平面电磁弹性固体的虚边界元——最小二乘配点法

从电磁弹性固体平面问题的基本方程出发,依据弹性力学虚边界元法的基本思想,利用电磁弹性固体平面问题的基本解,提出了电磁弹性固体平面问题的虚边界元——最小二乘配点法。电磁弹性固体的虚边界元法在继承传统边界元法优点的同时,有效地避免了传统边界元法的边界积分奇异性的问题。由于仅在虚实边界选取配点,此方法不需要网格剖分,并且不用进行积分计算。最后给出了一些具体算例,并和已有的解析解进行了对比,结果表明提出的虚边界元方法有很高的精度。     

超弹性材料过盈配合的轴对称平面应力解答

主要讨论了一种采用超弹性材料轴对称过盈配合的橡胶减震元件,推导了橡胶材料过盈配合平面应力的大变形解析解,并应用 ABAQUS 有限元软件进行数值模拟,分析和对比了解析解和数值解的结果,定量分析材料泊松比和体积刚度对问题的影响。     

Drucker-Prager弹塑性本构关系积分:考虑非关联流动与各向同性硬化

考虑非关联流动法则以及各向同性硬化条件,采用广义中点法(Generalized Midpoint Method,GMM)进行Drucker-Prager(DP)弹塑性本构关系数值积分,给出调整后最终应力的解析解.GMM 属于隐式算法,具有良好的计算精度与数值稳定性;最近点投影法(Closest Point Project Method,CPPM)是其特例,具有一阶精度并且无条件稳定.DP 塑性势函数的特殊性质导致上述GMM 解由初始应力状态与应变增量显式确定,无需迭代求解,因此计算效率大幅提高,同时避免了迭代过程的收敛性问题.数值算例证明:当加载偏离角度较大时,GMM(ξ=1/2)的计算精度高于CPPM,可适应更大的加载步长;而对于比例加载,任意GMM 等同于精确解,采用CPPM 可获得最高的计算效率.推导了满足DP 屈服准则厚壁圆筒的弹塑性理论解,对比验证算法精度.采用非关联流动各向同性线性硬化DP 材料模拟厚壁圆筒变形局部化效应.     

楔形体匀速和自由落体水弹性砰击的半解析法求解EI北大核心CSCD

针对二维弹性楔形体入水过程的流固耦合问题,提出一种基于耦合Wagner理论和模态叠加法的半解析解方法。结构湿表面的速度势基于Wagner理论求解并考虑了结构弹性影响。砰击压力根据伯努利方程求解,为提高求解精度考虑了伯努利方程中速度平方项。通过平均弹性速度修正模型推导出附加质量和阻尼矩阵,将其代入固体动力学方程从而建立统一的流固耦合方程,耦合方程通过基于隐式的Newmark-β算法实现求解。通过计算楔形体垂直恒速和自由落体入水两种运动状态,并与基于半解析、数值和试验的文献结果进行了对比,验证了所提理论的可靠性。     

有限元法中间构形初始解预示的Laplace-Beltrami方程法

一步有限元法具有高效的计算能力，在板料成形模拟方面得到了广泛的应用，但它存在应力计算精度不足的问题。为弥补这一不足，通过增加中间构形的方式，人们提出多步有限元法。而中间构形需根据初始解迭代计算获得，因此，初始解预示算法是多步有限元法的一个关键问题。该文把中间构形解耦分解为弯曲变形和拉伸变形两个独立的变形过程，且将弯曲变形作为中间构形的初始解预示，改善了多步有限元法的稳定性；并根据大位移小应变理论，建立了节点的位移约束条件；进一步，首次通过Laplace-Beltrami方程的建立和求解，实现了中间构形初始解的快速预示，该方法易于编程实现，稳定性好。通过典型零件数值算例的高效准确计算，验证了该算法的可行性和有效性。     

挤压成形过程灵敏度分析及模具型腔参数优化设计

以高温下的挤压成形加工过程优化设计问题为背景,针对应变率相关粘性固体本构关系的材料稳态非弹性变形过程提出了形状灵敏度分析方法,并对算法的效率进行了讨论,在此基础上研究了挤压成形模具的形状优化设计问题的数学模型和数值求解算法。给出了挤压成形模具的二维形状优化设计算例,数值结果验证了所给出的灵敏度分析算法和优化设计模型的正确性和可用性。     

三维热弹性力学问题的混合边界元法

本本文给出了三维无限大域内点热源作用下的位移、应力场基本解。采用基于虚拟热源法的间接边界元法和直接边界元法的混合边界元法求解三维有限域热弹性力学问题,有效地避免了热弹性力学问题中域内积分的处理。数值计算表明混合边界元法求热弹性力学问题具有简单方便、精度较高的优点。     

