无网格局部强弱法求解不规则域问题
发布时间：2018-08-07 21:37
【摘要】：无网格局部彼得洛夫-伽辽金(meshless local Petrov-Galerkin,MLPG)法是一种具有代表性的无网格方法,在计算力学领域得到广泛应用.然而,这种方法在边界上需执行积分运算,通常很难处理不规则求解域问题.为了克服MLPG法的这种局限性,提出了无网格局部强弱(meshless local strong-weak,MLSW)法.MLSW法采用MLPG法离散内部求解域,采用无网格介点(meshless intervention-point,MIP)法施加自然边界条件,并采用配点法施加本质边界条件,避免执行边界积分运算,可适用于求解各类复杂的不规则域问题.从理论上讲,这种结合式方法,既保持了MLPG法稳定而精确计算的优势,同时兼备配点型方法在处理复杂结构问题时简洁而灵活的优势,实现了弱式法和强式法的优势互补.此外,MLSW法采用移动最小二乘核(moving least squares core,MLSc)近似法来构造形函数,是对传统移动最小二乘(moving least squares,MLS)近似法的一种改进.MLSc使用核基函数代替通常的基函数,有利于数值求解的精确性和稳定性,而且其导数近似计算变得更为简单.数值算例结果初步表明:这种新方法实施简单,求解稳定、精确,表现出适合工程运用的潜力.
[Abstract]:The meshless local Petrov-Galerkin (meshless local (meshless local) method is a representative meshless method, which is widely used in the field of computational mechanics. However, this method needs to perform integral operations on the boundary, and it is usually difficult to deal with irregular domain problems. In order to overcome the limitation of the MLPG method, a meshless local strong / weak (meshless local strong-weak MLSW method is proposed. The MLPG method is used to discretize the internal solution domain, the meshless intervention-point MLPG method is used to impose the natural boundary condition, and the collocation method is used to impose the essential boundary condition. It can be used to solve all kinds of complex irregular domain problems by avoiding boundary integral operation. Theoretically speaking, this combined method not only maintains the advantages of MLPG method in stable and accurate calculation, but also has the advantages of simplicity and flexibility in dealing with complex structural problems. The weak method and the strong method complement each other. In addition, the moving least square kernel (moving least squares coreSc approximation method is used to construct the shape function, which is an improvement of the traditional moving least squares (moving least squares MLS approximation method. MLSc uses kernel basis function instead of the usual basis function. It is advantageous to the accuracy and stability of the numerical solution, and the approximate calculation of its derivative becomes more simple. The results of numerical examples show that the new method is simple, stable and accurate, and shows the potential for engineering application.
【作者单位】： 长沙理工大学道路结构与材料交通行业重点实验室;长沙理工大学交通运输工程学院;
【基金】：国家自然科学基金(51478053) 交通行业重点实验室(长沙)开放基金(KFJ120201)资助项目
【分类号】：O241.82
本文编号：2171424
[Abstract]:The meshless local Petrov-Galerkin (meshless local (meshless local) method is a representative meshless method, which is widely used in the field of computational mechanics. However, this method needs to perform integral operations on the boundary, and it is usually difficult to deal with irregular domain problems. In order to overcome the limitation of the MLPG method, a meshless local strong / weak (meshless local strong-weak MLSW method is proposed. The MLPG method is used to discretize the internal solution domain, the meshless intervention-point MLPG method is used to impose the natural boundary condition, and the collocation method is used to impose the essential boundary condition. It can be used to solve all kinds of complex irregular domain problems by avoiding boundary integral operation. Theoretically speaking, this combined method not only maintains the advantages of MLPG method in stable and accurate calculation, but also has the advantages of simplicity and flexibility in dealing with complex structural problems. The weak method and the strong method complement each other. In addition, the moving least square kernel (moving least squares coreSc approximation method is used to construct the shape function, which is an improvement of the traditional moving least squares (moving least squares MLS approximation method. MLSc uses kernel basis function instead of the usual basis function. It is advantageous to the accuracy and stability of the numerical solution, and the approximate calculation of its derivative becomes more simple. The results of numerical examples show that the new method is simple, stable and accurate, and shows the potential for engineering application.
【作者单位】： 长沙理工大学道路结构与材料交通行业重点实验室;长沙理工大学交通运输工程学院;
【基金】：国家自然科学基金(51478053) 交通行业重点实验室(长沙)开放基金(KFJ120201)资助项目
【分类号】：O241.82
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