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In this paper an efficient method is developed for the formation of null bases of finite element models (FEMs) composed of rectangular and triangular plane stress and plane strain elements, corresponding to highly sparse and banded flexibility matrices. This is achieved by associating special graphs to the finite element models and selecting approp...
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Citations
... In another contribution by Kaveh and Ebrahimi (2012), an efficient method is developed for forming null bases of finite element models composed of rectangular and triangular plane stress and plane strain elements. The method involves associating special graphs with the finite element models and selecting appropriate subgraphs for forming localized self-stress systems. ...
This research introduces an innovative mixed finite element methodology for analysing functionally graded plates (FGP). The new method employs an isoparametric formulation in the natural (ξ, η) plane and integrates an exponential material gradient and a constant Poisson ratio for the FGP, providing a new perspective on FGP analysis. The effectiveness of this new method is demonstrated by employing numerical modelling in a representative example involving an FGP under tension. Results are comprehensively compared with numerical and analytical solutions found in the existing literature to establish validity and accuracy. The findings reveal that the proposed methodology exhibits superior computational efficiency and accuracy in evaluating the tension behaviour of FGP, with a particular focus on the impact of a reduced number of degrees of freedom. The outcomes of this study contribute to advancing the analysis and design of FGP for various applications.
In this chapter force method finite element models comprising of low order elements are presented.
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. © Springer International Publishing Switzerland 2014. All rights are reserved.
