Stress distribution caused by two neighboring out-of-plane locally cophasally curved fibers in a composite material

In the present paper, within the framework of a piecewise homogenous body model, with the use of the exact three-dimensional equations of elasticity theory, a method proposed earlier is developed for investigating the stress distribution caused by two neighboring out-of-plane locally cophasally curved fibers located along two parallel planes in an infinite elastic body. The body is loaded at infinity by uniformly distributed normal forces in the direction of fiber location. The self-equilibrated normal and shear stresses caused by the curved fibers are analyzed, and the influences of interaction between the fibers and of the geometric nonlinearity on the distribution of these stresses are studied. Numerical results for this interaction are obtained.     

Stress Distribution in an Infinite Elastic Body with a Locally Curved Fiber in a Geometrically Nonlinear Statement

Within the framework of a piecewise homogeneous body model, with the use of three-dimensional geometrically nonlinear exact equations of elasticity theory, a method for determining the stress—strain state in unidirectional fibrous composites with locally curved fibers is developed for the case where the interaction between the fibers is neglected. All the investigations are carried out for an infinite elastic body containing a single locally curved fiber. Numerical results illustrating the effect of geometrical nonlinearity on the distribution of the self-balanced normal and shear stresses acting on the interface and arising as a result of local curving of the fiber are presented.__________Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 41, No. 4, pp. 433–448, July–August, 2005.     

Influence of the Interaction between Two Neighboring Periodically Curved Fibers on the Stress Distribution in a Composite Material

A method is developed for a stress analysis in an infinite elastic body containing two neighboring periodically cophasaly curved fibers located along two parallel lines. The stress distribution is studied when the body is loaded at infinity by uniformly distributed normal forces in the fiber direction. The investigation is carried out within the framework of a piecewise homogeneous body model with the use of exact three-dimensional equations of elasticity theory. Numerical results related to the stress distribution considered and the influence of interaction between the fibers on this distribution are given.     

A problem of fracture mechanics for composite materials with locally curved layers

Based on a piecewise homogeneous body model, by using the exact equations of linear theory of elasticity, a method for calculating the stress intensity factor in composites with locally curved layers containing cracks parallel to the direction of external normal loads is worked out. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 42, No. 1, pp. 75–86, January–February, 2006.     

Near-surface failure of layered viscoelastic materials

Within the framework of a piecewise homogeneous body model, with the use of exact equations of the geometrically nonlinear theory of viscoelastic bodies, the distribution of near-surface self-balanced normal stresses in a body consisting of a viscoelastic half-plane, an elastic locally curved bond layer, and a viscoelastic covering layer is investigated. A method for solving the problem considered by employing the Laplace and Fourier transformations is developed. Numerical results for the self-balanced normal stresses caused by a local curving (imperfection) of an elastic bond layer upon tension and compression of the body mentioned along the free face plane are presented and analyzed. The viscoelasticity of the materials is described by the Rabotnov fractional-exponential operators. A macroscopic failure criterion is proposed, and the validity of this criterion is examined.     

Stress distribution in an infinite elastic body with a covered periodically curved fiber

Within the frame work of a piecewise homogeneous body model, with the use of the three-dimensional geometrically nonlinear exact equations of elasticity theory, a method is developed for determining the stress distribution in unidirectional fibrous composites with periodically curved fibers. The distribution of the normal and shear stresses acting on interfaces for the case where there exists a bond covering cylinder of constant thickness between the fiber and matrix is considered. The concentration of fibers in the composite is assumed to be low, and the interaction between them is neglected. Numerous numerical results related to the stress distribution in the body considered are obtained, and the influence of geometrical nonlinearity on this distribution is analyzed. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 45, No. 2, pp. 269-288, March-April, 2009.     

Three-Dimensional Stress Analysis for a Thick Plate of a Composite Material with a Spatially Locally Curved Structure

The stress distribution in a thick rectangular plate of a multilayered composite with a spatially locally curved structure is investigated with the use of three-dimensional exact equations of elasticity theory. The investigations are carried out within the framework of the continuum approach proposed by Akbarov and Guz'. It is supposed that the plate edges are clamped and uniformly distributed normal forces are applied to its upper face. The corresponding boundary-value problem is solved by employing the three-dimensional FEM modeling. Numerical results for the normal stresses acting in the thickness direction of the plate are given. The influence of the spatial local curving on the distribution of these stresses is analyzed.     

