Improving the Numerical Efficiency of a High Accuracy Shell Element for Soft Tissues - Abu Sharkh, Abdal Aziz (Université d'Ottawa / University of Ottawa, 2019)
For the finite element (FE) simulation of relatively thin organs under complex dynamic loadings that are relevant in the biomedical engineering field, shell elements, compared to volume elements, have the potential to capture the whole thickness of the organ at once. Shell elements, are also known to feature efficiently large critical time steps, ensuring competitive computational times in dynamic structural analysis projects. As an improvement to the tools available for modelling and analysis, a new general nonlinear thick continuum-based (CB) shell FE embedded in an updated Lagrangian formulation and an explicit time integration scheme was recently developed. It can account for irregular and complex geometries, and hyper-elastic, large, nearly incompressible anisotropic 3D deformations characteristic of soft tissues. The original proof of concept was developed in MATLAB, which despite known advantages, is very slow. As a result, computational times, even for simple problems, have not been competitive. Therefore, the present work focused on re-writing the code in an efficient programming language with execution speed in mind in order to compete with the available elements which, in spite of having inferior capabilities, have better running times. In addition, a programming algorithm was needed to improve running time. Once it was implemented, the running time was reduced in half on a benchmark problem. Optimization was then exploited to introduce workarounds and design improvements that reduced running time further to 95% of its original value. The new version of the code was implemented in C++ and reached the goal of reducing running time while maintaining the expected functionality.
Keywords: Soft tissues; Matlab; Numerical; FEA