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1.
提出了一种计算二维有限变形弹塑性摩擦接触问题形状设计灵敏度的算法. 采用主动 集策略和mortar方法处理接触边线上的约束条件. 在mortar接触边线的切线和法线方向上 采用相同的名义罚函数,提出基于名义罚函数的移动摩擦锥算法来正则化接触约束条件,发 展了一种新的二维多体有限变形摩擦接触算法. 在此基础上, 通过将离散形式的摩擦接触问题 控制方程对形状设计变量微分,得到了该路径相关问题的直接微分法解析设计灵敏度 计算格式, 其节点位移灵敏度方程在每个增量步不用迭代、直接求解. 与国际上现有 的二维多体有限变形摩擦接触问题的解析设计灵敏度算法相比,本算法不需分 解为法向和切向推导,表达式较简洁,便于编程实现. 数值算例验证了算法的精度 和有效性.  相似文献   

2.
形状设计灵敏度分析的改进的再生核质点法   总被引:3,自引:0,他引:3  
基于物质导数概念和直接微分法,将再生核质点法应用于形状设计灵敏度分析(DSA)中。导出了基于无网格近似的灵敏度方程,特别强调了在考虑形状函数关于设计变量的物质导数时无网格方法与有限元法的不同。通过对RKPM形状函数及其物质导数进行矩式显式表述,提高了无网格方法的计算效率。对两个二维线弹性问题进行了位移灵敏度和应力灵敏度分析,计算结果与解析解吻合的很好;同时通过对通常的RKPM和改进的RKPM计算耗时的比较,显示了该方法不仅有效,而且可以显著地提高计算效率。  相似文献   

3.
大变形中摩擦接触问题的数值模拟及应用   总被引:11,自引:0,他引:11  
大变形的摩擦接触是复杂的非线性问题 ,本文介绍了一种处理摩擦接触问题的数值方法。采用接触单元技术模拟接触界面 ,基于弹塑性理论形式的非经典Coulomb摩擦定律及罚函数方法建立了摩擦接触的增量本构关系。结合大变形的增量分析格式给出了积分摩擦接触本构方程的回映方法。这种处理摩擦接触问题的方法计算简单、使用方便。给出的计算实例及应用实例说明了方法的精度与稳定性  相似文献   

4.
基于非均匀有理B样条(NURBS)曲面建模技术,边界物理量同样用NURBS基函数插值,推导出三维声场等几何边界积分方程。进一步以控制点为设计变量,用直接微分法推导出等几何敏感度边界积分方程,给出声场声压对形状参量的敏感度。针对边界积分方程中的超奇异积分,使用奇异相消技术并结合Cauchy主值积分和Hadamard有限部分积分处理,给出了超奇异积分的NURBS插值半解析表达式。数值算例验证了本文算法求解声学结构形状敏感度的有效性,为声学结构的整体形状优化打下基础。  相似文献   

5.
薛冰寒  林皋  胡志强  庞林 《力学学报》2016,48(3):615-623
摩擦接触问题是计算力学领域最具挑战性的问题之一,接触系统的泛函具有非线性、非光滑的特点,导致接触算法的收敛性与精确性难以保证.因此将比例边界等几何分析(scaled boundary isogeometric analysis,SBIGA)与B可微方程组(B differential equation,BDE)相结合,提出了求解二维摩擦接触问题的比例边界等几何B可微方程组方法.在比例边界等几何坐标变换的基础上,通过虚功原理推导了关于边界控制点变量的接触平衡方程,表示成B可微方程组形式的接触条件可被严格满足,求解B可微方程组的算法的收敛性有理论保证.此比例边界等几何B可微方程组方法 (SBIGA-BDE)只需在接触体边界进行等几何离散,使问题降低一维,能精确描述接触边界,并可通过节点插入算法进行真实接触区域的识别.此外,由于几何建模和数值分析使用相同的基函数,节约了划分网格的时间.以赫兹接触问题和悬臂梁摩擦接触问题为例,通过与解析解及数值计算软件ANSYS计算结果进行对比,验证了该方法求解二维摩擦接触问题的有效性及高精度等特点.  相似文献   