Stress distribution in an infinite elastic body containing two neighboring locally curved fibers

A method is developed for analyzing the stresses in an infinite elastic body containing two neighboring inphase locally curved fibers located along two parallel lines. The body is loaded at infinity by uniformly distributed nor mal forces in the direction of fibers. The investigation is carried out within the frame work of a piecewise homogeneous body model with the use of the three-dimensional ex act equations of the elasticity theory. Numerical results for stress distributions in the body and for the influence of interaction between fibers on these distributions are given. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 45, No. 3, pp. 457-478, May-June, 2009.     

平面弹性裂纹分析的一种有效边界元方法

提出了一种简单而有效的平面弹性裂纹应力强度因子的边界元计算方法．该方法由Crouch与Starfield建立的常位移不连续单元和闫相桥最近提出的裂尖位移不连续单元构成A·D2在该边界元方法的实施过程中,左、右裂尖位移不连续单元分别置于裂纹的左、右裂尖处,而常位移不连续单元则分布于除了裂尖位移不连续单元占据的位置之外的整个裂纹面及其它边界．算例(如单向拉伸无限大板中心裂纹、单向拉伸无限大板中圆孔与裂纹的作用)说明平面弹性裂纹应力强度因子的边界元计算方法是非常有效的．此外,还对双轴载荷作用下有限大板中方孔分支裂纹进行了分析．这一数值结果说明平面弹性裂纹应力强度因子的边界元计算方法对有限体中复杂裂纹的有效性,可以揭示双轴载荷及裂纹体几何对应力强度因子的影响．     

A bounce back-immersed boundary-lattice Boltzmann model for curved boundary

In this paper, a bounce back-immersed boundary-lattice Boltzmann model(BB-IB-LBM) is proposed for curved boundary.In the present model, a modified density distribution function is proposed for curved boundary including stationary and moving curved boundaries. A special treatment is also developed to satisfy no-slip boundary condition for the curved boundary with large curvature. On Lagrangian boundary points, the modified distribution functions are implemented to replace the artificial correction force in conventional immersed boundary-lattice Boltzmann methods(IB-LBMs). Numerical experiments are given to illustrate the accuracy and efficiency of present BB-IB-LBM. The drag coefficient of the test cases predicted by the present model is in better agreement with the results of experimental results than that of the previous IB-LBMs. It is also concluded that the average drag coefficient of present model are consistent with the experimental results. Comparing with conventional IB-LBMs, the present model eliminates the non-physical vortex at the tail of an airfoil. Simulation of flow over a sphere also proves the extensibility of present method in three-dimensional simulation.     

On wheel–rail contact problem with material properties varying with depth

Numerous laboratory experiments indicate that the use of a layer or a coating material attached to the conventional steel body reduce the magnitude of contact stress. Therefore in this paper we solve numerically the wheel–rail contact problem with friction and wear assuming the existence of a small elastic layer on the rail surface. Material properties of this layer are changing with its depth. The friction between the bodies is governed by Coulomb law. In contact zone Archard's law of wear is assumed. We take special features of this rolling contact problem and use so-called quasistatic approach to solve this contact problem. Finite element method is used as a discretization method. The numerical results including the distribution of normal stress along the contact boundary are provided and discussed. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Shape and topology optimization of contact problems by level set methods

This paper deals with the numerical solution of a topology and shape optimization problems of an elastic body in unilateral contact with a rigid foundation. The contact problem with the prescribed friction is considered. The structural optimization problem consists in finding such shape of the boundary of the domain occupied by the body that the normal contact stress along the contact boundary of the body is minimized. In the paper shape as well as topological derivatives formulae of the cost functional are provided using material derivative and asymptotic expansion methods, respectively. These derivatives are employed to formulate necessary optimality condition for simultaneous shape and topology optimization. Level set based numerical algorithm for the solution of the shape optimization problem is proposed. Level set method is used to describe the position of the boundary of the body and its evolution on a fixed mesh. This evolution is governed by Hamilton – Jacobi equation. The speed vector field driving the propagation of the boundary of the body is given by the shape derivative of a cost functional with respect to the free boundary. Numerical examples are provided. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Constructing orthogonal curvilinear meshes by solving initial value problems

Summary The purpose of this paper is to develop methods for constructing orthogonal curvilinear meshes suitable for solving partial differential equations over plane regions with smooth, curved boundaries. These curved meshes cover an annular strip along the boundary of the region which is included in the mesh. In this strip difference approximations of partial differential equations and boundary conditions can be set up as easily as they can for halfspace problems. The rest of the region and a suitable part of the annular strip can be covered by a square or rectangular mesh. In the present paper we consider the problem of determining curved meshes by solving nonlinear hyperbolic initial value problems which are formally related to the Cauchy-Riemann equations.This work was sponsored by the Swedish Institute for Applied Mathematics (ITM)     

