Search

We present a robust and efficient form of the smoothed finite element method (S-FEM) to simulate hyperelastic bodies with compressible and nearly-incompressible neo-Hookean behaviour. The resulting method is stable, free from volumetric locking and robust on highly distorted meshes. To ensure inf-sup stability of our method we add a cubic bubble function to each element. The weak form for the smoothed hyperelastic problem is derived analogously to that of smoothed linear elastic problem. Smoothed strains and smoothed deformation gradients are evaluated on sub-domains selected by either edge information (edge-based S-FEM, ES-FEM) or nodal information (node-based S-FEM, NS-FEM). Numerical examples are shown that demonstrate the efficiency and reliability of the proposed approach in the nearly-incompressible limit and on highly distorted meshes. We conclude that, strain smoothing is at least as accurate and stable, as the MINI element, for an equivalent problem size.

Particle Swarm Optimization (PSO) is a new paradigm of Swarm Intelligence which is inspired by concepts from 'Social Psychology' and 'Artificial Life'. Essentially, PSO proposes that the co-operation of individuals promotes the evolution of the swarm. In terms of optimization, the hope would be to enhance the swarm's ability to search on a global scale so as to determine the global optimum in a fitness landscape. It has been empirically shown to perform well with regard to many different kinds of optimization problems. PSO is particularly a preferable candidate to solve highly nonlinear, non-convex and even discontinuous problems. In this paper, one enhanced version of PSO: Modified Lbest based PSO (LPSO) is proposed and applied to one of the most challenging fields of optimization -- truss topological optimization. Through a benchmark test and a spatial structural example, LPSO exhibited competitive performance due to improved global searching ability.

This thesis presents the extension of the gradient smoothing technique for finite\ud element approximation (so-called Smoothed Finite Element Method (S-FEM)) and\ud its bubble-enhanced version for non-linear problems involving large deformations\ud in nearly-incompressible and incompressible hyperelastic materials.\ud Finite Element Method (FEM) presents numerous challenges for soft matter\ud applications, such as incompressibility, complex geometries and mesh distortion\ud from large deformation. S-FEM was introduced to overcome the challenges mentioned\ud of FEM. The smoothed strains and the smoothed deformation gradients\ud are evaluated on the smoothing domain selected by either edge information, nodal\ud information or face information.\ud This thesis aims the extension of S-FEM in finite elasticity as a means of alleviating\ud locking and avoiding mesh distortion. S-FEM employs a “cubic” bubble\ud enhancement of the element shape functions with edge-based and face-based\ud S-FEMs, adding a linear displacement field at the centre of the element. Thereby\ud bubble-enhanced S-FEM affords a simple and efficient implementation.\ud This thesis reports the properties and performance of the proposed method for\ud quasi-incompressible hyperelastic materials. Benchmark tests show that the\ud method is well suited to soft matter simulation, overcoming deleterious locking\ud phenomenon and maintaining the accuracy with distorted meshes.