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Title: Plasticity and Large Deformation Problems by the Finite Element Method.
Author: Nayak, G. C.
ISNI:       0000 0001 3440 1513
Awarding Body: University College Swansea
Current Institution: Swansea University
Date of Award: 1971
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An attempt has been made to develop efficient and versatile displacement type finite element computer programs which contain general constitutive relations, a family of isoparametric elements, a variety of nonlinear solution algorithms and systematic convergence tests in order to break some of the 'non-linear and cost barriers'. A unified finite element formulation for geometrically and physically nonlinear problems in matrix form has been developed and the isoparametric elements are shown to be highly versatile in both Lagrangian and Eulerian forms. Several alternative nonlinear solution algorithms have been studied and amongst them the newly developed 'alpha constant stiffness method' of accelerated iteration has been shown to possess computer economy. This new method has enabled the first solutions of 'strain softening and non-associated flow laws' to be obtained. Indeed the method has been extended for cracking and large deformation problems. The 'residual force' calculated from direct numerical integration has been used to check the equilibrium at every stage. This routine has now become an essential ingredient of all the nonlinear solution algorithms. The explicit forms of several elastic and elasticplastic stress-strain relationships for small and large strain cases have been presented. A useful form of an angular invariant has enabled several plasticity forms such as Tresca, Von Mises, Mohr-Coulomb, Drucker-Prager and several other yield and potential functions to be included into one program. The elastic-plastic relationships are also generalised to include non-associated flow rule and kinematic hardening rule. S-2 Comparative studies of various solution algorithms, element types, plasticity forms and reduced integration order have been made. For many cases parabolic elements with reduced 2-point integration rule give optimum results. In addition the preliminary investigations of complex material behaviour and a floating airport study based on the analysis of axisymmetric plate on elastic foundation are given. As an off-shoot an attempt has been made to find the order of magnitude of limiting value of deflection for von Karman plate theory. The finite deformation theory expressions which are usually available in tensor notation are redexived in matrix form. Finally the thesis reflects the power of numerical integration techniques and isoparametric elements for nonlinear analysis.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available