Generalized variational principles for linear elastic materials with voids

In this paper, the idea of variational principles of linear elastic theory is used to establish generalized variational principles for linear elastic materials with voids. The fundamental equations of linear elastic materials with voids used have already been established in Ref. [5].     

自动控制中弹性器件的弹力计算方法

基于能量守恒定律,推导出一种弹力的简单计算方法.该方法适用于电气自动控制过程中作为执行器件的线性和非线性弹性器件.考虑到自动控制过程中需要对器件能否产生弹力进行判断,特提出判定方法.举出实例对器件的弹力进行了分析和计算.     

Relection of elastic waves at the elastically supported boundary of a couple stress elastic half-space

The relection elastic waves at the elastically supported boundary of a couple stress elastic half-space are studied in this paper. Different from the classical elastic solid, there are three kinds of elastic waves in the couple stress elastic solid, and two of them are dispersive. The boundary conditions of a couple stress elastic half-space include the couple stress vector and the rotation vector which disappear in the classical elastic solids. These boundary conditions are used to obtain a linear algebraic equation set, from which the amplitude ratios of relection waves to the incident wave can be determined. Then, the relection coeficients in terms of energy lux ratios are calculated numerically, and the normal energy lux conservation is used to validate the numerical results. Based on these numerical results,the inluences of the boundary parameters, which relect the mechanical behavior of elastic support, on the relection energy partition are discussed. Both the incident longitudinal wave(the P wave) and incident transverse wave(the SV wave) are considered.     

Reflection and transmission of elastic waves through a couple-stress elastic slab sandwiched between two half-spaces

The reflection and transmission of elastic waves through a couple-stress elastic slab that is sandwiched between two couple-stress elastic half-spaces are studied in this paper. Because of the couple-stress effects, there are three types of elastic waves in the couple-stress elastic solid, two of which are dispersive. The interface conditions between two couple-stress solids involve the surface couple and rotation apart from the surface traction and displacement. The nontraditional interface conditions between the slab and two solid half-spaces are used to obtain the linear algebraic equation sets from which the amplitude ratios of reflection and transmission waves to the incident wave can be determined. Then, the energy fluxes carried by the various reflection and transmission waves are calculated numerically and the normal energy flux conservation is used to validate the numerical results. The special case, couple-stress elastic slab sandwiched by the classical elastic half-spaces, is also studied and compared with the situation that the classical elastic slab sandwiched by the classical elastic half-spaces. Incident longitudinal wave (P wave) and incident transverse wave (SV wave) are both considered. The influences of the couple-stress are mainly discussed based on the numerical results. It is found that the couple-stress mainly influences the transverse modes of elastic waves.     

平行微裂纹削弱的弹性体的各向异性有效性能与双周期裂纹模型

平行微裂纹损伤模型被用于构建各向异性损伤理论.当施加在代表性体积单元上的边界条件满足Hill条件时,基于平均场理论论证了由平行穿透裂纹损伤的弹性体仅有6个独立有效弹性常数.除了原各向同性基体的2个弹性常数外,与损伤相关的另外4个常数中,3个描述有效弹性常数的折减,1个描述损伤导致的拉剪耦合效应.结合单胞模型和有限元方法分析了双周期阵列平行裂纹问题,数值结果显示:裂纹呈一般双周期阵列时,拉剪耦合参数相比其它模量小很多;当裂纹密度一定时,改变裂纹的排列形式,面内剪切模量和面外剪切模量的折减呈现出不同的规律.     

Simulation of beam plastic forming with variable bending moments

A versatile generic elastic/plastic moment/curvature equation is used to simulate beam deflections. Solutions are obtained numerically and used to investigate whether forming equations based on the assumption of pure bending can be extended in a rational way to more complicated loadings. It is concluded that the answer is affirmative, with only knowledge of the elastic/plastic behavior associated with pure bending and the elastic behavior associated with the actual loading being needed to make the extension.     

On using many-particle interatomic potentials to compute elastic properties of graphene and diamond

The elastic properties of diatomic crystals are considered. An approach is proposed that permits calculating the elastic characteristics of crystals by using the interatomic interaction parameters specified as many-particle potentials, i.e., potentials that take into account the effect of the environment on the diatomic interaction. The many-particle interaction is given in the general form obtained in the framework of linear elastic deformation. It is shown that, by expanding in series in small deformation parameters, a group of nonlinear potentials frequently used to model covalent structures can be reduced to this general form. An example of graphene and diamond lattices is used to determine how adequately these potentials describe the elastic characteristics of crystals.     

Flutter analysis of rotating beams with elastic restraints

The aeroelastic stability of rotating beams with elastic restraints is investigated. The coupled bending-torsional Euler-Bernoulli beam and Timoshenko beam models are adopted for the structural modeling. The Greenberg aerodynamic model is used to describe the unsteady aerodynamic forces. The additional centrifugal stiffness effect and elastic boundary conditions are considered in the form of potential energy. A modified Fourier series method is used to assume the displacement field function and solve the governing equation. The convergence and accuracy of the method are verified by comparison of numerical results. Then, the flutter analysis of the rotating beam structure is carried out, and the critical rotational velocity of the flutter is predicted. The results show that the elastic boundary reduces the critical flutter velocity of the rotating beam, and the elastic range of torsional spring is larger than the elastic range of linear spring.     

