改进的速度迭代弹塑性大变形动力半显式算法

提出了基于速度迭代的弹塑性大变形动力半显式算法，并且在此基础上采用拟弯曲膜单元，结合有模卸载方式数值模拟了U形弯曲以及S形导轨回弹过程，着重比较了动力半显式算法与动力显式算法和实验的回弹结果．给出了动力半显式算法的迭代格式和收敛标准．     

刚粘塑性强化球形薄壳在撞击体作用下的大变形动力分析

本文研究了在平头圆柱体的冲击下，薄球形壳的动力大变形。通过等度量变换，给出了球壳的变形模态。在Ｐｅｒｚｙｎａ和Ｓｙｍｏｎｄｓ的粘塑性本构模型基础上，设材料从Ｍｉｓｅｓ屈服条件，并假定弯矩的膜力不耦合。根据刚粘塑性强化材料的变分原理。给出球壳的运动方程结果与实验进行了比较，二者吻合较好。     

变形—损伤耦合的超塑性恒压轴对称充模胀形的有限元模拟

采用大变形刚粘塑性有限元法模拟超塑性恒压轴对称充模胀形过程，分析了模具几何参数及材料参数对胀形过程中材料的流变行为、胀形制件厚度分布和成形时间的影响规律，给出了质点的流动轨迹，不同时刻制件的剖面形状及应力、应变分布；基于修正的Ｇｕｒｓｏｎ粘塑性势推导了内部空洞体积分数累积增大模型并据此进行了变形－损伤耦合计算。     

粘塑性材料成形过程的有限元分析

为了确定大型铝机轮等温锻造的变形力及揭示轮缘处形成折叠的原因,本文用刚一粘塑性有限元法对模拟件的成形过程进行了全面数值模拟。模拟计算和实验结果表明,有限元确定的等温锻造过程的变形力,可作为选择设备吨位的依据,根据刚-粘塑性有限元法所预测的金属流动规律,发现零件的形状很大程度上决定了轮缘处容易形成折叠。适当改进模具结构和改善润滑条件,有助于避免折叠缺陷的产生。     

金属体积成形三维数值仿真的研究进展

金属体积成形是一个具有几何非线性和物理非线性的复杂的塑性大变形问题,采用基于刚塑性／刚粘塑性有限元法的ＣＡＥ仿真技术对其分析,则可掌握其详细的变形规律．本文对体积成形三维有限元仿真技术的发展作了全面的回顾,并详细总结了其中的关键技术、存在的技术难点和发展趋势．     

基于最小加速度原理的刚塑性动力问题

应用有限变形的最小加速度原理，推导出了小变形或有限变形构件受到刚性飞射物撞击时的刚塑性运动方程，指出该方法具有直接、简捷和可靠的特点。     

用隐式方法和WENO格式计算悬停旋翼跨声速无粘流场

寻找一种能够准确计算以涡为主要特征的复杂流场和克服尾迹耗散问题的数值方法,一直是旋翼空气动力学研究的热点和难点。本文发展了一种基于高阶迎风格式计算悬停旋翼无粘流场的隐式数值方法。无粘通量采用Roe通量差分分裂格式,为提高精度,使用五阶WENO格式进行左右状态插值,并与MUSCL插值进行比较。为提高收敛到定常解的效率,时间推进采用LU-SGS隐式方法。用该方法对一跨声速悬停旋翼无粘流场进行了数值计算,数值结果表明WENO-Roe的激波分辨率高于MUSCL-Roe,体现出了格式精度的提高对计算结果的改善,LU-SGS隐式方法的计算效率比5步Runge-Kutta显式方法的高。     

基于刚（粘）塑性流动理论的自然单元法研究

将自然单元法与刚（粘）塑性流动理论相结合,对自然单元法在金属塑性成形过程数值模拟中的应用进行了研究。采用基于Voronoi图和Delaunay三角化结构的Non-Sibsonian插值方法构造近似速度场向量,实现无网格方法中速度边界条件的直接精确施加,提出了基于刚（粘）塑性流动理论的无网格自然单元法。运用不完全广义变分...     

近似不可压软材料动力分析的完全拉格朗日物质点法

物质点法(MPM)在模拟非线性动力问题时具有很好的效果,其已被广泛应用于许多大变形动力问题的分析中.然而传统的MPM在模拟不可压或近似不可压材料的动力学行为时会产生体积自锁,极大地影响模拟精度和收敛性.本文针对近似不可压软材料的大变形动力学行为,提出一种混合格式的显式完全拉格朗日物质点法(TLMPM).首先基于近似不可压软材料的体积部分应变能密度,引入关于静水压力的方程;之后将该方程与动量方程基于显式物质点法框架进行离散,并采用完全拉格朗日格式消除物质点跨网格产生的误差,提升大变形问题的模拟精度;对位移和压强场采用不同阶次的B样条插值函数并通过引入针对体积变形的重映射技术改进了算法,提升算法的准确性.此外,算法通过实施一种交错求解格式在每个时间步对位移场和压强场依次进行求解.最后,给出几个典型数值算例来验证本文所提出的混合格式TLMPM的有效性和准确性,计算结果表明该方法可以有效处理体积自锁,准确地模拟近似不可压软材料的大变形动力学行为.     

