational method for structural analysis, called the Eigen-Force (EF) method is proposed. The study involves fundamental theorems of the EF method and the associated numerical algorithms corresponding to a variety of structural changes. Plane triangular elements are used in this study to discretize a planar continuum structure. The commonly used finite element is based on the Direct Stiffness (DS) method which involves the assembly of stiffness matrix and solving the coupled equilibrium equations. Establishing and solving simultaneous equations is often time consuming and costly, especially when repetitive analyses are required for problems such as non-linear analysis and structural optimisation. In contrast, the proposed EF method which is essentially a force-based approach for structural analysis, avoids solving simultaneous equations and obtains new results due to structural variations by making use of the original results. In a linearly elastic continuum problem, a total approach of the EF method is derived to illustrate the procedure of first analysis and subsequent analyses caused by structural variations which include changes in geometry and topology. Numerical examples are presented to compare the accuracy and computational speed of the EF method with the DS method. The relative speed between these two methods depends primarily on the number of iterations and the number of loaded degrees of freedom. For problems involving non-linear material, an incremental approach of the proposed EF method is formulated to compute the response for an incremental loading. The EF method involves mainly matrix and vector multiplications which can readily be uncoupled. This advantage can be exploited for solving local stress problems. A numerical example of a notched specimen subjected to tension demonstrates the fast computations of the incremental EF method. The material considered is bilinear elasto-plastic. Operation count studies for selected problems are also presented for both the total approach and the incremental approach of the EF method, in comparison with the DS method and a substructural analysis method. From computational point of view, the proposed EF method has a high concurrency and independency. It can thus be easily implemented in a parallel computing environment Two types of parallel processing configurations are implemented on a PC transputer system. Fust, a flood-fill approach is used with minimum effort in the conversion of the sequential code to a parallel code. This approach, however, may not necessarily make effective use of all available transputers. Second, a subdomain decomposition approach involving a user-defined configured is adopted. As shown by a numerical study, this approach is suitable for the EF method and has a high parallel processing efficiency.