The performance of automatic adaptive edge-based smoothed finite element method in engineering mechanics applications

Abstract

The thesis investigates the performance of an edge-based smoothed finite element method (ES-FEM) combined with an automatic mesh refinement (AMR) algorithm to provide the solutions of in-plane elastic engineering mechanics applications. The ES-FEM adopts a strain smoothing technique over the edges adjoining the two adjacent triangular-shape meshes, whilst a layer of singular yet compatible five-node elements in addition to standard three-node ES-FEs can be employed to overcome the problems associated with stress singularity.

The proposed framework enables the effective model construction of realistic engineering structures with complex geometry at modest computational resources. The AMR algorithm adopts the newest node bisection scheme that automatically sub-divides the parent critical elements into a suitable number of smaller children members at the longest edge of three-node elements overcoming the hang-node problems. The set of critical members is determined by the L2-norm error estimator functions defining the difference between the computed numerical von Mises stress solutions and recovery stress values. A number of illustrative, including classical benchmarks, examples were successfully processed by the proposed numerical analysis platform. These hence present the efficiency of the developed analysis framework in approximating the accurate elastic responses of structures under applied forces.