Stress Distribution in an Elastic Body with a Periodically Curved Row of Fibers

Within the framework of a piecewise homogeneous body model, with the use of exact three-dimensional equations of elasticity theory for anisotropic bodies, a method is developed for investigating the stress distribution in an infinite elastic matrix containing a periodically curved row of cophasal fibers. It is assumed that fiber materials are the same and fiber midlines lie in the same plane. The self-balanced stresses arising in the interphase in uniaxial loading the composite along the fibers are investigated. The influences of problem parameters on these stresses are analyzed. The corresponding numerical results are presented.     

The boundary element method in stress-state problems for an anisotropic plate with holes

We propose a method of solving the problem of the stress state of an anisotropic plate with holes of arbitrary shape. The method is based on approximating the boundary of a region by curved boundary elements. These elements are taken to be a family of semi-ellipses. To satisfy the boundary conditions we use the pointwise least-square method. Numerical experiments showed good agreement of the computations with results known earlier. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 24, 1993, pp. 44–49.     

The hp-MITC finite element method for the Reissner–Mindlin plate problem

The popular MITC finite elements used for the approximation of the Reissner–Mindlin plate are extended to the case where elements of non-uniform degree p distribution are used on locally refined meshes. Such an extension is of particular interest to the hp-version and hp-adaptive finite element methods. A priori error bounds are provided showing that the method is locking-free. The analysis is based on new approximation theoretic results for non-uniform Brezzi–Douglas–Fortin–Marini spaces, and extends the results obtained in the case of uniform order approximation on globally quasi-uniform meshes presented by Stenberg and Suri (SIAM J. Numer. Anal. 34 (1997) 544). Numerical examples illustrating the theoretical results and comparing the performance with alternative standard Galerkin approaches are presented for two new benchmark problems with known analytic solution, including the case where the shear stress exhibits a boundary layer. The new method is observed to be locking-free and able to provide exponential rates of convergence even in the presence of boundary layers.     

A dynamical model of storm surges along island coasts

A time-independent dynamical model of storm surge along island coasts using orthogonal curvilinear coordinates is presented. The curved annulus between an island coast and an arbitrary deep-water boundary is mapped conformally onto a rectangular image. Two configurations of island coasts are investigated; circular and elliptic coasts. The corresponding coordinates are circular polar and elliptic respectively. The linearized vertically-integrated equations of motion are used to model storm surges with two assumptions: (i) bottom stress is proportional to horizontal transport, and (ii) storm forces are shear stresses on water surface. Analytical solutions are presented for three dynamical cases: (i) a constant-depth basin acted upon by a uniform storm stress, (ii) variable-depth basin acted upon by a uniform-direction variable-magnitude stress, and. (iii) a basin with closed depth contours acted upon by vortex-shaped storm stress. The obtained solutions clarify the relative importance of the various parameters and variables that affect surge height distribution along island coasts. These solutions may be used to test a time-dependent, numerical dynamical storm model.     

A least-squares finite-element method for viscoelastic fluids

We present a least-squares finite element method for the steady Oldroyd type viscoelastic fluids. The nonlinear iteration is coupled with global mesh refinement, and locally weighted norms are used to mitigate effects of boundary singularities. Discretization accuracy in a meaningful normis shown to be optimal when using conforming piecewise polynomial elements for the velocity, pressure and extra stress, and Raviart-Thomas finite elements for the total stress. Numerical results are given for an Oldroyd-B fluid in a 4-1 planar contraction. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

应力函数一般解的补充

本文指出平面问题极坐标形式应力函数一般解并不完备,不能处理曲杆受任意边界分布力的问题.为此,提出两个新的应力函数,将一般解作若干补充之后,能解曲杆r=a,b上受任意分布力的问题.这是包含区域边界几何参数的新的应力函数.     

Viscoelastic flow in a curved channel: A similarity solution for the Oldroyd-B fluid

A similarity solution is used to analyse the flow of the Oldroyd fluid B, which includes the Newtonian and Maxwell fluids, in a curved channel modelled by the narrow annular region between two circular concentric cylinders of large radius. The solution is exact, including inertial forces. It is found that the non-Netonian kinematics are very similar to the Newtonian ones, although some stress components can become very large. At high Reynolds number a boundary layer is developed at the inner cylinder. The structure of this boundary layer is asymptotically analysed for the Newtonian fluid. Non-Newtonian stress boundary layers are also developed at the inner cylinder at large Reynolds numbers.