An adaptive mesh refinement technique for dynamics of solids

Simulation of dynamics problems generally is heavily dependent on mesh size for convergence and accuracy. In many cases, the requirement of mesh size reaches to such proportions that the problem becomes unsolvable for the available computational resources. We perceive that such problems can be solved by refining and unrefining mesh adaptively during time stepping. Adaptive mesh refinement techniques available in popular literature are marred by various limitations, such as element-specific techniques, algorithm-specific techniques, etc. We utilize Conforming Hierarchical Refinement Methods (CHARMS) [32] for our purpose since it relies on the refinement of finite element basis instead of geometric sub-division of elements. Refinement in this fashion produces conforming meshes during adaptive mesh refinement for a wide range of elements. We improve CHARMS to incorporate time stepping problems. In order to show the effectiveness of such an algorithm, we modify an explicit Newmark solver to incorporate it within the adaptive mesh refinement framework. We perform the analysis of conservation properties of the modified algorithm to understand its limitations. Later, we demonstrate application of such development with a very practical example, simulation of an NDE experiment using ultrasonic guided waves. Details presented in [76] has shown that such a simulation would otherwise not have been possible. We further study the guided wave experiment and optimize various parameters of the algorithm to validate experimental result