自适应一致性高阶无单元伽辽金法
发布时间：2018-08-06 19:31
【摘要】：近来提出的一致性高阶无单元伽辽金法通过导数修正技术大幅度减少了所需积分点数目,并能够精确地通过线性和二次分片试验,显著改善标准无单元伽辽金法的计算效率、精度和收敛性.本文在此基础之上,充分利用无单元法易于在局部区域添加节点的优势,发展了一致性高阶无单元伽辽金法的h型自适应分析方法.根据应变能密度梯度该方法自适应地确定需节点加密的区域,基于背景积分网格的局部多层细化要求生成新的计算节点,同时考虑了节点分布由密到疏渐进过渡的情形.采用相邻两次计算的应变能的相对误差作为自适应过程的停止准则,将所发展自适应无网格法应用于由几何外形、边界外载和体力等因素造成的应力集中问题的计算分析.数值结果表明,所发展方法能够自适应地对高应力梯度区域进行节点加密,自动给出合理的计算节点分布.与已有的标准无网格法的自适应分析相比,所发展方法在计算效率、精度和应力场光滑性等方面均展现出显著优势.与采用节点均匀分布的一致性高阶无单元伽辽金法相比,它大幅度地减少了计算节点数目,有效提高了一致性高阶无单元伽辽金法在分析应力集中等存在局部高梯度问题时的计算效率和求解精度.
[Abstract]:Recently, the consistent higher-order element-free Galerkin method has greatly reduced the number of integral points required by derivative correction, and has been able to improve the computational efficiency of the standard element-free Galerkin method by linear and quadratic piecewise experiments. Accuracy and convergence. On the basis of this, this paper makes full use of the advantage of element free method which is easy to add nodes in the local region, and develops an h type adaptive analysis method of consistent higher order element free Galerkin method. According to the strain energy density gradient this method adaptively determines the region requiring node encryption and generates a new computational node based on the local multi-layer refinement requirement of background integral grid. At the same time the case of node distribution transition from dense to sparsely progressive is considered. Using the relative error of the strain energy calculated by the adjacent two times as the stopping criterion of the adaptive process, the developed adaptive meshless method is applied to the calculation and analysis of the stress concentration caused by the factors such as geometric shape, external load and physical force. Numerical results show that the developed method can adaptively encrypt nodes in high stress gradient region and automatically give reasonable node distribution. Compared with the existing standard meshless adaptive analysis, the developed method shows significant advantages in computational efficiency, accuracy and stress field smoothness. Compared with the uniform higher-order element-free Galerkin method with uniform distribution of nodes, it greatly reduces the number of nodes. The computational efficiency and accuracy of the consistent higher-order element-free Galerkin method for the analysis of locally high gradient problems such as stress concentration are effectively improved.
【作者单位】： 大连理工大学工业装备结构分析国家重点实验室;成都理工大学地质灾害防治与地质环境保护国家重点实验室;武汉大学水资源与水电工程科学国家重点实验室;
【基金】：国家自然科学基金(11232003,11372066) 中央高校基本科研业务费专项资金(DUT15LK07) 辽宁省教育厅重点实验室基础研究(LZ2014002) 水资源与水电工程科学国家重点实验室开放基金(2015SGG03) 地质灾害防治与地质环境保护国家重点实验室开放基金(SKLGP2016K007)资助项目
【分类号】：O241.8
[Abstract]:Recently, the consistent higher-order element-free Galerkin method has greatly reduced the number of integral points required by derivative correction, and has been able to improve the computational efficiency of the standard element-free Galerkin method by linear and quadratic piecewise experiments. Accuracy and convergence. On the basis of this, this paper makes full use of the advantage of element free method which is easy to add nodes in the local region, and develops an h type adaptive analysis method of consistent higher order element free Galerkin method. According to the strain energy density gradient this method adaptively determines the region requiring node encryption and generates a new computational node based on the local multi-layer refinement requirement of background integral grid. At the same time the case of node distribution transition from dense to sparsely progressive is considered. Using the relative error of the strain energy calculated by the adjacent two times as the stopping criterion of the adaptive process, the developed adaptive meshless method is applied to the calculation and analysis of the stress concentration caused by the factors such as geometric shape, external load and physical force. Numerical results show that the developed method can adaptively encrypt nodes in high stress gradient region and automatically give reasonable node distribution. Compared with the existing standard meshless adaptive analysis, the developed method shows significant advantages in computational efficiency, accuracy and stress field smoothness. Compared with the uniform higher-order element-free Galerkin method with uniform distribution of nodes, it greatly reduces the number of nodes. The computational efficiency and accuracy of the consistent higher-order element-free Galerkin method for the analysis of locally high gradient problems such as stress concentration are effectively improved.
【作者单位】： 大连理工大学工业装备结构分析国家重点实验室;成都理工大学地质灾害防治与地质环境保护国家重点实验室;武汉大学水资源与水电工程科学国家重点实验室;
【基金】：国家自然科学基金(11232003,11372066) 中央高校基本科研业务费专项资金(DUT15LK07) 辽宁省教育厅重点实验室基础研究(LZ2014002) 水资源与水电工程科学国家重点实验室开放基金(2015SGG03) 地质灾害防治与地质环境保护国家重点实验室开放基金(SKLGP2016K007)资助项目
【分类号】：O241.8
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