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 ).•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.