类橡胶材料变形直到破坏的显式本构模型

本文通过直接、显式的方法提出一个多轴可压缩应变能弹性势来模拟类橡胶材料受载荷直到软化破坏的变形行为．首先，我们提出一个多轴可压缩应变能函数；其次，通过特定的不变量，该多轴应变能函数在单轴拉伸，平面应变和等双轴拉伸三个基准实验的情况下，可以退化为各自的单轴形函数形式；再次，我们显式给出带有软化破坏特性的形函数；最后，模型结果和试验数据可以精确匹配，同时可以预测材料临近破坏以后，接下来的变形行为．     

Theoretical model for elliptical tube laterally impacted by two parallel rigid plates

An analytical model is developed to study the crushing behavior and energy absorption capability of a single elliptical tube impacted by two parallel rigid plates, with and without consideration of the strain hardening effect. The four-hinge collapse mechanism is used, and the governing equation is derived from Lagrange equations of the second kind. The numerical simulation of the dynamic response of the elliptical tube under impact using the finite element explicit code LS-DYNA is performed. The reaction force-displacement curve and displacement-time curve of the plate obtained from the two methods are in good agreement.     

Rough surface contact analysis by means of the Finite Element Method and of a new reduced model

This article presents two approaches of a normal frictionless mechanical contact between an elastoplastic material and a rigid plane: a full scale finite element analysis (FEA) and a reduced model. Both of them use a representative surface element (RSE) of an experimentally measured surface roughness. The full scale FEA is performed with the Finite Element code Zset using its parallel solver. It provides the reference for the reduced model. The ingredients of the reduced model are a series of responses that are calibrated by means of FEA on a single asperity and phenomenological rules to account for asperity–asperity interaction. The reduced model is able to predict the load–displacement curve, the real contact area and the free volume between the contacting pair during the compression of a rough surface against a rigid plane. The CPU time is a few seconds for the reduced model, instead of a few days for the full FEA.     

Explicit computational method of dynamic response for non-viscously damped structure systems

Non-viscous damping models in which the damping forces depend on the past history of velocities via convolution integrals over some kernel functions have been raised in many engineering fields. This paper describes an explicit computational method of dynamic response for the non-viscously damped structure systems. The explicit formula is derived using the differential property of convolution and the central difference formula of acceleration. The explicit computational procedure of dynamic response is given in detail. Finally, the dynamic responses of MDOF structure system with double exponential model dampers and SDOF structure system with Gaussian model damper are computed using the proposed explicit method. The accuracy and efficiency are discussed by comparison with other two developed methods.     

Formulating Three-Dimensional Contact Dynamics Problems

ABSTRACT

Complementarity formulations are a promising approach for solving dynamic multi-rigid-body contact problems. Two aspects of simulating contact in a complementarity setting are addressed here. First, an explicit formulation of the differential equations governing contact points for bodies of general surface geometry is developed. These equations may be used to integrate the contact position and to set up the basic dynamics equations. Second, an efficient method for handling frictionless planar contacts of arbitrary boundary shape is presented. Throughout, the problem is set up as explicitly as possible, with special attention being given to the way that the contact geometry is related to the dynamics.     

Impact of a finite elastic-viscoplastic bar

A method for predicting the response of strain-rate sensitive structures under dynamic loading is developed. It is based on a finite difference method, the incremental theory of plasticity, and an elastic work-hardening viscoplastic material idealization. The strain-rate effect, loading and unloading conditions, and wave interactions are automatically accounted for, and adjusted if necessary, as the deformation proceeds. No iteration is required even if the field equations are nonlinear (e.g. non-linear constitutive equations, large deformation, or complicated geometry). We solve as an example the small deflection of a finite bar with a concentrated tip mass. The accuracy is comparable to that obtained by the well-known method of characteristics, a powerful tool for solving elastic-viscoplastic wave problems but which is restricted to small deflections and simple geometry. Because of the form of the constitutive relation selected (elastic work-hardening visco-plastic), several important new features of the dynamics response are brought out. These features are not revealed when simpler, computationally-convenient constitutive relations, such as rigid ideal-viscoplastic, rigid work-hardening viscoplastic and elastic ideal-viscoplastic are used.     

An analysis of the plane-strain compression of a three-layer strip

Summary  The problem considered here is that of the plane-strain compression of a long symmetric strip of a three-layered material between rigid, parallel, rough plates. Two combinations of layers are examined: (a) a viscoplastic material placed between two layers of a rigid/perfectly plastic material, and (b) a rigid/perfectly plastic material placed between two layers of a viscoplastic material. Closed-form solutions are presented for each combination, and qualitative differences between these solutions and solutions obtained for homogeneous materials are discussed. A possible effect of asymptotic behaviour of the solution in the vicinity of maximum-friction surfaces on the general structure of the solution is mentioned. Received 24 July 2000; accepted for publication 6 February 2001     

On dynamic plastic mode-form solutions

Discussion is given of the significance and calculation of dynamic plastic mode-form solutions for small deflections of structures of rigid perfectly-plastic materials subjected to load systems of fixed distribution and magnitude. These solutions have separated form, with velocity the product of a scalar function of time by a vector-valued function of space variables. The relation is shown on the one hand to mode-form solutions for a structure of viscoplastic material, and on the other hand to limit-load solutions for those of perfectly-plastic behavior. Numerical examples are given for circular plates of material obeying the Tresca and Mises laws.     

Quasi-static compression and spreading of an asymptotically thin nonlinear viscoplastic layer

The problem of quasi-static compression and spreading (squeezing) of a thin viscoplastic layer between approaching absolutely rigid parallel-arranged plates is solved using asymptotic integration methods rapidly developed in recent years in the mechanics of deformable thin bodies. A solution symmetric about the coordinate axes is sought in the same region of the layer as in the classical Prandtl problem. The layer material is characterized by a yield point and a hardening function relating the intensities of the stress and strain rate tensors. The conditions of no-flow and reaching certain values by tangential stresses are imposed on the plate surfaces. The coefficients at the terms of the asymptotic expansions corresponding to the minus first and zero powers of the small geometrical parameter are obtained. An approximate analytical solution in the case of power hardening and large Saint-Venant numbers is given. The physical meaning of the roughness coefficient characterizing the cohesion between the plates and viscoplastic material is discussed.