6.
比例边界有限元是一种只需在边界上划分网格且无需基本解的半解析方法,能有效处理应力奇异性和无边界问题.论文提出了一种比例边界有限元的二阶灵敏度分析方法,可以准确而高效地求解响应关于参数的二阶梯度.首先通过建立仅需右特征向量的哈密顿矩阵特征灵敏度分析方程,发展了一种改进的比例边界有限元一阶灵敏度分析方法;其次,进一步通过构建二阶哈密顿矩阵特征灵敏度分析方程,并对比例边界有限元系统方程进行一系列二次直接微分,提出了一种半解析形式的比例边界有限元二阶灵敏度分析方法.该方法被应用于线弹性裂纹结构的形状灵敏度分析和不确定性传播分析.最后,给出了两个数值算例验证论文方法的有效性.  相似文献   

7.
多体系统动力学设计灵敏度分析直接微分法   总被引:1,自引:0,他引:1  
针对受完整约束的多体系统动力学微分/代数方程数学模型动态最优化设计问题,建立了通用的目标函数和约束方程,并以此为基础,用直接微分方法系统地推导出了计算设计灵敏度的通用公式,最后通过平面机械臂模型对理论结果和相应算法进行了验证.  相似文献   

8.
张磊  张严  丁喆 《力学学报》2022,54(4):1113-1124
时域响应灵敏度分析是时域梯度优化算法的基础. 灵敏度分析通常只涉及对设计变量的微分运算, 但时域响应灵敏度问题还涉及时间域的离散化. 因此, 微分和离散的先后顺序可能对时域响应灵敏度结果产生影响. 针对黏性阻尼系统时域响应灵敏度求解问题, 基于改进精细积分方法, 分别推导了先微分后离散和先离散后微分两种伴随变量方法. 其中, 先微分后离散法首先对由伴随变量构造的增广函数微分, 再利用改进精细积分方法在各离散时间点求解时域响应灵敏度; 而先离散后微分方法则首先在各离散时间点引入残值方程构造增广函数, 再对各增广函数进行微分以求解时域响应灵敏度. 通过数值算例验证了所提出方法的有效性和准确性, 并与传统基于Newmark的方法进行比较. 结果表明, 积分方案、数值离散误差以及离散和微分的先后顺序共同影响灵敏度的一致性误差. 综合考虑精度、效率和一致性问题, 基于改进精细积分的先微分后离散伴随变量法表现更优, 最适合应用于黏性阻尼系统时域梯度优化算法.   相似文献   

9.
富立  胡鸿奎  富腾 《力学学报》2017,49(5):1115-1125
基于非光滑动力学方法的多体系统接触碰撞分析是目前多体系统动力学的研究热点.本文采用牛顿-欧拉方法建立多体系统接触、碰撞问题的动力学模型,给出一种牛顿-欧拉型线性互补公式.该建模方法与目前一般采用的拉格朗日建模方法的不同之处是约束条件中除了库仑摩擦、单边约束之外还含有光滑等式约束.在建立系统动力学模型时,首先解除摩擦约束和单边约束得到原系统对应的基本系统.牛顿-欧拉方法采用最大数目坐标建立基本系统的动力学方程,由于坐标不相互独立,因此基本系统中带有等式约束,其数学模型为一组微分代数方程.借助约束雅可比矩阵,在基本系统微分代数方程中添加摩擦接触和单边约束对应的拉氏乘子,就可以得到系统全局运动的具有变拓扑结构特征的动力学方程,再结合非光滑约束互补条件便可构成完备的系统动力学模型.完备的动力学模型由动力学微分方程以及等式约束和不等式约束组成.线性互补公式采用分块矩阵形式进行推导,简化了推导过程.数值计算采用基于线性互补的时间步进算法.时间步进算法是目前流行的非光滑数值算法,其突出特点是可以免去数值积分中繁琐的事件检测过程,而数值积分过程中通过对线性互补问题的求解可以确定系统的触-离状态.通过对典型的曲柄滑块间隙机构进行数值分析,验证本文方法的有效性.  相似文献   

10.
本文用参数二次规划法来解有间隙带摩擦弹性接触问题。借助罚函数分别推导和详细描述了这类问题的接触刚度阵,从最小势能原理出发,得出相应的计算模型。对几个典型实例进行分析讨论,证明本文所提算法是比较有效的。最后,对接触流动函数及参变量的意义作了详细说明。  相似文献   

