无网格法在弹塑性问题中的应用

在弹塑性问题中引入无网格法,得到了弹塑性无网格法的控制方法;计算了中心裂纹板的塑性区分布以及极限荷载;数值结果表明了该方法的可行性和有效性。     

考虑摩擦三维弹塑性接触边界元法

边界元法与其它数值方法相比，由于具有应力和面力计算精度高的特点，非常适合于接触问题的分析，本文建立了考虑摩擦三维弹塑性接触问题的边界元法，采用此方法对板带轧制这一典型的弹塑性接触问题进行了分析，证明本文人出的方法是有效的。     

弹塑性有限元分析的拟线性法

本文在理论分析的基础上,建立了弹塑性有限元分析的拟线性法.这种方法可用于解算理想弹塑性材料、强化和软化材料的弹塑性问题.计算时可只采用一个弹性刚度矩阵.选用了三个算例以说明本法的计算精度.     

解Drucker-Prager塑性问题的二阶锥互补法

基于经典弹塑性理论中多数屈服准则具有凸锥数学结构的事实,将在大规模计算中更具潜力的锥规划法引入弹塑性分析。考虑到弹塑性流动理论有关联与非关联之分,本文提出利用锥型互补法求解弹塑性问题。具体以Drucker-Prager弹塑性模型为例,首先利用最大塑性功耗散原理和圆锥对偶理论等工具,建立了弹塑性本构方程的等价二阶锥互补模型;然后,基于参变量变分原理和有限元技术,建立了弹塑性增量分析的二阶锥线性互补模型;最后,利用一类半光滑Newton算法求解。数值算例表明了本文方法的有效性。     

有初始几何缺陷的壳体弹塑性大变形分析

在等温小变形弹塑性内时本构方程偏量形式的基础上，导出了适用于大位移、小应变分析的弹塑性内时本构方程。并导出了带有初始几何缺陷的非线性弹塑性问题的有限元方程。文中给出的算例表明本方法是可行有效的。     

弹塑性扭转问题具多项式基的径向点插值无网格法

对于弹塑性扭转问题描述的椭圆变分不等式,采用具多项式基的径向点插值法无网格方法与Uzawa方法耦舍,得到了带松弛因子的离散迭代算法,并给出了数值算例,分析了参数对结果的影响.通过与有限元法比较,表明该方法是求解弹塑性扭转问题的有效的方法之一.     

钢构件设计中的弹塑性力学问题

分析我国现行《钢结构设计规范》GB50017-2003,对比美、欧规范,针对钢结构常用受力构件设计的强度问题和稳定问题涉及到的弹塑性理论应用,通过课堂教学环节,讲授钢结构构件设计原理和弹塑性设计方法,让学生深刻体会弹性设计理论和弹塑性设计理论的差异,认识弹塑性理论在钢结构设计中应用的必要性. 同时也让学生学习正确运用力学知识解决工程问题的思维方法,激发学生学习力学理论的兴趣,培养学生综合应用知识解决工程问题的能力.     

弹塑性接触问题的非光滑非线性方程组方法

将求解三维弹性摩擦接触问题的非光滑非线性方程组方法推广到弹塑性(Mises材料)情形，提出了两种应用方法：一种是将非光滑非线性方程组方法和求解弹塑性问题常用的Newton—Raphson迭代方法结合起来；另一种是将问题写成统一的非光滑非线性方程组，直接求解。数值算例验证了两种方法的有效性，并进行了结果比较。     

三维弹塑性问题的半解析解

1.前言半解析数值方法是一类在各科学计算与工程分析领域中有着广泛应用前景的新的计算方法,在各种工程力学分析中已有广泛应用。但这种方法目前只限于线性问题。很少有物理非线性问题结果,特别是三维问题。半解析元法综合了解析法与有限元法的特点,是比较适合于求解弹塑性问题的一种方法。由于它在空间离散中引入了解析函数,使其在空间上由三维降为一维数值问题(大约省二个数量级),使弹塑性分析也得以在一般微机上实现,为固体力学中三维弹塑性问题求解探索一条较为简便而实用的途径。本文探     

薄板弹塑性弯曲的X样条有限条方法

薄板弹塑性弯曲的Ｘ样条有限条方法叶金铎，杨海元（天津大学冶金分校，３００４００）（天津大学，３０００７２）关键词Ｘ样条有限条，弹塑性，分层方案，不分展方案，不规则区域１前言采用有限元法解弹塑性问题，计算量大、计算费用高，采用传统有限条法解弹塑性问题又...     

