负泊松比蜂窝材料的动力学响应及能量吸收特性

针对传统正方形蜂窝,通过用更小的双向内凹结构胞元替代原蜂窝材料的结构节点,得到了一种具有负泊松比特性的节点层级蜂窝材料模型。利用显式动力有限元方法,研究了冲击荷载作用下该负泊松比蜂窝结构的动力学响应及能量吸收特性。研究结果表明,除了冲击速度和相对密度,负泊松比蜂窝材料的动力学性能亦取决于胞元微结构。与正方形蜂窝相比,该负泊松比层级蜂窝材料的动态承载能力和能量吸收能力明显增强。在中低速冲击下,试件表现为拉胀材料明显的"颈缩"现象,并展示出负泊松比材料独特的平台应力增强效应。基于能量吸收效率方法和一维冲击波理论,给出了负泊松比蜂窝材料的密实应变和动态平台应力的经验公式,以预测该蜂窝材料的动态承载能力。本文的研究将为负泊松比多胞材料冲击动力学性能的多目标优化设计提供新的设计思路。     

On the measurement of Poisson's ratio for modeling clay

Resonance testing of Plasticine clay indicates that, for small strains (≤10^?5) in the frequency range 100–3000 Hz, the material can be considered to be a linear viscoelastic solid with parameters which depend on temperature, frequency and prior large-strain history. In order to measure Poisson's ratio, it is necessary to take special precautions to eliminate large straining between small-strain tests of different tensorial character. A simple but effective test configuration for measuring Poisson's ratio is described and test results are displayed.     

Analytical solution of the contact problem for a system of bodies under collective wear

The contact problem is considered for a system of bodies subject to wear on a common base. The deformation properties of the bodies and the base are described by the Winkler model. The problem is reduced to a system of ordinary differential equations and an integral equation of hereditary type with difference kernel. The solution of the problem is constructed with the use of the Laplace transform. The asymptotics of the solution at large times is studied. The continuity conditions for the contact of each of the bodies with the base are derived.     

Analytical solution of the contact problem of a rigid indenter and an anisotropic linear elastic layer

We use the Stroh formalism to study analytically generalized plane strain deformations of a linear elastic anisotropic layer bonded to a rigid substrate, and indented by a rigid cylindrical indenter. The mixed boundary-value problem is challenging since the a priori unknown deformed indented surface of the layer contacting the rigid cylinder is to be determined as a part of the solution of the problem. For a rigid parabolic prismatic indenter contacting either an isotropic layer or an orthotropic layer and a flat rigid punch indenting a half space, the computed solutions are found to agree well with those available in the literature. Parametric studies have been conducted to delimit the length and the thickness of the layer for which the derived relation between the axial load and the indentation depth caused by the rigid cylinder is valid. The indentation of a face centered cubic crystal with the plane of indentation oriented differently from the principal planes of symmetry has also been studied to illustrate the applicability of the technique to general layers made of anisotropic materials. Results presented herein can serve as benchmarks with which to compare solutions obtained by other methods.     

泡沫金属的微惯性效应和动态塑性泊松比

采用三维Voronoi技术和显式有限元方法来研究闭孔和开孔两种泡沫金属的动态塑性泊松比问题和微惯性效应。细观数值模拟的结果表明:塑性泊松比随着轴向应变的增加而下降,塑性泊松比的峰值随着冲击速度的增加而下降;相对密度增加时,泡沫金属塑性泊松比增加;微惯性对平台应力的影响不大。该数值模拟结果能够解释侧向约束情况下闭孔泡沫金属的压溃应力随着加载速率的提高而下降的实验现象。     

Note on the expansion in powers of Poisson's ratio of solutions in elastostatics

In this paper we examine the power-series development with respect to Poisson's ratio of the solution to the second boundary-value problem (surface tractions prescribed) in three-dimensional classical elastostatics for the case of vanishing body forces. The individual terms of this expansion, by means of steady-state thermoelasticity theory, are found to admit an independent physical interpretation. This interpretation, in turn, permits certain conclusions concerning the dependence upon the elastic constants of solutions to space problems. In particular, it is shown that for a body of arbitrary connectivity all stresses are independent of the elastic constants if and only if the dilatation (and the mean normal stress) is a linear function of the cartesian coordinates. The feasibility of successive approximations of solutions appropriate to sufficiently small values of Poisson's ratio is also considered.The results communicated in this paper were obtained in the course of an investigation conducted under Contract Nonr 562(25) of Brown University with the Office of Naval Research, Washington, D.C.     

Analytical analysis for optimizing mass ratio of nonlinear tuned mass dampers

Nonlinear Dynamics - This paper investigates the forced vibration and dynamic stability of a simply supported axially moving beam coupled to a nonlinear energy sink with the aim of passive...     

