# Mathematical and computational aspects of the enhanced strain finite element method

 dc.contributor.advisor Reddy, B Daya en_ZA dc.contributor.author Arunakirinathar, Kanagaratnam en_ZA dc.date.accessioned 2015-12-28T06:03:33Z dc.date.available 2015-12-28T06:03:33Z dc.date.issued 1995 en_ZA dc.identifier.citation Arunakirinathar, K. 1995. Mathematical and computational aspects of the enhanced strain finite element method. University of Cape Town. en_ZA dc.identifier.uri http://hdl.handle.net/11427/15964 dc.description Bibliography: pages 102-107. en_ZA dc.description.abstract This thesis deals with further investigations of the enhanced strain finite element method, with particular attention given to the analysis of the method for isoparametric elements. It is shown that the results established earlier by B D Reddy and J C Simo for affine-equivalent meshes carry over to the case of isoparameric elements. That is, the method is stable and convergent provided that a set of three conditions are met, and convergence is at the same rate as in the standard method. The three conditions differ in some respects, though, from their counterparts for the affine case. A procedure for recovering the stress is shown to lead to an approximate stress which converges at the optimal rate to the actual stress. The concept of the equivalent parallelogram associated with a quadrilateral is introduced. The quadrilateral may be regarded as a perturbation of this parallelogram, which is most conveniently described by making use of properties of the isoparametric map which defines the quadrilateral. The equivalent parallelogram generates a natural means of defining a regular family of quadrilaterals; this definition is used together with other properties to obtain in a relatively simple manner estimates, in appropriate seminorms or norms, of the isoparametric map and it's Jacobian, for use in the determination of finite element interpolation error estimates, with regard to computations, a new basis for enhanced strains is introduced, and various examples have been tested. The results obtained are compared with those obtained using other bases, and with those found from an assumed stress approach. Favourable comparisons are obtained in most cases, with the present basis exhibiting an improvement over existing bases. Convergence of the finite element results are verified; it is observed numerically that the improvement of results due to enhancement is as a result of a smaller constant appearing in the error estimates. en_ZA dc.language.iso eng en_ZA dc.subject.other Mathematics and Applied Mathematics en_ZA dc.title Mathematical and computational aspects of the enhanced strain finite element method en_ZA dc.type Thesis / Dissertation en_ZA uct.type.publication Research en_ZA uct.type.resource Thesis en_ZA dc.publisher.institution University of Cape Town dc.publisher.faculty Faculty of Science en_ZA dc.publisher.department Department of Mathematics and Applied Mathematics en_ZA dc.type.qualificationlevel Doctoral en_ZA dc.type.qualificationname PhD en_ZA uct.type.filetype Text uct.type.filetype Image
﻿