共查询到20条相似文献,搜索用时 203 毫秒
1.
V. A. Buryachenko V. I. Kushch 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2006,57(3):491-505
We consider a transversal loading of a linearly elastic isotropic media containing the identical isotropic aligned circular
fibers at non-dilute concentration c. By the use of solution obtained by the Kolosov–Muskhelishvili complex potential method for two interacting circles subjected
to three different applied stresses at infinity, and exact integral representations for both the stress and strain distributions
in a microinhomogeneous medium, one estimates the effective moduli of the composite accurately to order c2.
Received: March 4, 2003; revised: August 8, 2003 相似文献
2.
3.
V. A. Buryachenko 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2005,56(6):1107-1115
We consider a linearly elastic composite medium, which consists of a homogeneous matrix containing a statistically uniform
random set of aligned fibers. Effective elastic moduli as well as the stress concentrator factors in the components are estimated.
The micromechanical approach is based on the Green’s function technique as well as on the generalization of the “multiparticle
effective field method” (MEFM, see for references, Buryachenko [1]). The refined version of the MEFM takes into account the
variation of the effective fields acting on each pair of fibers. The dependence of effective elastic moduli and stress concentrator
factors on the radial distribution function of the fiber locations is analyzed.
Received: October 20, 2004 相似文献
4.
D. Iaşan 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2009,60(1):138-153
This paper is concerned with the linear theory of anisotropic porous elastic bodies. The extension and bending of orthotropic
porous elastic cylinders subjected to a plane temperature field is investigated. The work is motivated by the recent interest
in the using of the orthotropic porous elastic solid as model for bones and various engineering materials. First, the thermoelastic
deformation of inhomogeneous beams whose constitutive coefficients are independent of the axial coordinate is studied. Then,
the extension and bending effects in orthotropic cylinders reinforced by longitudinal rods are investigated. The three-dimensional
problem is reduced to the study of two-dimensional problems. The method is used to solve the problem of an orthotropic porous
circular cylinder with a special kind of inhomogeneity.
相似文献
5.
In this paper, we elaborated a spectral collocation method based on differentiated Chebyshev polynomials to obtain numerical solutions for some different kinds of nonlinear partial differential equations. The problem is reduced to a system of ordinary differential equations that are solved by Runge–Kutta method of order four. Numerical results for the nonlinear evolution equations such as 1D Burgers’, KdV–Burgers’, coupled Burgers’, 2D Burgers’ and system of 2D Burgers’ equations are obtained. The numerical results are found to be in good agreement with the exact solutions. Numerical computations for a wide range of values of Reynolds’ number, show that the present method offers better accuracy in comparison with other previous methods. Moreover the method can be applied to a wide class of nonlinear partial differential equations. 相似文献
6.
Xian-Fang Li Kang Yong Lee 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2006,57(4):636-651
The transient response of a semi-infinite transversely isotropic piezoelectric layer containing a surface crack is analyzed
for the case where anti-plane mechanical and in-plane electric impacts are suddenly exerted at the layer end. The integral
transform techniques are used to reduce the associated mixed initial boundary value problem to a singular integral equation
of the first kind, which can be solved numerically via the Lobatto–Chebyshev collocation technique. Dynamic field intensity
factors are determined by employing a numerical inversion of the Laplace transform. The dynamic stress intensity factors are
presented graphically and the effects of the material properties and geometric parameters are examined.
Received: June 30, 2003 相似文献
7.
Andrej T. Il’ichev 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2006,57(4):547-566
Stability of solitary waves in a thin inextensible and unshearable rod of infinite length is studied. Solitary-wave profile
of the elastica of such a rod without torsion has the form of a planar loop and its speed depends on a tension in the rod.
The linear instability of a solitary-wave profile subject to perturbations escaping from the plane of the loop is established
for a certain range of solitary-wave speeds. It is done using the properties of the Evans function, an analytic function on
the right complex half-plane, that has zeros if and only if there exist the unstable modes of the linearization around a solitary-wave
solution. The result follows from comparison of the behaviour of the Evans function in some neighbourhood of the origin with
its asymptotic at infinity. The explicit computation of the leading coefficient of the Taylor series of the Evans function
near the origin is performed by means of the symbolic computer language.
Received: April 6, 2004; revised: December 12, 2004 相似文献
8.
