正交各向异性弹塑性摩擦接触问题的数值求解

采用正交各向异性摩擦定律对三维弹塑性摩擦接触问题进行分析,基于参变量变分原理,经过有限元离散,将问题化为线性互补问题模型,之后给出一个求解互补问题的非内点光滑化算法．对三维接触问题,滑动方向的确定一直是个难点,为此,该文采用作者提出的组合规划法和迭代法对各向异性摩擦本构模型进行分析,数值结果说明了模型与算法的正确性。     

正交各向异性摩擦接触分析的一个二阶锥线性互补法

建立了用于各向异性摩擦接触分析的一个新型互补模型:二阶锥线性互补模型.通过与弹塑性力学的类比,并引入"线性二阶锥互补"的概念,将正交各向异性摩擦接触定律表达为一个二阶锥线性互补模型.在此基础上,在参变量变分原理的框架下,建立了正交各向异性摩擦接触问题的有限元列式.由于避免了对摩擦锥的显式线性化,使得该文模型的变量个数较线性互补模型小很多,而解的精度又高很多.文末通过算例,说明了方法对于正交各向异性摩擦接触分析的有效性.     

浅论力学研究中的一些思维方法与力学美

 浅论力学研究中的对偶互补(阴阳互补)与对称性、简单性、顺向思维与逆向思维、以 及力学美等问题.     

简论岩体的力学模型

从岩体的地质特征和力学行为出发，分别讨论岩体的力学模型，运用劳丹的科学合理性模式分析连续介质和不连续介质两类力学模型的作用和地位，提出两类模型不是对产的而是互补的，今后的发展是建立既能反映性又能反映不连续性的统一的岩体力学模型。     

纤维增强复合材料界面的力学行为

研究材料的界面和表面的力学行为与破坏机理,是当代材料科学、力学、物理学的前沿课题之一,而复合材料界面问题更有其自身的特殊性和复杂性。本文结合笔者的研究工作重点讨论了纤维复合材料界面力学的共性问题,阐述了复合材料界面的性质、复合材料界面的力学模型和理论、界面力学表征的实验研究、界面损伤破坏机理、界面对复合材料力学性能的影响等5个方面。     

接触问题的互补变分原理及非线性互补模型

给出了接触问题的互补虚功原理,互补能量原理及变分不等式等变分提法,并讨论了三类提法的关系。其此建立了有限维非线性互补模型并给出解的存在唯一性定理。文中还阐明了有,无摩擦接触问题之间以及二维和三维有摩擦接触问题之间的本质区别。     

接触问题的互补变分原理及非线性互补模型

给出了接触问题的互补虚功原理，互补能量原理及变分不等式等变分提法，并讨论了三类提法的关系。其此建立了有限维非线性互补模型并给出解的存在唯一性定理。文中还阐明了有，无摩擦接触问题之间以及二维和三维有摩擦接触问题之间的本质区别。     

不连续介质力学分析的块体-夹层模型

基于岩体等不连续介质的实际结构特征，利用约束变分原理，建立了可同时用于不连续介质和连续介质力学分析的块体 夹层模型．该方法利用拉格朗日乘子法和罚函数法把单元间的连续条件作为约束条件引入泛函中，把不连续介质问题和连续介质问题统一处理，既能方便地求解连续介质力学问题，更重要的是能方便地处理不连续介质力学问题，如岩体结构．由块体 夹层模型可导出刚性有限元和弹性有限元（常应变元）的列式，而且块体的形状可以是任意多边形     

粗糙颗粒的随机离散元模拟——随机法向接触定律

真实颗粒的力学性质会受到其随机粗糙表面的影响,然而在传统离散元模拟中通常假设颗粒具有光滑表面,因此有必要在定量考虑颗粒表面粗糙度的基础上改进离散元的接触模型。本文基于经典 Greenwood-Williamson(GW)模型通过理论分析和数值模拟提出了一种可以考虑颗粒表面粗糙度的法向接触定律;开发了基于 Newton-Raphson迭代的数值计算方法,通过输入颗粒重叠量和一系列表面粗糙系数计算总接触力;讨论了改进计算方法效率和准确性的相关问题。相对于 GW模型中接触关系的复杂积分表示,拟合得到新随机接触定律的表达式具有类似 Hertz定律的简单结构,只包含一个表征颗粒表面粗糙度标准偏差的新增参数,σ,可以方便的引入当前离散元模拟程序中进行计算。     

求解力学模型的过程中选择数学工具易出现的问题

针对一些力学模型,特别是力学中断裂模型的求解及特殊材料力学特征分析和描述过程中所采用的数学工具(如保形映照、幂级数展开、周期性和双周期性假设等)的准确性,进行了分析和说明。指出了一些在具体问题求解过程中采用特殊数学工具或方法可能产生的问题和忽略的因素,以及产生这些问题的原因。本文对同行在研究具体力学模型求解时的数学方法选择具有一定的参考作用。     

工程力学中的互补问题:算法

工程力学里很多问题存在互补关系,文献[1]介绍了有关的数学模型。本文介绍了近年来求解互补问题的几种主要方法,包括投影方法、内点方法、方程组方法、延拓方法以及无约束优化方法。与此同时,也介绍了作者近期在互补问题算法方面的一些研究工作。     

A positive interior-point algorithm for nonlinear complementarity problems

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Planar multiple-contact problems subject to unilateral and bilateral kinetic constraints with static Coulomb friction