Solving material nonlinear structural problems by a finite analytic method in local coordinates

The purpose of this paper is to develop a finite analytic (FA) numerical solution for the elasto-plastic problem of the total theory. Schemes for the FA method in local coordinates for solving non-linear governing equations in the form of Navier equations are derived, which can be utilized to solve the problem in a domain of arbitrary geometry. Numerical illustration shows that the schemes are effective and practical.     

Quaternion Regularization of the Equations of the Perturbed Spatial Restricted Three-Body Problem: I

We develop a quaternion method for regularizing the differential equations of the perturbed spatial restricted three-body problem by using the Kustaanheimo–Stiefel variables, which is methodologically closely related to the quaternion method for regularizing the differential equations of perturbed spatial two-body problem, which was proposed by the author of the present paper.A survey of papers related to the regularization of the differential equations of the two- and threebody problems is given. The original Newtonian equations of perturbed spatial restricted three-body problem are considered, and the problem of their regularization is posed; the energy relations and the differential equations describing the variations in the energies of the system in the perturbed spatial restricted three-body problem are given, as well as the first integrals of the differential equations of the unperturbed spatial restricted circular three-body problem (Jacobi integrals); the equations of perturbed spatial restricted three-body problem written in terms of rotating coordinate systems whose angular motion is described by the rotation quaternions (Euler (Rodrigues–Hamilton) parameters) are considered; and the differential equations for angular momenta in the restricted three-body problem are given.Local regular quaternion differential equations of perturbed spatial restricted three-body problem in the Kustaanheimo–Stiefel variables, i.e., equations regular in a neighborhood of the first and second body of finite mass, are obtained. The equations are systems of nonlinear nonstationary eleventhorder differential equations. These equations employ, as additional dependent variables, the energy characteristics of motion of the body under study (a body of a negligibly small mass) and the time whose derivative with respect to a new independent variable is equal to the distance from the body of negligibly small mass to the first or second body of finite mass.The equations obtained in the paper permit developing regular methods for determining solutions, in analytical or numerical form, of problems difficult for classicalmethods, such as the motion of a body of negligibly small mass in a neighborhood of the other two bodies of finite masses.     

A new approach to the group analysis of one-dimensional stochastic differential equations

Stochastic evolution equations are investigated using a new approach to the group analysis of stochastic differential equations. It is shown that the proposed approach reduces the problem of group analysis for this type of equations to the same problem of group analysis for evolution equations of special form without stochastic integrals.     

Initial-value problem for coupled Boussinesq equations and a hierarchy of Ostrovsky equations

We consider the initial-value problem for a system of coupled Boussinesq equations on the infinite line for localised or sufficiently rapidly decaying initial data, generating sufficiently rapidly decaying right- and left-propagating waves. We study the dynamics of weakly nonlinear waves, and using asymptotic multiple-scale expansions and averaging with respect to the fast time, we obtain a hierarchy of asymptotically exact coupled and uncoupled Ostrovsky equations for unidirectional waves. We then construct a weakly nonlinear solution of the initial-value problem in terms of solutions of the derived Ostrovsky equations within the accuracy of the governing equations, and show that there are no secular terms. When coupling parameters are equal to zero, our results yield a weakly nonlinear solution of the initial-value problem for the Boussinesq equation in terms of solutions of the initial-value problems for two Korteweg-de Vries equations, integrable by the Inverse Scattering Transform. We also perform relevant numerical simulations of the original unapproximated system of Boussinesq equations to illustrate the difference in the behaviour of its solutions for different asymptotic regimes.     

New Statement of the elasticity problem for a layer

The problem on the equilibrium of an inhomogeneous anisotropic elastic layer is considered. The classical statement of the problem in displacements consists of three partial differential equations with variable coefficients for the three displacements and of three boundary conditions posed at each point of the boundary surface. Sometimes, instead of the statement in displacements, it is convenient to use the classical statement of the problem in stresses [1] or the new statement of the problem in stresses proposed by B. E. Pobedrya [2]. In the case of the problem in stresses, it is necessary to find six components of the stress tensor, which are functions of three coordinates. The choice of the statement of the problem depends on the researcher and, of course, on the specific problem. The fact that there are several statements of the problem makes for a wider choice of the method for solving the problem. In the present paper, for a layer with plane boundary surfaces, we propose a new statement of the problem, which, in contrast to the other two statements indicated above, can be called a mixed statement. The problem for a layer in the new statement consists of a system of three partial differential equations for the three components of the displacement vector of the midplane points. The system is coupled with three integro-differential equations for the three longitudinal components of the stress tensor. Thus, in the new statement, just as in the other statements in stresses, one should find six functions. In the new statement, three of these functions (the displacements of the midplane points) are functions of two coordinates, and the other three functions (the longitudinal components of the stress tensor) are functions of three coordinates. It is shown that all equations in the new statement are the Euler equations for the Reissner functional with additional constraints. After the problem is solved in the new statement, three components of the displacement vector and three transverse components of the stress tensor are determined at each point of the layer. The new statement of the problem can be used to construct various engineering theories of plates made of composite materials.     