Calculation of the added mass matrix of water impact of elastic wedges by the discrete vortex method

The discrete vortex method is used to obtain the added mass matrix of water entry of elastic structures. Based on the Wagner theory, the hydrodynamic loads are evaluated by the “flat-disc” approximation. The structural deformation is described by modal decomposition and the velocity potential of the flow can be decomposed by the principal coordinates. The impacts of a rigid wedge and an elastic plate are first investigated to analytically validate our method in obtaining the added mass matrix. Then the impact of an elastic wedge made up of two beams symmetrically onto the water surface is analyzed. It is shown that the discrete vortex method can be used to obtain the added mass matrix of elastic wedge impact accurately and efficiently.     

A new approach for dynamic analysis of flexible manipulator systems

In this paper, a new approach for dynamic analysis of the flexible multibody manipulator systems is described. The organization of the computer implementations which are used to automatically construct and numerically solve the system of loosely coupled dynamic equations expressed in terms of the absolute, joint and elastic coordinates is discussed. The main processor source code consists of three main modules: constraint module, mass module and force module. The constraint module is used to numerically evaluate the relationship between the absolute and joint accelerations. The mass module is used to numerically evaluate the system mass matrix as well as the non-linear Coriolis and centrifugal forces associated with the absolute, joint and elastic coordinates. At the same time, the force module is used to numerically evaluate the generalized external and elastic forces associated with the absolute, joint and elastic coordinates. Computational efficiency is achieved by taking advantage of the structure of the resulting system of loosely coupled equations. The absolute, joint and elastic accelerations are integrated forward in time using direct numerical integration methods. The absolute positions and velocities can then be determined using the kinematic relationships. The flexible 2-DOF double-pendulum and spatial manipulator systems are used as illustrated examples to demonstrate and verify the application of the computational procedures discussed in this paper.     

Cloaking of a circular cylindrical elastic inclusion from antiplane elastic waves and resonance effects

Cloaking of a circular cylindrical elastic inclusion embedded in a homogeneous linear isotropic elastic medium from antiplane elastic waves is studied. The transformation or change-of-variables method is used to determine the material properties of the cloak and the homogenization theory of composites is used to construct a multilayered cloak consisting of many bi-material cells. The large system of algebraic equations associated with this problem is solved by using the concept of multiple scattering with wave expansion coefficient matrices. Numerical results for cloaking of an elastic inclusion and a rigid inclusion are compared with the case of a cavity. It is found that while the cloaking patterns for the three cases are similar, the major difference is that standing waves are generated in the elastic inclusion and the multilayered cloak cannot prevent the motion inside the elastic inclusion, even though the cloak seems nearly perfect. Waves can penetrate into and cause vibrations inside the elastic inclusion, where the amplitude of standing waves depend on the material properties of the inclusion but are very much reduced when compared to the case when there is no cloak. For a prescribed mass density, the displacements inside the elastic cylinder decrease as the shear modulus increases. Moreover, the cloaking of the elastic inclusion over a range of wavenumbers is also investigated. There is significant low frequency scattering even if the cloak consists of a large number of layers. When the wavenumber increases, the multilayered cloak is not effective if the cloak consists of an insufficient number of layers. Resonance effects that occur in cloaking of elastic inclusions are also discussed.     

Impact bifurcation of semi-infinite elastic thin bars

The dynamic buckling problem of elastic bars subjected to axial impact has been investigated by many authors in different ways. In this paper the problem, in which the elastic bars are assumed to be ideally straight, is reformulated in connection with the bifurcation due to the stress wave propagation. The example of a semi-infinite elastic bar is used for illustration.     

基于迭代法的非线性弹性均质化研究

微观结构对复合材料的宏观力学性能具有至关重要的影响, 通过合理设计复合材料微观结构可以得到期望的宏观性能. 均质化方法作为一种有效的设计方法, 它从微观结构的角度出发, 利用均匀化的概念, 实现了对复合材料宏观力学性能的预测和设计. 而当考虑非线性因素, 均质化的实现就非常困难. 本文利用双渐近展开方法, 将位移按照宏观位移和微观位移展开, 推导了非线性弹性均质化方程. 通过直接迭代法, 对非线性弹性均质化方程进行了求解, 并给出了具体的迭代方法和实现步骤. 本文基于迭代步骤和非线性弹性均质化方程编写MATLAB 程序, 对3种典型本构关系的周期性多孔材料平面问题进行了计算, 对比细致模型的应变能、最大位移和等效泊松比, 对程序及迭代方法的准确性进行了验证. 之后对一种三元橡胶基复合材料进行多尺度均质化, 将其分为芯丝尺度和层间尺度. 用线弹性的均质化方法得到了芯丝尺度的等效弹性参数, 并将其作为层间尺度的材料参数. 在层间尺度应用非线性弹性均质化方法对结构进行计算, 得到材料的宏观等效性能, 并以实验结果为基准进行评价.      