This paper is concerned with contact problems. A planar multiple-contact problem subject to unilateral and bilateral kinetic constraints with static friction is studied using the complementarity method. First, this paper discusses the one-to-one correspondence of solutions of the contact problems of concern and of the corresponding complementarity models. An enhanced complementarity model is proposed by adding missed tangential acceleration constraints into previous complementarity models. Solutions of the proposed complementarity model and solutions of the contact problem are proven to exhibit one-to-one correspondence, which may not be guaranteed in the previous complementarity models. Then, this paper applies linear complementarity theory to investigate the properties of the solutions of the proposed complementarity model. For both unilaterally constrained contact problems and bilaterally constrained contact problems, the existence of solutions and boundedness of solutions are proven. Sufficient conditions for the uniqueness of solutions and finiteness of the number of solutions are also provided. Several numerical examples are given to show the non-uniqueness of solutions or the infiniteness of the number of solutions. Such phenomena demonstrate the non-smoothness of the contact problems discussed herein.     

CrMnFeCoNi纳米晶温度相关的拉伸行为研究

摘要：高熵合金是一种由多种主元元素组成的新型合金。实验研究表明等原子比CrMnFeCoNi高熵合金在低温下具有比室温更高的拉伸强度和断裂韧性。本文针对这一现象,利用分子动力学模拟对平均晶粒尺寸为6 nm的CrMnFeCoNi纳米晶在300、200和77 K下分别进行拉伸模拟。模拟研究揭示了纳米尺度CrMnFeCoNi高熵合金力学行为的温度效应和强韧机理。微结构演化分析表明：低温下,塑性变形阶段,滑移系开动的较少,位错滑移所受的阻力越大,屈服强度和抗拉强度越大;模型破坏时,孔洞缺陷形核较慢,更多孔洞缺陷演化成断口,更多的断口分摊拉伸应变,使得高熵合金纳米晶的低温韧性更好。     

RECURRENT NEURAL NETWORK MODEL BASED ON PROJECTIVE OPERATOR AND ITS APPLICATION TO OPTIMIZATION PROBLEMS

The recurrent neural network (RNN) model based on projective operator was studied. Different from the former study, the value region of projective operator in the neural network in this paper is a general closed convex subset of n-dimensional Euclidean space and it is not a compact convex set in general, that is, the value region of projective operator is probably unbounded. It was proved that the network has a global solution and its solution trajectory converges to some equilibrium set whenever objective function satisfies some conditions. After that, the model was applied to continuously differentiable optimization and nonlinear or implicit complementarity problems. In addition, simulation experiments confirm the efficiency of the RNN.     

CONTACT PROBLEMS AND DUAL VARIATIONAL INEQUALITY OF 2－D ELASTOPLASTIC BEAM THEORY

ＣＯＮＴＡＣＴＰＲＯＢＬＥＭＳＡＮＤＤＵＡＬＶＡＲＩＡＴＩＯＮＡＬＩＮＥＱＵＡＬＩＴＹＯＦ２－ＤＥＬＡＳＴＯＰＬＡＳＴＩＣＢＥＡＭＴＨＥＯＲＹＤａｖｉｄＹａｎｇＧａｏ（高扬）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ．ＶｉｒｇｉｎｉａＰｏｌｙｔ...     

Formulating Dynamic Multi-Rigid-Body Contact Problems with Friction as Solvable Linear Complementarity Problems

A linear complementarity formulation for dynamic multi-rigid-body contact problems with Coulomb friction is presented. The formulation, based on explicit Euler integration and polygonal approximation of the friction cone, is guaranteed to have a solution for any number of contacts and contact configuration. A model with the same property, based on the Poisson hypothesis, is formulated for impact problems with friction and nonzero restitution coefficients. An explicit Euler scheme based on these formulations is presented and is proved to have uniformly bounded velocities as the stepsize tends to zero for the Newton–Euler formulation in body co-ordinates.     

New models for a class of adhesive grippers. The hemivariational inequality approach

Summary A hemivariational inequality model for adhesive grasping problems is proposed and studied in this paper. The unilateral frictionless and frictional contact effects between the fingertips and the grasping object that lead to linear complementarity problems with singular matrices for the study of static equilibrium of the gripper-object system are generalized here to cover adhesive multifingered grippers. Adhesive effects are modelled by appropriately defined, generally nonconvex, yield sets in the space of contact stresses, friction stresses, gaps or frictional slips and their combinations. The hemivariational inequality problem that arises may involve copositive plus, symmetric matrices and nonempty closed sets for the frictionless gripper problem and copositive plus, nonsymmetric matrices with starshaped sets for the frictional case. Solvability conditions that guarantee the existence of a solution to the gripper problem are given. They specify the conditions which are required to hold between external forces, fingertip mechanical behavior and finger placement in order to solve the gripper problem.     

Numerical method for dynamics of multi-body systems with two-dimensional Coulomb dry friction and nonholonomic constraints

Based on the dynamical theory of multi-body systems with nonholonomic constraints and an algorithm for complementarity problems, a numerical method for the multi-body systems with two-dimensional Coulomb dry friction and nonholonomic constraints is presented. In particular, a wheeled multi-body system is considered. Here,the state transition of stick-slip between wheel and ground is transformed into a nonlinear complementarity problem(NCP). An iterative algorithm for solving the NCP is then presented using an event-driven method. Dynamical equations of the multi-body system with holonomic and nonholonomic constraints are given using Routh equations and a constraint stabilization method. Finally, an example is used to test the proposed numerical method. The results show some dynamical behaviors of the wheeled multi-body system and its constraint stabilization effects.