Quasi-Green’s function method for free vibration of simply-supported trapezoidal shallow spherical shell

The idea of quasi-Green’s function method is clarified by considering a free vibration problem of the simply-supported trapezoidal shallow spherical shell. A quasi-Green’s function is established by using the fundamental solution and boundary equation of the problem. This function satisfies the homogeneous boundary condition of the prob-lem. The mode shape differential equations of the free vibration problem of a simply-supported trapezoidal shallow spherical shell are reduced to two simultaneous Fredholm integral equations of the second kind by the Green formula. There are multiple choices for the normalized boundary equation. Based on a chosen normalized boundary equa-tion, a new normalized boundary equation can be established such that the irregularity of the kernel of integral equations is overcome. Finally, natural frequency is obtained by the condition that there exists a nontrivial solution to the numerically discrete algebraic equations derived from the integral equations. Numerical results show high accuracy of the quasi-Green’s function method.     

The equations of motion of a system under the action of the impulsive constraints

In order to solve the problem of motion for the system with n degrees of freedom under the action of p impulsive constraints, we must solve the simultaneous equations consisting of n+p equations. In this paper, it has been shown that the undetermined multipliers in the equations of impact can be cancelled for the cases of both the generalized coordinates and the quasi-coordinates. Thus there are only n-p equations of impact. Combining these equations with p impulsive constraint equations, we have simultaneous equations consisting of n equations. Therefore, only n equations are necessary to solve the problem of impact for the system subjected to impulsive constraints. The method proposed in this paper is simpler than ordinary methods.     

Quasi-Green＇s function method for free vibration of simply-supported trapezoidal shallow spherical shell

The idea of quasi-Green＇s function method is clarified by considering a free vibration problem of the simply-supported trapezoidal shallow spherical shell. A quasi- Green＇s function is established by using the fundamental solution and boundary equation of the problem. This function satisfies the homogeneous boundary condition of the prob- lem. The mode shape differential equations of the free vibration problem of a simply- supported trapezoidal shallow spherical shell are reduced to two simultaneous Fredholm integral equations of the second kind by the Green formula. There are multiple choices for the normalized boundary equation. Based on a chosen normalized boundary equa- tion, a new normalized boundary equation can be established such that the irregularity of the kernel of integral equations is overcome. Finally, natural frequency is obtained by the condition that there exists a nontrivial solution to the numerically discrete algebraic equations derived from the integral equations. Numerical results show high accuracy of the quasi-Green＇s function method.     

Extension of Whittaker equations to non-holonomic mechanical systems

In 1904, using the energy integral Whittaker studied the reduction of a dynamical problem to a problem with fewer degrees of freedom for the holonomic conservative systems and obtained the Whittaker equation^[1].In this article, Whittaker equations are extended to non-holonomic systems and the generalized Whittaker equations are obtained. And then these equations are transformed into Kiel-sen’s form.Finally an example is given.     

Boundary integral equations of unique solutions in elasticity

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｂｏｕｎｄａｒｙｅｌｅｍｅｎｔｍｅｔｈｏｄ（ＢＥＭ）ｐｒｏｖｉｄｅｓａｎａｔｔｒａｃｔｉｖｅａｌｔｅｒｎａｔｉｖｅｆｏｒｔｈｅａｎａｌｙｓｉｓｏｆｅｎｇｉｎｅｅｒｉｎｇｐｒｏｂｌｅｍｓ．Ｉｔｓｍａｉｎａｄｖａｎｔａｇｅｓａｒｅｅｃｏｎｏｍｉｃａｌａｎｄｐａｒｔｉｃｕｌａｒｌｙｃｏｎｖｅｎｉｅｎｔｆｏｒｕｎｂｏｕｎｄｅｄｄｏｍａｉｎａｎｄｓｔｒｅｓｓｃｏｎｃｅｎｔｒａｔｉｏｎｐｒｏｂｌｅｍｓ．Ｔｈｅｂｏｕｎｄａｒｙｉｎｔｅｇｒａｌｅｑｕａｔｉｏｎ（ＢＩＥ）ｉｓｔｈｅ…