DEM simulation of particle flow and separation in a vibrating flip-flow screen

Vibrating flip-flow screens (VFFS) with stretchable polyurethane sieve mats have been widely used in screening fine-grained materials in recent years. In this work, the discrete element method (DEM) is used to study the screening process in VFFS to explain particle flow and separation behavior at the particle scale. Unlike traditional vibrating screens, for VFFS, the amplitude response of each point on the elastic sieve mat is different everywhere. This study measures the kinematics of the elastic sieve mat under different conditions such as different stretched lengths and material loads. To establish the elastic sieve mat model in a DEM simulation, the continuous elastic sieve mat is discretized into multiple units, and the displacement signal of each unit tested is analyzed by Fourier series. The Fourier series analysis results of each unit are used as the setting parameters for motion. In this way, the movement of the elastic sieve mat is approximately simulated, and a DEM model of VFFS is produced. Through the simulation, the flow and separation of different-sized particles in VFFS are studied, and the reasonability of the simulation is verified by a pilot-scale screening experiment. The present study demonstrates the potential of the DEM method for the analysis of screening processes in VFFS.     

Viscometric flows of polymeric melts treated according to the rational theory of Eckart's continuum. I. General theory

The purely rational theory of Eckart continua (i.e. elastic bodies with a variable relaxed state) is applied to viscometric flows of polymeric melts. The main assumptions are thermodynamic non-interaction of inelastic behaviour and of non-elastic stress, as well as elastic isotropy. After establishing the time-dependent differential equations of viscometric flow, these equations are simplified to a set of algebraic equations describing steady-state flow. From this we deduce two general equations connecting the three elastic steady-state viscometric functions which do not depend upon the elastic behaviour. The law of rubber elasticity used in this paper is described in the Appendix.     

A framework for numerical integration of crystal elasto-plastic constitutive equations compatible with explicit finite element codes

In this paper we summarize the elements of a numerical integration scheme for elasto-plastic response of single crystals. This is intended to be compatible with large-scale explicit finite element codes and therefore can be used for problems involving multiple crystals and also overall behavior of polycrystalline materials. The steps described here are general for anisotropic elastic and plastic response of crystals. The crystallographic axes of the lattice are explicitly stored and updated at each time step. A plastic predictor–elastic corrector scheme is used to calculate the plastic strain rates on all active slip systems based on a rate-dependent physics-based constitutive model without the need of further auxiliary assumptions. Finally we present the results of numerous calculations using a physics-based rate- and temperature-dependent model of copper and the effect of elastic unloading, elastic crystal anisotropy, and deformation-induced lattice rotation are emphasized.     

Equilibrium of a Prestressed Strip Reinforced with Elastic Plates

The contact problem for a prestressed elastic strip reinforced with equally spaced elastic plates is considered. The Fourier integral transform is used to construct an influence function of a unit concentrated force acting on the infinite elastic strip with one edge constrained. The transmission of forces from the thin elastic plates to the prestressed strip is analyzed. On the assumption that the beam bending model and the uniaxial stress model are valid for an elastic plate subjected to both vertical and horizontal forces, the problem is mathematically formulated as a system of integro-differential equations for unknown contact stresses. This system is reduced to an infinite system of algebraic equations solved by the reduction method. The effect of the initial stresses on the distribution of contact forces in the strip under tension and compression is studied     

Effective elastic properties of matrix composites with transversely-isotropic phases

The present work addresses the problem of calculation of the macroscopic effective elastic properties of composites containing transversely isotropic phases. As a first step, the contribution of a single inhomogeneity to the effective elastic properties is quantified. Relevant stiffness and compliance contribution tensors are derived for spheroidal inhomogeneities. The limiting cases of spherical, penny-shaped and cylindrical shapes are discussed in detail. The property contribution tensors are used to derive the effective elastic moduli of composite materials formed by transversely isotropic phases in two approximations: non-interaction approximation and effective field method. The results are compared with elastic moduli of quasi-random composites.     

Indentation of a spherical cavity in an elastic body by a rigid spherical inclusion: influence of non-classical interface conditions

This paper examines the indentation of an elastic body by a rigid spherical inclusion. In contrast to conventional treatments where the contact between a rigid inclusion and the elastic medium is regarded as being perfectly bonded, we examine the influence of non-classical interface conditions including frictionless bilateral contact, separation and Coulomb friction on the load–displacement behaviour of the spherical rigid inclusion. Both analytical methods and boundary element techniques are used to examine the inclusion/elastic medium interaction problems. This paper also provides a comprehensive review of non-classical interface conditions between inclusions and the surrounding elastic media.     

The elasto-plastic constitutive relation of generalized cap model for rock medium

In this paper,the rock behavior before yielding is analyzedby using the theory of continuum mechanics.The nonlinearlyelastic constitutive equation of rock medium is derived andcompared satisfactorily with the available experimental data.Moreover,the substitution of the linearly elastic hypothe-sis used in the conventional cap model with the nonlinearlyelastic one leads to the development of a new nonlinearly e-lastic-hardening plastic cap model as presented herein-