A novel hybrid shell element formulation (QUAD+ and TRIA+): A benchmarking and comparative study

This paper introduces a novel hybrid finite element (FE) formulation of shell element to enable assembly process simulation of compliant sheet-metal parts with higher efficiency and flexibility. Efficiency was achieved by developing both new hybrid quadrilateral and triangular elements. Quadrilateral element (QUAD+) was formulated by combining area geometric quadrilateral 6 (AGQ6) nodes and mixed interpolated tensorial components (MITC) to model membrane and bending/shear component respectively. Triangular element (TRIA+) was formulated by merging assumed natural deviatoric strain (ANDES) for membrane and MITC for bending/shear component. Flexibility was addressed by developing an open-source C++ code, enhanced by the OpenMP interface for multiprocessing programming. Tests and benchmarks were compiled and executed within Matlab using the MEX API interface. Extensive benchmark studies were accomplished to evaluate the performance of the proposed hybrid formulation and the shell formulations used in three FEM packages - ABAQUS, ANSYS and COMSOL- under static linear elastic condition with small strain assumption. It was observed that the proposed QUAD+ and TRIA+ elements performed better amongst the FE packages, especially when there was in-plane mesh distortion, with errors below 3%. It was also identified that the best efficiency is obtained by adopting dominant QUAD+ elements compared to the TRIA+ when working on complex geometries. This paper also contributes to present a wide set of benchmark studies required to verify new release of FE packages using shell element or evaluate the performance of new shell formulations.