A New Divergence Method for Plane Strain Element - Cheikhna , Sidi Mohamed (Universiti Teknologi PETRONAS, 2018)
Numerical methods have truly revolutionized computational engineering in the last decades. Complex engineering problems can be modelled and analysed thoroughly with high accuracy thanks to powerful computers and the advancements of numerical methods that allow fast and efficient computation for complex problems. With this fast-pace development, research has been continuously conducted on ways to improve the suitability and efficiency of numerical methods for engineering applications, such as improving the convergence rate with regard to the mesh size. Among the most popular numerical methods today are the Finite Element Method (FEM) and the Finite Volume Method (FVM). The FEM is dominating in structural mechanics applications whereas the FVM leads in the domain of fluid mechanics and problems involving moving boundaries. In both methods, parameters of interest are calculated at discrete places on a meshed geometry and both methods use interpolation functions in discretizing the problem. However, the finite volume method uses a constant flux for a linear interpolation. It is proposed in this project to investigate if this downside can be eliminated by combining the polynomial interpolation of the FEM with the divergence theorem which represents the basis of the FVM. The New Divergence Method (NDM) has already been studied for heat transfer problem with heat source and this project extends the study to 2 degrees of freedom isotropic plain strain element. The formulation of the NDM for plane strain element, for a cantilever beam problem, is shown in this report and the displacement results obtained from NDM are then validated by comparing them with FEM results for the same problem. The validation is done by conducting a convergence study comparing between the two methods NDM and FEM. Based on the results presented in this report, The New Divergence Method is found as able to provide converged results. The convergence study even shows that NDM performs almost equivalent to the FEM therefore it has the potential to be developed