为精确模拟浅水波非线性演化过程中的动边界,提出一种基于位移的Hamilton变分原理,并进而导出一种基于位移的浅水方程(Shallow Water Equation based on Displacement,SWE-D).SWE-D以位移为基本未知量,可以精确满足动边界处的零水深要...为精确模拟浅水波非线性演化过程中的动边界,提出一种基于位移的Hamilton变分原理,并进而导出一种基于位移的浅水方程(Shallow Water Equation based on Displacement,SWE-D).SWE-D以位移为基本未知量,可以精确满足动边界处的零水深要求并精确捕捉动态边界位置,且解具有协调性.在Hamilton变分原理的框架下,分别采用有限元和保辛积分算法对该浅水方程进行空间离散和时间积分,可有效地处理不平水底情况,保证对非线性演化进行长时间仿真的精度.数值算例表明该方法适用于浅水动边界问题的数值模拟.展开更多
In this paper, a locking-free nonconforming rectangular finite element scheme is presented for the planar elasticity problem with pure displacement boundary condition. Meanwhile, we prove that this element is also con...In this paper, a locking-free nonconforming rectangular finite element scheme is presented for the planar elasticity problem with pure displacement boundary condition. Meanwhile, we prove that this element is also convergent for stationary Stokes problem.展开更多
Most computational structural engineers are paying more attention to applying loads rather than to DBCs （Displacement Boundary Conditions） because most static stable mechanical structures are working under already p...Most computational structural engineers are paying more attention to applying loads rather than to DBCs （Displacement Boundary Conditions） because most static stable mechanical structures are working under already prescribed displacement boundary conditions. In all of the computational analysis of solving a system of algebraic equations, such as FEM （Finite Element Method）, three translational and three rotational degrees of freedom （DOF） should be constrained （by applying DBCs） before solving the system of algebraic equation in order to prevent rigid body motions of the analysis results （singular problem）. However, it is very difficult for an inexperienced engineer or designer to apply proper DBCs in the case of thermal stress analysis where no prescribed DBCs or constraints exist, for example in water quenching for heat treatment. Moreover, improper DBCs cause incorrect solutions in thermal stress analysis, such as stress concentration or unreasonable deformation phases. To avoid these problems, we studied a technique which performs the thermal stress analysis without any DBCs; and then removes rigid body motions from the deformation results in a post process step as the need arises. The proposed technique makes it easy to apply DBCs and prevent the error caused by improper DBCs. We proved it was mathematically possible to solve a system of algebraic equations without a step of applying DBCs. We also compared the analysis results with those of a traditional procedure for real castings.展开更多
文摘为精确模拟浅水波非线性演化过程中的动边界,提出一种基于位移的Hamilton变分原理,并进而导出一种基于位移的浅水方程(Shallow Water Equation based on Displacement,SWE-D).SWE-D以位移为基本未知量,可以精确满足动边界处的零水深要求并精确捕捉动态边界位置,且解具有协调性.在Hamilton变分原理的框架下,分别采用有限元和保辛积分算法对该浅水方程进行空间离散和时间积分,可有效地处理不平水底情况,保证对非线性演化进行长时间仿真的精度.数值算例表明该方法适用于浅水动边界问题的数值模拟.
文摘In this paper, a locking-free nonconforming rectangular finite element scheme is presented for the planar elasticity problem with pure displacement boundary condition. Meanwhile, we prove that this element is also convergent for stationary Stokes problem.
文摘Most computational structural engineers are paying more attention to applying loads rather than to DBCs （Displacement Boundary Conditions） because most static stable mechanical structures are working under already prescribed displacement boundary conditions. In all of the computational analysis of solving a system of algebraic equations, such as FEM （Finite Element Method）, three translational and three rotational degrees of freedom （DOF） should be constrained （by applying DBCs） before solving the system of algebraic equation in order to prevent rigid body motions of the analysis results （singular problem）. However, it is very difficult for an inexperienced engineer or designer to apply proper DBCs in the case of thermal stress analysis where no prescribed DBCs or constraints exist, for example in water quenching for heat treatment. Moreover, improper DBCs cause incorrect solutions in thermal stress analysis, such as stress concentration or unreasonable deformation phases. To avoid these problems, we studied a technique which performs the thermal stress analysis without any DBCs; and then removes rigid body motions from the deformation results in a post process step as the need arises. The proposed technique makes it easy to apply DBCs and prevent the error caused by improper DBCs. We proved it was mathematically possible to solve a system of algebraic equations without a step of applying DBCs. We also compared the analysis results with those of a traditional procedure for real castings.