完全隐式返回映射算法对岩土地基问题的求解

针对岩土工程中的复杂力学问题,在弹塑性力学理论框架和非线性有限元理论基础上,采用非关联等向硬化Drucker-Prager模型的完全隐式积分算法—返回映射算法(Return Mapping Algorithm)编制了有限元求解程序。该算法可以避免预测应力漂移屈服面的现象,对准静态变形条件下的本构方程可以获得准确解,在迭代中使用Newton-Raphson法获得近似平方的收敛速率,具有较高的精确性和稳定性。对岩土工程中的地基问题进行求解,计算得出位移、应力等结果,模拟了塑性区随载荷步增加的演化过程,对地基极限承载力进行了解析解和数值解的对比。结果表明了算法的优越性、程序的正确性和实用性。     

基于当前构形的虚场方法识别正交各向异性材料力学参数

正交各向异性材料刚度矩阵随坐标系转动而变化,虚场方法中虚位移场的定义与数据点坐标有关,常用的基于参考构形全局坐标系的虚场方法直接忽略了变形过程中数据点的移动和材料坐标系转动,这样即使在弹性变形这样的小变形条件下也将导致材料力学参数识别结果不准确。针对上述问题该文提出用基于当前构形的虚场方法识别正交各向异性材料弹性力学参数,并用模拟试验验证了该方法的可靠性;定量地分析了数据点移动和转动对力学性能参数识别结果的影响,结果表明基于当前构形虚场方法,能够提高参数Q₁₂、Q₂₂识别的准确性。     

弹性力学Hamilton体系下的稳定问题

通过在Hellinger-Reissner广义势能中引入应变的非线性项,推导出了弹性力学Hamilton体系下的屈曲基本方程。并运用弹性力学方程组一般解的统一理论给出其一般解。最后作为例子,给出了两端简支的梁、组合梁和四边简支板、组合板的临界载荷,并与经典解做了比较。结果是严格弹性力学意义(没有引入任何几何变形假设)下的精确解。为衡量各种计入剪切变形的薄板、中厚板理论的准确性提供了一个标准。     

超弹性柔性结构与流体耦合运动的浸入边界法研究

浸入边界法是模拟大变形柔性弹性结构和粘性流体相互作用的重要数值方法之一。该文有效结合传统的反馈力方法和混合有限元浸入边界方法,对圆柱和方柱绕流后柔性悬臂梁流固耦合振动问题进行数值模拟。其中,固体采用超弹性材料,利用有限单元法求解,流体为不可压缩牛顿流体,使用笛卡尔自适应加密网格,利用有限差分法进行求解。通过数值计算,得到柔性超弹性结构的耦合振动特性和流场动态分布特性,并将计算结果同其他文献计算结果进行比较,验证了该耦合计算方法的可靠性。     

Finite element analysis of 3D elastic–plastic frictional contact problem for Cosserat materials

The objective of this paper is to develop a finite element model for 3D elastic–plastic frictional contact problem of Cosserat materials. Because 3D elastic–plastic frictional contact problems belong to the unspecified boundary problems with nonlinearities in both material and geometric forms, a large number of calculations are needed to obtain numerical results with high accuracy. Based on the parametric variational principle and the corresponding quadratic programming method for numerical simulation of frictional contact problems, a finite element model is developed for 3D elastic–plastic frictional contact analysis of Cosserat materials. The problems are finally reduced to linear complementarity problems (LCP). Numerical examples show the feasibility and importance of the developed model for analyzing the contact problems of structures with materials which have micro-polar characteristics.     

A simple yet accurate finite element procedure for computing stress intensity factors

A new finite element procedure for calculating stress intensity factors in elastic crack problems is developed. In common with a number of other approaches in the literature, the procedure combines the analytical singular fields present in a problem with a finite element treatment of the residual regular problem. What distinguishes the procedure is the use of path-independent integrals to balance the analytical and numerical contributions. A set of test problems with exact solutions is analysed and demonstrates that the procedure is readily implemented and can accurately evaluate stress intensity factors with a modest amount of computational effort. The application of two competing methods to the test problems further demonstrates that the new procedure is markedly superior in both its initial accuracy and its rate of convergence. The paper concludes with two additional illustrations of the procedure as applied to the single-edge crack and the centre crack; these also yield accurate results for little computational effort.     

Explicit Reproducing Kernel Particle Methods for large deformation problems

The explicit Reproducing Kernel Particle Method (RKPM) is presented and applied to the simulations of large deformation problems. RKPM is a meshless method which does not need a mesh structure in its formulation. Because of this mesh-free property, RKPM is able to simulate large deformation problems without remeshing which is often required for the mesh-based methods such as the finite element method. The RKPM shape function and its derivatives are constructed by imposing the consistency conditions. An efficient treatment of essential boundary conditions is also proposed for explicit time integration. The Lagrangian method based on the reference configuration is employed for the RKPM simulation of large deformation problems. Several examples of non-linear elastic materials are solved to demonstrate the performance of the method. The numerical experiment for the problem of underwater bubble explosion is also performed using the explicit Lagrangian RKPM formulation. © 1998 John Wiley & Sons, Ltd.     

