Adaptive Finite Element Methods for Variational Inequalitieswith Application to Contact Problems and Plasticity

这项研究的目的是发展新的精确的分析方法来解决非线性固体力学中一类困难的静态和动态问题，即有摩擦和无摩擦的弹性和塑性接触问题。这项为期两年的研究项目包括发展由变分不等式描述的问题的可靠的后验误差估计，基于这些误差估计发展自适应策略，以及基于所发展的策略的算法发展。如果开发出一种有效的方法，它将提高制造过程和结构响应的数值模拟质量。

The purpose of this research is to develop new and accurate analysis procedures for solving a difficult class of static and dynamic problems in nonlinear solid mechanics, i.e. contact problems in elasticity and plasticity with and without friction. The two year research project involves the development of reliable a-posteriori error estimates of problems described by variational inequalities, development of adaptative strategies based on these error estimates and finally an algorithm development based on the developed strategies. If an efficient method is developed, it will enhance the quality of numerical simulation of manufacturing processes and structural responses.