11.
A multibody frictional mortar contact formulation (Gitterle et al., 2010) is extended for the simulation of solids undergoing finite strains with inelastic material behavior. The framework includes the modeling of finite strain inelastic deformation, the numerical treatment of frictional contact conditions and specific finite element technology. Several well-established and recent models are employed for each of these building blocks to capture the distinct physical aspects of the deformation behavior. The approach is based on a mortar formulation and the enforcement of contact constraints is realized with dual Lagrange multipliers. The introduction of nonlinear complementarity functions into the frictional contact conditions combined with the global equilibrium leads to a system of nonlinear equations, which is solved in terms of the semi-smooth Newton method. The resulting method can be interpreted as a primal–dual active set strategy (PDASS) which deals with contact nonlinearities, material and geometrical nonlinearities in one iterative scheme. The consistent linearization of all building blocks of the framework yields a robust and highly efficient approach for the analysis of metal forming problems. The effect of finite inelastic strains on the solution behavior of the PDASS method is examined in detail based on the complementarity parameters. A comprehensive set of numerical examples is presented to demonstrate the accuracy and efficiency of the approach against the traditional node-to-segment penalty contact formulation.  相似文献   

12.
Galin’s classical work (PMM J Appl Math Mech 9:413–424, 1945) on the contact of a rigid flat-ended indenter with an elastic half-plane with partial slip was the first successful attempt to take into account friction in the problem of normal contact. As Galin was unable to find an exact solution of the formulated problem, the problem of contact with partial slip of a rigid punch with an elastic half-plane was challenged by many researchers. At the same time Galin’s seminal work stimulated development of solutions for other contact problems with friction that feature different punch geometries and different material responses. This paper presents an overview of the developments in the area of elastic contact with partial slip. In the spirit of Galin’s work the focus is placed on contributions with substantial analytical merit.   相似文献   

13.
接触力学的发展概况   总被引:19,自引:0,他引:19  
接触问题的解法,最先在弹性理论中得到发展且比较完善;以后,考虑到粘弹性、塑性、各向异性、动力学和运动学特性,而大大地发展了各种接触问题,远远超过了弹性理论的范围.本文对接触问题进行了分类,介绍了经典、非经典的弹性接触理论的发展概况.最后,比较详细地分析了国内外当前的研究结果和发展动向.  相似文献   

14.
In structural analysis of large masonry structures, nondemanding computation effort, numerical stability and simplified model assembly and meshing often have a higher priority over precise details of local stress or strain responses. This paper presents the development of a Fourier-based incremental homogenisation technique, where the macro–micro transformations of mechanical variables are derived by incremental variational problems to minimise the potential energy in representative volume elements (RVEs) with respect to local fluctuating displacement fields expanded in Fourier series. In addition to the proposed homogenisation technique, a unilateral damage–plasticity constitutive model for mortar joints in the RVE is developed within the framework of thermomechanics, which accounts for the stiffness and strength degradation (or recovery) due to the transverse crack opening/closing in the mortar joints. The numerical solution for the homogenisation problem and the performances of the proposed coupled-damage plastic mode and Fourier-based homogenisation scheme verified by detailed case studies are presented. It has been shown that the computational effort of the analysis with the proposed modelling technique can be considerably reduced by more than 20% as compared with that of the discrete modelling technique.  相似文献   

15.
In this study the tangential partial slip problems in Hertzian contact regions are treated by a numerical technique. The tangential loading may include tangential forces in the contact plane and a twisting moment normal to the contact plane. The Coulomb’s law of friction and the property that the direction of friction must oppose the relative motion lead to nonlinear equations. The Newton-Raphson method is utilized to solve these nonlinear equations. Numerical results for tangential tractions and sizes of stick and slip zones may be determined, and they agree with existing analytical results for circular contacts.  相似文献   

