Interactive Real-time Structural Modelling - Solids

The aim of this master project is to develop a fast computing method for the analysis of structures with non-linear geometric behavior. The Dynamic Relaxation (DR) method is employed instead of the better known Newton-Raphson iteration process based on Finite Element Method (FEM). Different to a standard FEM method, DR computes forces and deformations at the element level without the need to assemble and invert a global mass, stiffness or damping matrix. This results in a less complex algorithm which is more suitable for real-time applications. Previous work on DR for structural analysis have focused on one-dimensional elements such as cable, beam and bars. This work presents a new DR formulation for solid elements, focusing on a tetrahedron type. Application of this formulation to structural analysis is shown through different case studies. Results are compared in terms of accuracy and speed with those obtained through a commercial FEM software. The benchmark shows that the DR formulation produces results which are in good accordance with respect to those produced by the commercial software. The time per iteration is significantly reduced owing to an explicit integration scheme. The method is also more robust than a standard FEM for certain problems.