高次有限元由于对问题具有更好的逼近效果及某些特殊的优点,如能解决弹性问题的闭锁现象(Poisson’s ratio locking),使得它们在实际计算中被广泛使用。但与线性元相比,它具有更高的计算复杂性。该文基于标量椭圆问题高次有限元离散化...高次有限元由于对问题具有更好的逼近效果及某些特殊的优点,如能解决弹性问题的闭锁现象(Poisson’s ratio locking),使得它们在实际计算中被广泛使用。但与线性元相比,它具有更高的计算复杂性。该文基于标量椭圆问题高次有限元离散化系统的代数多层网格(AMG)法,针对三维弹性问题高次有限元离散化线性系统的求解,设计了一种以块对角逆为预条件子的共轭梯度法(AMG-BPCG)。数值实验表明,该文设计的AMG-BPCG法较标准的ILU-型PCG法具有更好的计算效率和鲁棒性。展开更多
The singular hybrid boundary node method （SHBNM） is proposed for solving three-dimensional problems in linear elasticity. The SHBNM represents a coupling between the hybrid displacement variational formulations and ...The singular hybrid boundary node method （SHBNM） is proposed for solving three-dimensional problems in linear elasticity. The SHBNM represents a coupling between the hybrid displacement variational formulations and moving least squares （MLS） approximation. The main idea is to reduce the dimensionality of the former and keep the meshless advantage of the later. The rigid movement method was employed to solve the hyper-singular integrations. The ＇boundary layer effect＇, which is the main drawback of the original Hybrid BNM, was overcome by an adaptive integration scheme. The source points of the fundamental solution were arranged directly on the boundary. Thus the uncertain scale factor taken in the regular hybrid boundary node method （RHBNM） can be avoided. Numerical examples for some 3D elastic problems were given to show the characteristics. The computation results obtained by the present method are in excellent agreement with the analytical solution. The parameters that influence the performance of this method were studied through the numerical examples.展开更多
This paper studies the bending of simple-supported rectangular plate on point supports, line supports and elastic foundation. On the basis of three-dimensional elasticity theory, the exact expressions of the displacem...This paper studies the bending of simple-supported rectangular plate on point supports, line supports and elastic foundation. On the basis of three-dimensional elasticity theory, the exact expressions of the displacement functions, which satisfy the governing differential equations and the simply supported boundary conditions at four edges of the plate, are analytically derived. The reaction forces of the in- termediate supports are regarded as the unknown external forces acting on the lower surface of the plate. The unknown coefficients are then determined by the boundary conditions on the upper and lower surfaces of the plate. Comparing the numerical results obtained from the proposed method to those obtained from Kirchhoff plate theory, Mindlin plate theory and those obtained from the commer- cial finite element software ANSYS, the high accuracy of the present method has been demonstrated.展开更多
In the present paper, bending and stress analyses of two-directional functionally graded （FG） annular plates resting on non-uniform two-parameter Winkler-Pasternak founda- tions and subjected to normal and in-plane-...In the present paper, bending and stress analyses of two-directional functionally graded （FG） annular plates resting on non-uniform two-parameter Winkler-Pasternak founda- tions and subjected to normal and in-plane-shear tractions is investigated using the exact three- dimensional theory of elasticity. Neither the in-plane shear loading nor the influence of the two- directional material heterogeneity has been investigated by the researchers before. The solution is obtained by employing the state space and differential quadrature methods. The material proper- ties are assumed to vary in both transverse and radial directions. Three different types of variations of the stiffness of the foundation are considered in the radial direction： linear, parabolic, and sinu- soidal. The convergence analysis and the comparative studies demonstrate the high accuracy and high convergence rate of the present approach. A parametric study consisting of evaluating effects of different parameters （e.g., exponents of the material properties laws, the thickness to radius ratio, trends of variations of the foundation stiffness, and different edge conditions） is carried out. The results are reported for the first time and are discussed in detail.展开更多
文摘高次有限元由于对问题具有更好的逼近效果及某些特殊的优点,如能解决弹性问题的闭锁现象(Poisson’s ratio locking),使得它们在实际计算中被广泛使用。但与线性元相比,它具有更高的计算复杂性。该文基于标量椭圆问题高次有限元离散化系统的代数多层网格(AMG)法,针对三维弹性问题高次有限元离散化线性系统的求解,设计了一种以块对角逆为预条件子的共轭梯度法(AMG-BPCG)。数值实验表明,该文设计的AMG-BPCG法较标准的ILU-型PCG法具有更好的计算效率和鲁棒性。
基金Project supported by the Program of the Key Laboratory of Rock and Soil Mechanics of Chinese Academy of Sciences (No.Z110507)
文摘The singular hybrid boundary node method （SHBNM） is proposed for solving three-dimensional problems in linear elasticity. The SHBNM represents a coupling between the hybrid displacement variational formulations and moving least squares （MLS） approximation. The main idea is to reduce the dimensionality of the former and keep the meshless advantage of the later. The rigid movement method was employed to solve the hyper-singular integrations. The ＇boundary layer effect＇, which is the main drawback of the original Hybrid BNM, was overcome by an adaptive integration scheme. The source points of the fundamental solution were arranged directly on the boundary. Thus the uncertain scale factor taken in the regular hybrid boundary node method （RHBNM） can be avoided. Numerical examples for some 3D elastic problems were given to show the characteristics. The computation results obtained by the present method are in excellent agreement with the analytical solution. The parameters that influence the performance of this method were studied through the numerical examples.
基金Supported by the Innovation Foundation of Nanjing University of Science and Technology for PhD Graduates
文摘This paper studies the bending of simple-supported rectangular plate on point supports, line supports and elastic foundation. On the basis of three-dimensional elasticity theory, the exact expressions of the displacement functions, which satisfy the governing differential equations and the simply supported boundary conditions at four edges of the plate, are analytically derived. The reaction forces of the in- termediate supports are regarded as the unknown external forces acting on the lower surface of the plate. The unknown coefficients are then determined by the boundary conditions on the upper and lower surfaces of the plate. Comparing the numerical results obtained from the proposed method to those obtained from Kirchhoff plate theory, Mindlin plate theory and those obtained from the commer- cial finite element software ANSYS, the high accuracy of the present method has been demonstrated.
文摘In the present paper, bending and stress analyses of two-directional functionally graded （FG） annular plates resting on non-uniform two-parameter Winkler-Pasternak founda- tions and subjected to normal and in-plane-shear tractions is investigated using the exact three- dimensional theory of elasticity. Neither the in-plane shear loading nor the influence of the two- directional material heterogeneity has been investigated by the researchers before. The solution is obtained by employing the state space and differential quadrature methods. The material proper- ties are assumed to vary in both transverse and radial directions. Three different types of variations of the stiffness of the foundation are considered in the radial direction： linear, parabolic, and sinu- soidal. The convergence analysis and the comparative studies demonstrate the high accuracy and high convergence rate of the present approach. A parametric study consisting of evaluating effects of different parameters （e.g., exponents of the material properties laws, the thickness to radius ratio, trends of variations of the foundation stiffness, and different edge conditions） is carried out. The results are reported for the first time and are discussed in detail.