16.
砖墙在爆炸冲击震动作用下的动力反应非常复杂,本构关系很难精确建立。本文阐述了砖墙几种常用的有限元模拟方法,分析各种方法的优缺点,确定采用一种砖块和砂浆分开的精细化建模的三维砖墙有限元模型;通过LS-DYNA软件,得到砖墙在水平爆炸冲击震动荷载下的破坏过程,计算结果与实验现象很好。研究表明:该种分析模型综合考虑了砖块和砂浆之间复杂的相互作用,并且对砂浆层进行了单独建模,保证了砖墙在数值模拟上的真实性和正确性,因此可以准确地模拟出实验中砖块之间砂浆层的损伤积累破坏。  相似文献   

17.
A unified treatment of axisymmetric adhesive contact problems is provided using the harmonic potential function method for axisymmetric elasticity problems advanced by Green, Keer, Barber and others. The harmonic function adopted in the current analysis is the one that was introduced by Jin et al. (2008) to solve an external crack problem. It is demonstrated that the harmonic potential function method offers a simpler and more consistent way to treat non-adhesive and adhesive contact problems. By using this method and the principle of superposition, a general solution is derived for the adhesive contact problem involving an axisymmetric rigid punch of arbitrary shape and an adhesive interaction force distribution of any profile. This solution provides analytical expressions for all non-zero displacement and stress components on the contact surface, unlike existing ones. In addition, the newly derived solution is able to link existing solutions/models for axisymmetric non-adhesive and adhesive contact problems and to reveal the connections and differences among these solutions/models individually obtained using different methods at various times. Specifically, it is shown that Sneddon’s solution for the axisymmetric punch problem, Boussinesq’s solution for the flat-ended cylindrical punch problem, the Hertz solution for the spherical punch problem, the JKR model, the DMT model, the M-D model, and the M-D-n model can all be explicitly recovered by the current general solution.  相似文献   

18.
A multi-scale model for the structural analysis of the in-plane response of masonry panels, characterized by periodic arrangement of bricks and mortar, is presented. The model is based on the use of two scales: at the macroscopic level the Cosserat micropolar continuum is adopted, while at the microscopic scale the classical Cauchy medium is employed. A nonlinear constitutive law is introduced at the microscopic level, which includes damage, friction, crushing and unilateral contact effects for the mortar joints. The nonlinear homogenization is performed employing the Transformation Field Analysis (TFA) technique, properly extended to the macroscopic Cosserat continuum. A numerical procedure is developed and implemented in a Finite Element (FE) code in order to analyze some interesting structural problems. In particular, four numerical applications are presented: the first one analyzes the response of the masonry Representative Volume Element (RVE) subjected to a cyclic loading history; in the other three applications, a comparison between the numerically evaluated response and the micromechanical or experimental one is performed for some masonry panels.  相似文献   

19.
Elastic and viscoelastic indentation of flat surfaces by pyramid indentors   总被引:1,自引:0,他引:1  
The present work presents the results of frictionless and adhesionless contact of flat surfaces by pyramid indentors. The materials of the contacting solids were modelled as homogeneous and isotropic, linear elastic, as well as linear viscoelastic. The theoretical analysis is complemented by experiments and numerical calculations. The results include explicit relations between the normal applied load and the depth of penetration, details of the contact area shapes, the surface stresses and the contact pressure distributions. The standard shapes of the Vickers, Berkovich and Knoop pyramids were examined in particular. Certain aspects of geometrical imperfections, transverse isotropy and adhesion were considered. When elasticity or viscoelasticity provide adequate models of material behavior, micro- or nano-indentation by sharp pyramid indentors can be very useful and perhaps the only possible test in probing mechanical properties of small volumes of materials. The results can be particularly useful in using instrumented indentation for assessing mechanical properties of materials at cryogenic temperatures, of bio-materials and of micro-electro-mechanical components.  相似文献   

20.
水泥砂浆在主动围压下的动态力学性能   总被引:1,自引:0,他引:1  
水泥砂浆等脆性材料的力学性能与所受围压的大小密切相关。为了研究水泥砂浆在围压下的动态力学性能,研制了适于分立式Hopkinson压杆加载的主动围压装置,最大预加载主动围压大于30 MPa。实验得到了水泥砂浆在不同围压、不同应变率下的轴向应力应变曲线,发现材料在围压作用下抗压强度和韧性大大提高并且整体进入了伪塑性,而材料的应变率效应也是显著的。  相似文献   

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