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

Logah Perumal; Wei Hao Koh

doi:10.1016/j.mex.2023.102027

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

MethodsX. 2023 Jan 24:10:102027. doi: 10.1016/j.mex.2023.102027. eCollection 2023.

Authors

Logah Perumal¹, Wei Hao Koh¹

Affiliation

¹ Faculty of Engineering and Technology, Multimedia University, Jalan Ayer Keroh Lama, 75450 Melaka, Malaysia.

Abstract

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 (c₁, c₂ , and c₃ ).•The technique is found to be capable of producing alternate or similar forms for the test functions. Performances of the resultant (or final) formulations are shown by solving three benchmark problems. Additionally, a new technique to formulate strain-based triangular transition elements (denoted as SB-TTE) is introduced.•The new technique introduces another node (the fourth node) at one of the sides of a strain-based triangular element (mid-node, which is needed for the quadtree-based triangular mesh generation) without adding a degree of freedom.

Keywords: 1. Use of corrective coefficients for the formulation of strain-based finite elements. 2. Strain-based triangular transition element (SB-TTE).; Compatibility and equilibrium; Corrective coefficients; Quadtree-based triangular mesh; Strain-based elements; Transition element; Virtual node method.