Techniques for element formulation and quadtree-based triangular mesh generation for strain-based finite elements.

Finite elements are often formulated by imposing sufficient conditions to ensure convergence and good accuracy. This work demonstrates a new technique to impose compatibility and equilibrium conditions for membrane finite elements that are formulated based on the strain approach.•The compatibility and equilibrium conditions are imposed onto the initial formulations (or test functions) by using corrective coefficients ( , and ).

New approaches for Delaunay triangulation and optimisation.

New techniques are presented for Delaunay triangular mesh generation and element optimisation. Sample points for triangulation are generated through mapping (a new approach). These sample points are later triangulated by the conventional Delaunay method.

Analysis of thin plates with holes by using exact geometrical representation within XFEM.

This paper presents analysis of thin plates with holes within the context of XFEM. New integration techniques are developed for exact geometrical representation of the holes. Numerical and exact integration techniques are presented, with some limitations for the exact integration technique.