Unsymmetric finite elements for mesh-distortion tolerance performance

• Main Author: Ooi, Ean Tat
• Other Authors: Yeo Joon Hock
• Format: Theses and Dissertations
• Published: 2008
• Subjects: DRNTU::Engineering::Manufacturing
• Online Access: https://hdl.handle.net/10356/5254
• Institution: Nanyang Technological University

Although the finite element method is a mature field of research and its success in computational mechanics is widely recognized, there is still scope for further improvements. One such area is the development of mesh-distortion tolerant elements that yield accurate solutions even in the presence of mesh distortions. This thesis focuses on the development of a recent finite element formulation, called the unsymmetric formulation, which has high mesh-distortion tolerant properties. The scope of this research includes an extension of the unsymmetric formulation to geometric and material nonlinear problems in solid mechanics, a symmetric implementation of the unsymmetric formulation, and an investigation into some of the drawbacks of the unsymmetric formulation and its remedies. To begin with, the concept of the unsymmetric formulation, which is based on a reinterpretation of the virtual work principle, is revisited. The rationale behind the use of compatibility- and completeness-fulfilling shape functions for the virtual and trial displacements, respectively, is reviewed.