Successive linear approximation for boundary value problems of nonlinear elasticity in relative-descriptional formulation

A method of successive linear approximation in current configuration for solving boundary value problems of large deformation in finite elasticity is proposed. Instead of using Lagrangian or Eulerian formulation, we can also formulated the problem relative to the current configuration, and linearize the constitutive function at the present state so that it leads to a linear boundary value problem for an incremental time step. Therefore, as linearization at present state proceed in time, problem for large deformation can be formulated. The idea is similar to the Euler’s method for differential equations. As an example for the proposed method, numerical simulation of bending a rectangular block into a circular section for Mooney-Rivlin material is given for comparison with the exact solution, which is one of the well-known universal solutions in finite elasticity.     

A new efficient numerical method and the dynamic analysis of composite laminates with piezoelectric layers

Firstly, a numerical method for the inversion of Laplace transform is developed and its accuracy is shown through examples. Then, a state-vector equation for the dynamic problems of piezoelectric plates is deduced directly from a modified mixed variational principle for piezoelectric bodies and its exact solution for the dynamic problems of simply supported rectangle piezoelectric plate is simply given. For multilayered hybrid plates, we derive the solution in terms of the propagator matrices. The techniques accounts for the compatibility of generalized displacements and generalized stresses on the interface both the elastic layers and piezoelectric layers, and the transverse shear deformation and the rotary inertia of laminate are also considered in the global algebraic equation of structure. Meanwhile, there is no restriction on the thickness and the number of layers. As an application of the numerical inversion of Laplace transform presented in this paper, typical numerical examples of the harmonic vibration and transient response are proposed and discussed. Since the highly accurate numerical results, they can serve as benchmarks to test various thick plate theories and various numerical methods, such as the finite and boundary element methods for transient response problems.     

Computation of stresses in non-homogeneous elastic solids by local integral equation method: a comparative study

The paper deals with the numerical implementation of local integral equations for solution of boundary value problems and interior computations of displacements and their gradients in functionally graded elastic solids. Two kinds of meshless approximations and one element based approximation are employed in various formulations. The numerical stability, accuracy, convergence of accuracy and cost efficiency are investigated in numerous test examples with exact benchmark solutions.     

炭黑增强橡胶复合材料的大变形细观力学模型

为考察炭黑对橡胶复合材料超弹性力学行为的影响,首先,利用不同填充体积分数的炭黑增强橡胶复合材料的准静态力学试验数据,对现有的基于均质化方法的"变形放大"细观力学模型的大变形表征能力进行了评估。其次,在此基础上提出了新的"第一不变量放大"关系,并获得了较为合理的预测结果。最后,利用随机序列吸附算法建立了较接近材料真实细观结构的球形颗粒填充数值模型,进行了大变形情况下的三维数值模拟;为考察颗粒聚集效应的影响,还设置了颗粒均匀随机分布和团聚随机分布两种形式。计算结果与试验数据的对照表明:提出的三维细观数值模型已经能在一定程度上预测填充橡胶的大变形宏观力学行为,且颗粒团聚随机分布模型的预测能力更好一些。试验结果验证了该模型的合理性,所建模型为进一步的相关研究提供了参考。     

Analysis of orthotropic behavior in convected coordinate frames

The aim of this contribution is to present a theoretical and numerical model applicable to large strain analysis of orthotropic bodies. This three-dimensional constitutive law which uses the concept of convected coordinate frame is devoted to materials presenting elastic orthotropic behaviors in the large deformation field such as the elastomer-fabric composite materials. The proposed model is implemented in a finite element code and numerical examples are given to demonstrate the effectiveness of the model and the numerical algorithms. Finally, the model is compared to experimental results obtained from a bulge test.     

A hybrid-mixed finite element formulation for the geometrically exact analysis of three-dimensional framed structures

This paper addresses the development of a hybrid-mixed finite element formulation for the quasi-static geometrically exact analysis of three-dimensional framed structures with linear elastic behavior. The formulation is based on a modified principle of stationary total complementary energy, involving, as independent variables, the generalized vectors of stress-resultants and displacements and, in addition, a set of Lagrange multipliers defined on the element boundaries. The finite element discretization scheme adopted within the framework of the proposed formulation leads to numerical solutions that strongly satisfy the equilibrium differential equations in the elements, as well as the equilibrium boundary conditions. This formulation consists, therefore, in a true equilibrium formulation for large displacements and rotations in space. Furthermore, this formulation is objective, as it ensures invariance of the strain measures under superposed rigid body rotations, and is not affected by the so-called shear-locking phenomenon. Also, the proposed formulation produces numerical solutions which are independent of the path of deformation. To validate and assess the accuracy of the proposed formulation, some benchmark problems are analyzed and their solutions compared with those obtained using the standard two-node displacement/ rotation-based formulation.