A Performance Study on Configurational Force and Spring-Analogy Based Mesh Optimization Schemes

Abstract

Assessment of r-adaption algorithms based on configurational force method and spring analogy approach is made. Assessment is made based on qualitative and quantitative aspects of error estimates, convergence rates and mesh quality. Appropriate modifications to node relocation procedures are proposed for enhanced performance. A simple linear projection technique is used to improve convergence characteristics of the material force node relocation algorithm. Performing mesh adaption on initial mesh results in a considerable reduction in gradients of strain energy. Assessment based on suitability of mesh adaption algorithms for structured and unstructured initial meshes has been performed. It has been observed that the configurational force method is more robust. Comparitive study indicates the superiority of the configurational force method. The proposed enhancement to the mesh adaption is based on configuration force method for r-adaption together with weighted Laplacian smoothing and mesh enrichment through h-refinement based on estimated discretization error in energy norm. A further reduction in the potential energy and the relative error norm of the system is found to be achieved with combined r-adaption and mesh enrichment (in the form of h-refinement). Numerical study confirms that the proposed combined r − h adaption is more efficient than a purely h-adaptive approach and more flexible than a purely r-adaptive approach with better convergence characteristics.