Energy-conserving algorithms are necessary to solve nonlinear elastodynamic problems in order to recover long term time integration accuracy and stability. Furthermore, some physical phenomena (such as friction) can generate dissipation; then in this work, we present and analyse two energy-consistent algorithms for hyperelastodynamic frictional contact problems which are characterised by a conserving behaviour for frictionless impacts but also by an admissible frictional dissipation phenomenon. The first approach permits one to enforce, respectively, the Kuhn–Tucker and persistency conditions during each time step by combining an adapted continuation of the Newton method and a Lagrangean formulation. In addition the second method which is based on the work in [P. Hauret, P. Le Tallec, Energy-controlling time integration methods for nonlinear elastodynamics and low-velocity impact, Comput. Methods Appl. Mech. Eng. 195 (2006) 4890–4916] represents a specific penalisation of the unilateral contact conditions. Some numerical simulations are presented to underscore the conservative or dissipative behaviour of the proposed methods. 相似文献
9.
S. Torkarzewski J.J. Telega M. Pindor J. Gilewicz 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2003,54(4):713-726
We study a composite material consisting of two isotropic constituents with complex
transport modulus depending on a real parameter. By starting from the parametric estimations
reported by Baker [3], Bergman [5] and Milton [1] we propose a method of construction of the
bound on an imaginary part of an effective modulus versus its real part and reversely, on a real
part versus the imaginary one. The estimation obtained we call the total bound on a parametric
modulus of two-phase medium. Illustrative examples of the numerical evaluations of low order
total bounds are also provided. 相似文献
10.
Nicolas Leconte Bertrand Langrand Eric Markiewicz 《Journal of Computational and Applied Mathematics》2008
The paper deals with the modelling of riveted assemblies for full-scale complete aircraft crashworthiness. Many comparisons between experiments and FE computations of bird impacts onto aluminium riveted panels have shown that macroscopic plastic strains were not sufficiently developed (and localised) in the riveted shell FE in the impact area. Consequently, FE models never succeed in initialising and propagating the rupture in the sheet metal plates and along rivet rows as shown by experiments, without calibrating the input data (especially the damage and failure properties of the riveted shell FE). To model the assembly correctly, it appears necessary to investigate on FE techniques such as Hybrid-Trefftz finite element method (H-T FEM). Indeed, perforated FE plates developed for elastic problems, based on a Hybrid-Trefftz formulation, have been found in the open literature. Our purpose is to find a way to extend this formulation so that the super-element can be used for crashworthiness. To reach this aim, the main features of an elastic Hybrid-Trefftz plate are presented and are then followed by a discussion on the possible extensions. Finally, the interpolation functions of the element are evaluated numerically. 相似文献
11.
A finite element method for treating two-dimensional electron systems with Rashba spin–orbit interaction is developed. The Rashba spin–orbit interaction removes spin degeneracy, so that each spin contributes to the conductance differently. By accounting for the connection between a system and leads, this method yields the conductance of a nanoscale quantum device for each spin state. As an example, this calculation method is applied to a model of a quantum point contact. The results of this calculation indicate conductance quantization and a large spin polarization. We discuss the estimated accuracies of this calculation. 相似文献
12.
Igor V. Andrianov Vladyslav V. Danishevs’kyy Dieter Weichert 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2008,159(1):889-903
Improved bounds for effective transport properties of a random non-percolated composite with cylindrical fibres are developed
by means of the security-spheres approach. The key point of the method is to obtain a solution for a regular composite that
can be valid for all values of the volume fractions and properties of the components. For this aim we use the asymptotic homogenization
method; a cell problem is solved by a modified version of the boundary shape perturbation technique. 相似文献
13.
Antoine Gloria Stefan Neukamm 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2011,28(6):941
We prove under some general assumptions on elastic energy densities (namely, frame indifference, minimality at identity, non-degeneracy and existence of a quadratic expansion at identity) that homogenization and linearization commute at identity. This generalizes a recent result by S. Müller and the second author by dropping their assumption of periodicity. As a first application, we extend their Γ-convergence commutation diagram for linearization and homogenization to the stochastic setting under standard growth conditions. As a second application, we prove that the Γ-closure is local at identity for this class of energy densities. 相似文献
14.