Historical deformation analysis of elastoplastic structures as a parametric linear complementarity problem

Summary Discrete models of elastoplastic beams and frames are considered. The plastic deformability laws (bending moments versus plastic rotations) are piecewise linearized. Plastic deformations are sought as they develop along a proportional loading process. The historical analysis in this sense, is shown to be ameneable to the solution of a parametric linear complementarity problem. Recent mathematical results on this problem, due to R. W. Cottle, are used to obtain numerical solutions. Extensions are pointed out to stepwise proportional loading paths, allowing for the irreversible nature of plastic deformations.

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Sommario Si studiano modelli discreti di telai elastoplastici. I legami tra momento flettente e rotazione plastica sono lineari a tratti. Si determina l'intera evoluzione delle deformazioni plastiche al crescere proporzionale e monotono dei carichi, formulando e risolvendo un problema parametrico lineare di complementarietà. La tecnica numerica alquanto efficiente adottata, è fornita da recenti risultati di R. W. Cottle. Il metodo è esteso a processi di caricamento proporzionali a stadi, tenendo conto, tra stadio e stadio, della irreversibilità della deformazione plastica.

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All other symbols are defined when used for the first time.     

The homogenization method for the study of variation of Poisson's ratio in fiber composites

Summary Materials with specific microstructural characteristics and composite structures are able to exhibit negative Poisson's ratio. This fact has been shown to be valid for certain mechanisms, composites with voids and frameworks and has recently been verified for microstructures optimally designed by the homogenization approach. For microstructures composed of beams, it has been postulated that nonconvex shapes (with reentrant corners) are responsible for this effect. In this paper, it is numerically shown that mainly the shape, but also the ratio of shear-to-bending rigidity of the beams do influence the apparent (phenomenological) Poisson's ratio. The same is valid for continua with voids, or for composites with irregular shapes of inclusions, even if the constituents are quite usual materials, provided that their porosity is strongly manifested. Elements of the numerical homogenization theory and first attempts towards an optimal design theory are presented in this paper and applied for a numerical investigation of such types of materials. Received 11 March 1997; accepted for publication 12 September 1997     

Effects of orthotropy and variation of Poisson's ratio on the behaviour of tubes in pure flexure

The behaviour of tubes under conditions of pure bending is investigated for the cases where the material of which they are constructed is either orthotropic or of various Poisson's ratios. Large deflections and moderate nonlinear strains are considered and the modelling incorporates Timoshenko beam theory thereby allowing non-zero shear strains to develop. This in turn makes axially inhomogeneous deformation of the cross-section possible and, in particular, the compressed side can develop wrinkling. Numerical solutions are presented for various material types and tube dimensions and some interesting phenomena, such as mode interaction and jumping, are demonstrated.     

Dynamic analysis of two-dimensional frictional contact by linear complementarity problem formulation

Two-dimensional dynamic contact is formulated as a linear complementarity problem using contact compatibility conditions and the Coulomb friction law. For the time integration of dynamic response, displacements are approximated as second-order polynomials and a new scheme of considering velocity discontinuities is presented. The efficiency of the method is shown with three numerical examples.     

On the contact problem of classical elasticity

We deal with the contact problem of homogeneous and isotropic linear elastostatics in the exterior of a bounded convex domain of ${\Bbb{R}}^{3}$ . We prove existence and uniqueness of a solution, provided the elasticity tensor is only strongly elliptic.     

Stress analysis in rolling contact problem of a finite thickness FGM layer

The rolling contact problem of a non-homogeneous layer is considered here. The graded layer possesses a variable elastic modulus with an exponential distribution. The Poisons ratio is assumed to be constant. A rigid cylindrical indenter is rolling over the surface of the graded layer with a constant velocity. First, the Navier equations of equilibrium are solved in the Fourier domain. Later, the boundary and the continuity conditions are satisfied in order to extract the governing singular integral equations. The numerical solution of the integral equations is provided by means of the Gauss–Chebyshev integration method. Finally, the sensitivity of the solution is analyzed for the effective parameters namely: the stiffness ratio, the layer thickness and the coefficient of friction. The results indicate that a minimum value of the coating thickness is required to alleviate the severe stress gradients in the critical locations. If the coating thickness decreases by a 50% then the Von Mises stress will increases about 20%. Also, a softening graded layer can result in a lower stress level over the interface which may enhance the bonding strength.

     

Analytical solution of axisymmetric contact problem about indentation of a circular indenter into a soft functionally graded elastic layer

The paper addresses a contact problem of the theory of elasticity,i.e.,the penetration of a circular indenter with a flat base into a soft functionally graded elastic layer.The elastic properties of a functionally graded layer arbitrarily vary with depth,and the foundation is assumed to be elastic,yet much harder than a layer.Approximated analytical solution is constructed,and it is shown that the solutions are asymptotically exact both for large and small values of characteristic dimensionless geometrical parameter of the problem.Numerical examples are analyzed for the cases of monotonic and nonmonotonic variations of elastic properties.Numerical results for the case of homogeneous layer are compared with the results for nondeformable foundation.