Computational Structural Analysis and Finite Element Methods - Kaveh, A.

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Résumé :
Graph theory gained initial prominence in science and engineering through its strong links with matrix algebra and computer science. Moreover, the structure of the mathematics is well suited to that of engineering problems in analysis and design. The methods of analysis in this book employ matrix algebra, graph theory and meta-heuristic algorithms, which are ideally suited for modern computational mechanics. Efficient methods are presented that lead to highly sparse and banded structural matrices. The main features of the book include: application of graph theory for efficient analysis; extension of the force method to finite element analysis; application of meta-heuristic algorithms to ordering and decomposition (sparse matrix technology); efficient use of symmetry and regularity in the force method; and simultaneous analysis and design of structures.

Sommaire:
Basic concepts of structural analysis and graph theory.- Optimal force method of structural analysis.- Optimal displacement method of structural analysis.- Ordering for optimal patterns of structural matrices: graph theory methods.- Ordering for optimal patterns of structural matrices: algebraic graph theory and meta-heuristic methods.- Optimal force method for FEMs: low order elements.- Optimal force method for FEMs: high order elements.- Decomposition for parallel computing: graph theory methods.- Analysis of regular structures using graph products.- Simultaneous analysis, design and optimization of structures using force method and supervised CSS.