Hilmi Demiray 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2004,55(2):282-294
In the present work, treating the arteries as a tapered,
thin walled, long and circularly conical prestressed elastic tube
and using the longwave approximation, we have studied the
propagation of weakly nonlinear waves in such a fluid-filled
elastic tube by employing the reductive perturbation method. By
considering the blood as an incompressible inviscid fluid the
evolution equation is obtained as the Korteweg-de Vries equation
with a variable coefficient. It is shown that this type of
equations admit a solitary wave type of solution with variable
wave speed. It is observed that, the wave speed increases with
distance for positive tapering while it decreases for negative
tapering. 相似文献
15.
R. Bustamante R. W. Ogden 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2006,57(4):708-721
In the theory of nonlinear elasticity universal relations are relationships connecting the components of stress and deformation tensors that hold independently of the constitutive
equation for the considered class (or sub-class) of materials. They are classified as linear or nonlinear according as the
components of the stress appear linearly or nonlinearly in the relations. In this paper a general scheme is developed for
the derivation of nonlinear universal relations and is applied to the constitutive law of an isotropic Cauchy elastic solid.
In particular, we consider examples of quadratic and cubic universal relations. In respect of universal solutions our results confirm the general result of Pucci and Saccomandi [1] that nonlinear universal relations are necessarily generated
by the linear ones. On the other hand, for non-universal solutions we develop a general method for generating nonlinear universal
relations and illustrate the results in the case of cubic relations.
(Received: November 9, 2005) 相似文献
16.
In the present work, based on a one-dimensional model, the interaction of two solitary waves propagating in opposite directions in a collisionless plasma is investigated by use of the extended Poincaré–Lighthill–Kuo (PLK) method. It is shown that bi-directional solitary waves are propagated and the head-on collision of these two solitons occur. The phase shifts and the trajectories of these two solitons after the collision are obtained. 相似文献
17.
We provide operator-norm convergence estimates for solutions to a time-dependent equation of fractional elasticity in one spatial dimension, with rapidly oscillating coefficients that represent the material properties of a viscoelastic composite medium. Assuming periodicity in the coefficients, we prove operator-norm convergence estimates for an operator fibre decomposition obtained by applying to the original fractional elasticity problem the Fourier–Laplace transform in time and Gelfand transform in space. We obtain estimates on each fibre that are uniform in the quasimomentum of the decomposition and in the period of oscillations of the coefficients as well as quadratic with respect to the spectral variable. On the basis of these uniform estimates we derive operator-norm-type convergence estimates for the original fractional elasticity problem, for a class of sufficiently smooth densities of applied forces. 相似文献
18.
This paper is concerned with asymptotic and monotonicity properties of some parameter-dependent variational inequalities. The main part of the study deals with inequalities modelling friction problems with normal compliance or Tresca’s conditions in which the parameter stands for the friction coefficient. The corresponding inequalities are (generalizations) of variational inequalities of the second kind. We then study an inequality of the first kind representing the elastoplastic torsion problem where the parameter represents the plasticity yield. 相似文献
19.
Patrizio Neff Jena Jeong Ingo Münch Hamid Ramezani 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2009,60(3):479-497
We show that the averaged response of random isotropic Cauchy elastic material can be described analytically. It leads to
a higher gradient model with explicit expressions for the dependence on the second derivatives of the mean field. A subsequent
penalty formulation coincides with a linear elastic micro-stretch model with specific choice of constitutive parameters, depending
only on the average cut-off length (the internal characteristic length scale Lc > 0). Thus the microstretch displacement field can be interpreted as an approximated mean field response for these parameter
ranges. The mean field free energy in this micro-stretch formulation is not uniformly pointwise positive, nevertheless, the
model is well posed.
相似文献
20.
Yijiang Lian Zhiping Li 《Journal of Computational and Applied Mathematics》2011,236(5):834-842
A dual-parametric finite element method is introduced in this paper for the computation of singular minimizers in the 2D cavitation problem in nonlinear elasticity. The method overcomes the difficulties, such as the mesh entanglement and material interpenetration, generally encountered in the finite element approximation of problems with extremely large expansionary deformation. Numerical experiments show that the method is highly efficient in the computation of cavitation problems. Numerical experiments are also conducted on discrete problems without the radial symmetry to show the validity of the method to more general settings and the potential of its application to the study of mechanism of cavity nucleation in nonlinear elastic materials. 相似文献