Two-dimensional large deformation analysis of hyperelastic and elasto-plastic solids based on the Meshless Local Petrov-Galerkin method （MLPG） is presented. A material configuration based the nonlinear MLPG formulat...Two-dimensional large deformation analysis of hyperelastic and elasto-plastic solids based on the Meshless Local Petrov-Galerkin method （MLPG） is presented. A material configuration based the nonlinear MLPG formulation is introduced for the large deformation analysis of both path-dependent and path-independent materials. The supports of the MLS approximation functions cover the same sets of nodes during material deformation, thus the shape function needs to be computed only in the initial stage. The multiplicative hyperelasto-plastic constitutive model is adopted to avoid objective time integration for stress update in large rota- tion. With this constitutive model, the computational formulations for path-dependent and path-independent materials become identical. Computational efficiency of the nonlinear MLPG method is discussed and optimized in several aspects to make the MLPG an O（N） algorithm. The numerical examples indicate that the MLPG method can solve large deformation problems accurately. Moreover, the MLPG computations enjoy better convergence rate than the FEM under very large particle distortion.展开更多
建立了无网格MLPG(Meshless Local Petrov-Galerkin)混合配点法求解二维弹性体位移、应力的数学模型,使用罚函数法添加本质边界条件,并将其应用到结构形状优化,结合遗传算法提出了一种新的连续体结构优化设计方法。对于节点支持域半径...建立了无网格MLPG(Meshless Local Petrov-Galerkin)混合配点法求解二维弹性体位移、应力的数学模型,使用罚函数法添加本质边界条件,并将其应用到结构形状优化,结合遗传算法提出了一种新的连续体结构优化设计方法。对于节点支持域半径的选取进行了重点探讨,提出一种动态支持域选择方法,建立了基于MLPG混合配点法的优化模型,对两个实际工程算例进行了形状优化,并与现有结果比较,验证了该方法的有效性。展开更多
In this paper,dynamic behavior of non-symmetric Functionally Graded(FG)cylindrical structure under shock loading is carried out.Dynamic equations in the polar coordinates are drawn out using Meshless Local Petrov-Gale...In this paper,dynamic behavior of non-symmetric Functionally Graded(FG)cylindrical structure under shock loading is carried out.Dynamic equations in the polar coordinates are drawn out using Meshless Local Petrov-Galerkin(MLPG)method.Nonlinear volume fractions are used for radial direction to simulate the mechanical properties of Functionally Graded Material(FGM).To solve dynamic equations of nonsymmetric FG cylindrical structure in the time domain,the MLPG method are combined with the Laplace transform method.For computing the inverse Laplace transform in the present paper,the Talbot algorithm for the numerical inversion is used.To verify the obtained results by the MLPG method,these results are compared with the analytical solution and the Finite Element Method(FEM).The obtained results through the MLPG method show a good agreement in comparison to other results and the MLPG method has high accuracy for dynamic analysis of non-symmetric FG cylindrical structure.The capability of the present method to dynamic analysis of non-symmetric FG cylindrical structure is demonstrated by dynamic analysis of the cylinder with different volume fraction exponents under harmonic and rectangular shock loading.The present method shows high accuracy,efficiency and capability to dynamic analysis of non-symmetric FG cylindrical structure with nonlinear grading patterns,which furnishes a ground for a more flexible design.展开更多
The local Petrov-Galerkin methods (MLPG) have attracted much attention due to their great flexibility in dealing with numerical model in elasticity problems. It is derived from the local weak form (WF) of the equilibr...The local Petrov-Galerkin methods (MLPG) have attracted much attention due to their great flexibility in dealing with numerical model in elasticity problems. It is derived from the local weak form (WF) of the equilibrium equations and by inducting the moving last square approach for trial and test functions in (WF) is discussed over local sub-domain. In this paper, we studied the effect of the configuration parameters of the size of the support or quadrature domain, and the effect of the size of the cells with nodes distribution number on the accuracy of the methods. It also presents a comparison of the results for the Shear stress, the deflections and the error in energy.展开更多
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...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.展开更多
基金The project supported by the National Natural Science Foundation of China (10472051). The English text was polished by Keren Wang
文摘Two-dimensional large deformation analysis of hyperelastic and elasto-plastic solids based on the Meshless Local Petrov-Galerkin method （MLPG） is presented. A material configuration based the nonlinear MLPG formulation is introduced for the large deformation analysis of both path-dependent and path-independent materials. The supports of the MLS approximation functions cover the same sets of nodes during material deformation, thus the shape function needs to be computed only in the initial stage. The multiplicative hyperelasto-plastic constitutive model is adopted to avoid objective time integration for stress update in large rota- tion. With this constitutive model, the computational formulations for path-dependent and path-independent materials become identical. Computational efficiency of the nonlinear MLPG method is discussed and optimized in several aspects to make the MLPG an O（N） algorithm. The numerical examples indicate that the MLPG method can solve large deformation problems accurately. Moreover, the MLPG computations enjoy better convergence rate than the FEM under very large particle distortion.
文摘建立了无网格MLPG(Meshless Local Petrov-Galerkin)混合配点法求解二维弹性体位移、应力的数学模型,使用罚函数法添加本质边界条件,并将其应用到结构形状优化,结合遗传算法提出了一种新的连续体结构优化设计方法。对于节点支持域半径的选取进行了重点探讨,提出一种动态支持域选择方法,建立了基于MLPG混合配点法的优化模型,对两个实际工程算例进行了形状优化,并与现有结果比较,验证了该方法的有效性。
文摘In this paper,dynamic behavior of non-symmetric Functionally Graded(FG)cylindrical structure under shock loading is carried out.Dynamic equations in the polar coordinates are drawn out using Meshless Local Petrov-Galerkin(MLPG)method.Nonlinear volume fractions are used for radial direction to simulate the mechanical properties of Functionally Graded Material(FGM).To solve dynamic equations of nonsymmetric FG cylindrical structure in the time domain,the MLPG method are combined with the Laplace transform method.For computing the inverse Laplace transform in the present paper,the Talbot algorithm for the numerical inversion is used.To verify the obtained results by the MLPG method,these results are compared with the analytical solution and the Finite Element Method(FEM).The obtained results through the MLPG method show a good agreement in comparison to other results and the MLPG method has high accuracy for dynamic analysis of non-symmetric FG cylindrical structure.The capability of the present method to dynamic analysis of non-symmetric FG cylindrical structure is demonstrated by dynamic analysis of the cylinder with different volume fraction exponents under harmonic and rectangular shock loading.The present method shows high accuracy,efficiency and capability to dynamic analysis of non-symmetric FG cylindrical structure with nonlinear grading patterns,which furnishes a ground for a more flexible design.
文摘The local Petrov-Galerkin methods (MLPG) have attracted much attention due to their great flexibility in dealing with numerical model in elasticity problems. It is derived from the local weak form (WF) of the equilibrium equations and by inducting the moving last square approach for trial and test functions in (WF) is discussed over local sub-domain. In this paper, we studied the effect of the configuration parameters of the size of the support or quadrature domain, and the effect of the size of the cells with nodes distribution number on the accuracy of the methods. It also presents a comparison of the results for the Shear stress, the deflections and the error in energy.
文摘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.
