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Mixed Galerkin and least-squares formulations for isogeometric analysis. / CHENNAKESAVA KADAPA

Swansea University Author: CHENNAKESAVA, KADAPA

Abstract

This work is concerned with the use of isogeometric analysis based on Non- Uniform Rational B-Splines (NURBS) to develop efficient and robust numerical techniques to deal with the problems of incompressibility in the fields of solid and fluid mechanics. Towards this, two types of formulations, mixed...

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Published: 2014
Institution: Swansea University
Degree level: Doctoral
Degree name: Ph.D
URI: https://cronfa.swan.ac.uk/Record/cronfa42221
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spelling 2020-09-03T09:07:53.7188187 v2 42221 2018-08-02 Mixed Galerkin and least-squares formulations for isogeometric analysis. 352463b2495c26eee144f0df68443825 CHENNAKESAVA KADAPA CHENNAKESAVA KADAPA true false 2018-08-02 This work is concerned with the use of isogeometric analysis based on Non- Uniform Rational B-Splines (NURBS) to develop efficient and robust numerical techniques to deal with the problems of incompressibility in the fields of solid and fluid mechanics. Towards this, two types of formulations, mixed Galerkin and least-squares, are studied. During the first phase of this work, mixed Galerkin formulations, in the context of isogeometric analysis, are presented. Two-field and three-field mixed variational formulations - in both small and large strains - are presented to obtain accurate numerical solutions for the problems modelled with nearly incompressible and elasto-plastic materials. The equivalence of the two mixed formulations, for the considered material models, is derived; and the computational advantages of using two-field formulations are illustrated. Performance of these formulations is assessed by studying several benchmark examples. The ability of the mixed methods, to accurately compute limit loads for problems involving elastoplastic material models; and to deal with volumetric locking, shear locking and severe mesh distortions in finite strains, is illustrated. Later, finite element formulations are developed by combining least-squares and isogeometric analysis in order to extract the best of both. Least-squares finite element methods (LSFEMs) based on the use of governing differential equations directly - without the need to reduce them to equivalent lower-order systems - are developed for compressible and nearly incompressible elasticity in both the small and finite strain regimes; and incompressible Navier-Stokes. The merits of using Gauss-Newton scheme instead of Newton-Raphson method to solve the underlying nonlinear equations are presented. The performance of the proposed LSFEMs is demonstrated with several benchmark examples from the literature. Advantages of using higher-order NURBS in obtaining optimal convergence rates for non-norm-equivalent LSFEMs; and the robustness of LSFEMs, for Navier-Stokes, in obtaining accurate numerical solutions without the need to incorporate any artificial stabilisation techniques, are demonstrated. E-Thesis Applied mathematics.;Mechanics. 31 12 2014 2014-12-31 COLLEGE NANME COLLEGE CODE Swansea University Doctoral Ph.D 2020-09-03T09:07:53.7188187 2018-08-02T16:24:28.4797839 College of Engineering Engineering CHENNAKESAVA KADAPA 1 0042221-02082018162437.pdf 10797923.pdf 2018-08-02T16:24:37.5900000 Output 13443761 application/pdf E-Thesis true 2018-08-02T00:00:00.0000000 false
title Mixed Galerkin and least-squares formulations for isogeometric analysis.
spellingShingle Mixed Galerkin and least-squares formulations for isogeometric analysis.
CHENNAKESAVA, KADAPA
title_short Mixed Galerkin and least-squares formulations for isogeometric analysis.
title_full Mixed Galerkin and least-squares formulations for isogeometric analysis.
title_fullStr Mixed Galerkin and least-squares formulations for isogeometric analysis.
title_full_unstemmed Mixed Galerkin and least-squares formulations for isogeometric analysis.
title_sort Mixed Galerkin and least-squares formulations for isogeometric analysis.
author_id_str_mv 352463b2495c26eee144f0df68443825
author_id_fullname_str_mv 352463b2495c26eee144f0df68443825_***_CHENNAKESAVA, KADAPA
author CHENNAKESAVA, KADAPA
author2 CHENNAKESAVA KADAPA
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hierarchy_parent_title College of Engineering
department_str Engineering{{{_:::_}}}College of Engineering{{{_:::_}}}Engineering
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description This work is concerned with the use of isogeometric analysis based on Non- Uniform Rational B-Splines (NURBS) to develop efficient and robust numerical techniques to deal with the problems of incompressibility in the fields of solid and fluid mechanics. Towards this, two types of formulations, mixed Galerkin and least-squares, are studied. During the first phase of this work, mixed Galerkin formulations, in the context of isogeometric analysis, are presented. Two-field and three-field mixed variational formulations - in both small and large strains - are presented to obtain accurate numerical solutions for the problems modelled with nearly incompressible and elasto-plastic materials. The equivalence of the two mixed formulations, for the considered material models, is derived; and the computational advantages of using two-field formulations are illustrated. Performance of these formulations is assessed by studying several benchmark examples. The ability of the mixed methods, to accurately compute limit loads for problems involving elastoplastic material models; and to deal with volumetric locking, shear locking and severe mesh distortions in finite strains, is illustrated. Later, finite element formulations are developed by combining least-squares and isogeometric analysis in order to extract the best of both. Least-squares finite element methods (LSFEMs) based on the use of governing differential equations directly - without the need to reduce them to equivalent lower-order systems - are developed for compressible and nearly incompressible elasticity in both the small and finite strain regimes; and incompressible Navier-Stokes. The merits of using Gauss-Newton scheme instead of Newton-Raphson method to solve the underlying nonlinear equations are presented. The performance of the proposed LSFEMs is demonstrated with several benchmark examples from the literature. Advantages of using higher-order NURBS in obtaining optimal convergence rates for non-norm-equivalent LSFEMs; and the robustness of LSFEMs, for Navier-Stokes, in obtaining accurate numerical solutions without the need to incorporate any artificial stabilisation techniques, are demonstrated.
published_date 2014-12-31T04:02:09Z
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score 10.774176