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Title: Limit state analysis : adaptive finite element approach to the evaluation at the limit load of a von Mises rigid-plastic material body in plane stress
Author: Cordero, R. A.
Awarding Body: University of Wales Swansea
Current Institution: Swansea University
Date of Award: 2005
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A new approach to the computation of the limit load of a von Mises rigid-plastic material structure modelled in plane stress is assessed. The present aim of the research project is to develop numerical technology based on the finite element method to calculate the limit state of two-dimensional solids in plane stress. The upper bound theorem of limit analysis is implemented by means of a Lagrangian optimization technique solved by the Newton-Raphson method with Line Search. A control parameter to deal with the singularity of the tangent stiffness matrix due to the yielding condition is used along the range of admissible rate of deformations for a rigid-plastic material. The lower bound theorem is then applied by performing a technique to equilibrate the inter-element tractions, kinematically solving a sequence of local problems using the equilibrated tractions as an updated load input, which lets us determine the element-wise contribution to both the upper and lower bounds. An adaptive technique is then implemented, based on the elemental contributions to the difference between the upper bound and the lower bound of the collapse multiplier. Both non-adaptive and adaptive results are evaluated. Results show a good performance of the solution technique, both in comparison with well known plane stress bound values and also in the graphical output obtained in the form of refined regions which describe the occurrence of slip-line patterns and/or localized yielding regions.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available