作　　者： (张申）; (肖映雄）; (郭瑞奇）;

机构地区： 湘潭大学土木工程与力学学院,湖南湘潭411105

出　　处： 《广西大学学报（自然科学版）》 2017年第4期1291-1298,共8页

摘　　要： 对三维薄结构问题,在进行网格剖分时,为了减少单元数目,常采用六面体薄单元,相应的高阶单元在计算精度、抗畸变程度等方面具有明显优势,但也大大增加了计算复杂性。Wilson元通过在单元内部设置附加自由度的方式来提高完全多项式的次数,具有计算精度高且自由度又少的优点,因而在实际计算中被广泛使用。但要提高这种非协调元分析效率还需为相应离散系统设计好的求解方法。本文针对一般变系数三维薄结构热传导问题,建立了Wilson元计算格式,并将DAMG法应用于与8节点三线性元谱等价的Wilson元离散系统的求解。数值实验结果表明,与常用方法相比,基于"距离矩阵"的代数多重网格(DAMG)法具有更好的计算效率和鲁棒性(robustness)。 When the finite element（ FEM） method is applied to analyze the thin-walled structures in three dimensions,thin hexahedral elements are usually used in order to reduce the number of elements,and the corresponding higher-order elements are preferred since they have some obvious advantages in the calculation accuracy,the degree of anti-distortion and so on. However,the computational complexity is greatly increased as well. The Wilson elements improve the degree of polynomial by setting extra degrees of freedom in the elements considered and have the advantages of few degrees of freedom, high accuracy and so on. Thus, they are widely used in practical computation. It is necessary to design some faster solvers for the corresponding system of linear algebraic equations in order to improve the efficiency of the FEM analysis. In this paper,the computational format of eight-node Wilson element is presented for the heat conduction problems ofthree-dimensional thin-walled structures with the general variable coefficients, and the DAMG method,which is suitable for the anisotropic mesh problems,is applied to the corresponding system of linear algebraic equations. The numerical results show that the DAMG method based on the distance matrix has better efficiency and robustness comparing with those commonly used methods.

关 键 词： 热传导问题 薄结构 元 距离矩阵 代数多重网格法