中文摘要：

针对接触问题提出了基于应变能梯度的自适应无网格伽辽金方法。通过对自适应无网格伽辽金方法的原理讨论，给出了基于背景网格的误差估计方法，并对自适应求解流程进行了阐述。研究了无网格节点加密技术和自适应搜索半径等关键技术。编程求解了圆柱体接触问题，并与理论解和均匀密化数值解进行比较，给出了接触计算中合理的参数范围，对真实粗糙表面接触问题进行了计算，计算结果表明，在相当计算精度下，自适应加密计算耗时仅为同等整体加密计算的18．6％。

英文摘要：

An adaptive element--free Galerkin （EFG） model based on the gradient of strain energy for two--dimensional contact problems was implemented. A scheme based on the strain energy gradient was proposed, and a cell error estimation based on background cells was given. Strain energy gradient--based adaptive EFG program flowchart used to solve the 2--D contact problems was introduced. A local domain refinement technique and an adaptive algorithm which can change the size of influence domain with difference local nodal density were introduced. By applying the adaptive model, a rigid cylinder contacting with an elastic plane and a rough surface with a plane were analyzed by comparing with the theoretical solution and the uniformly refined nodes distributions solution. Proper parameters were chosen to solve the contact problems. The results show that the cost of the CPU time of adaptive model is only about 18. 6% of that of the uniformly refined node calculation under the same conditions.