| Summary: | The application of extended finite element method (XFEM) formulation for nonlinear structural analyses is presented in this thesis. It aims to capture accurately the elastic response of a beam with an internal pin connection and the elasto-plastic response of a beam or a plate structure at a relatively low computational cost by utilizing the XFEM Timoshenko beam and Reissner-Mindlin plate elements.
In the XFEM formulation for an internal pin, a step function is employed in the enriched rotation approximation field and an absolute level set function is adopted in the enriched translation approximation field. The enrichment function for a plastic hinge is formulated by using Hermite function over the high gradient zone resulted from the plastic hinge. The Hermite function regularizes the discontinuous enrichment function for an internal pin to be a continuous function with a high gradient zone. The strain fields derived from the enriched displacement approximation fields remain continuous inside an element. As the absolute level set function is constructed by standard finite element shape functions, such an enrichment function is also called ‘local’ enrichment function. The local enrichment function is applied in the XFEM plate element in this thesis. However, it is found that such local enrichment function is not suitable for the formulation of a 9-node quadrilateral plate element. Hence a global enrichment function is proposed. The global enrichment function is constructed on the structure level and independent of mesh scheme. Thus, it is applicable for both triangular and quadrilateral plate elements.
Shear locking mitigation method is one of the major concerns in the present XFEM formulation. Two methods, including reduced integration and assumed shear strain methods, are employed to control shear locking in this thesis. In the assumed shear strain method, the mixed interpolation of tensorial components (MITC) technique and the discrete shear gap (DSG) technique are adopted in the XFEM plate elements.
Numerical examples are given for different applications including an internal pin in a beam, a plastic hinge in a beam and a yield line in a plate. The numerical results show that the XFEM formulation is able to capture the discontinuous displacement over an internal pin connection and the locally high gradient displacement resulting from a plastic hinge or a yield line. It is also shown that shear locking can be controlled effectively by the reduced integration method and the assumed shear strain method.
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