Three-dimensional stability of a rectangular plate under uniaxial tension

The paper studies the three-dimensional stability of an isotropic, linear elastic, rectangular plate under a uniform tensile load applied to its sides. The concept of free strains is used to reduce the three-dimensional problem to a two-dimensional one. It is solved using the three-dimensional linearized theory of stability. An approximate solution of the buckling problem is obtained by the finite-difference method. Numerical results are presented __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 7, pp. 116–123, July 2006.     

Unsteady problem of crack propagation in the beam approximation

Unsteady crack propagation is studied in the beam approximation. The Euler and Timoshenko models of beam theory are used. Crack propagation is described using an energy balance equation. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 5, pp. 177–189, September–October, 2008.     

Numerical solution to the buckling problem for a sandwich plate under uniaxial compression

A thin rectangular sandwich plate with isotropic linear elastic layers is considered. The plate is in a plane-strain state under uniaxial compression. An exact statement of the buckling problem is given. Its approximate solution is found by the finite-difference method. The concept of base scheme is used to formulate discrete problems in explicit and compact form. As an example, the critical parameters of the plate are calculated using a computation optimization procedure. Its efficiency is demonstrated __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 9, pp. 98–105, September 2006.     

局部荷载作用下有梁矩形板的弹性分析

写出了任意局部荷载作用下各种不同边界条件矩形板的解的表达式．通过梁与板的边界协调分析，求出不同荷载作用下的有梁矩形板解析解，并通过改变其中参数EI与GIt的数值，可以得出局部荷载作用下各种不同边界条件下矩形板的解．     

BENDING SOLUTION OF A RECTANGULAR PLATE WITH ONE EDGE BUILT－IN AND ONE CORNER POINT SUPPORTED SUBJECTED TO UNIFORM LOAD

ＢＥＮＤＩＮＧ　ＳＯＬＵＴＩＯＮ　ＯＦ　Ａ　ＲＥＣＴＡＮＧＵＬＡＲ　ＰＬＡＴＥ　ＷＩＴＨ　ＯＮＥ　ＥＤＧＥ　ＢＵＩＬＴ－ＩＮ　ＡＮＤ　ＯＮＥ　ＣＯＲＮＥＲ　ＰＯＩＮＴ　ＳＵＰＰＯＲＴＥＤ　ＳＵＢＪＥＣＴＥＤ　ＴＯ　ＵＮＩＦＯＲＭ　ＬＯＡＤＸｕＱｉｌｏ...     

Stress-strain field near crack tip and calculation of critical stress of crack propagation in a pure bending beam of rectangular section with one-sided mode i crack

This paper studies the stress-strain field near crack tip in a pure bending beam of rectangular section with one-sided mode I crack by the analytic method of Ref. [1], then it gives the stress and strain components at the crack tip when the crack propagates and further it obtains the formulas of calculating the elastic deformed area width, the deformed intensity area width and the equation groups of calculating the critical stress of crack propagation, last the equation group of calculating critical stress of crack propagation is verified by calculating instance. The maximum error is 0.18%. First Received May 7, 1994.     

Influence of Geometrical Parameters on the Critical Load in Three-Dimensional Stability Problems for Rectangular Plates and Beams

Two- and three-dimensional stability problems for a rectangular plate under uniaxial compression are solved by the mesh method. It is shown that the difference between the critical loads obtained in the three- and two-dimensional problems is not greater than 5% for arbitrary fixation conditions and arbitrary length and thickness ratio of the plate     

Stress state of a piezoelectric ceramic body with a plane crack under antisymmetric loads

The static equilibrium of an electroelastic transversely isotropic space with a plane crack under antisymmetric mechanical loads is studied. The crack is located in the plane of isotropy. Relationships are established between the stress intensity factors (SIFs) for an infinite piezoceramic body and the SIFs for a purely elastic body with a crack of the same form under the same loads. This makes it possible to find the SIFs for an electroelastic body without the need to solve specific electroelasitc problems. As an example, the SIFs are determined for a piezoelastic body with penny-shaped and elliptic cracks under shear __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 2, pp. 32–42, February 2006.     

Contact problem for a plane crack under a normally incident antiplane shear wave

The contact-interaction problem for a stationary plane crack with friction between its edges under the action of a normal (to the crack plane) harmonic shear wave is addressed. Antiplane deformation conditions are considered. The distribution of contact forces and displacement discontinuity of crack edges are studied Published in Prikladnaya Mekhanika, Vol. 43, No. 5, pp. 138–142, May 2007.     

The fundamental solutions for the plane problem in piezoelectric media with an elliptic hole or a crack

1.IntroductionItiswell-knownthatthefundame,ltalsolutionsorGreen'sfunctionsplayanimportantroleilllinearelasticity.Forexample,theycanbeusedtoconstructmanyanalyticalsolutionsofpracticalproblems.Itismoreimportantthattheyareusedasthefundamentalsolutionsintheboundaryelementmethod(BEM)tosolvesomecomplicatedproblem.Withthewidely-increasingapplicationofpiezoelectricmaterialsinengineeringproblems,thestudyregardingtheGreen'sfLlnctionsinpiezoelectricsolidshasreceivedmuchinterest.The3DGreen'sfunctionsi…     

Analytical solutions for plane problem of functionally graded magnetoelectric cantilever beam

In this paper, an exact analytical solution is presented for a transversely isotropic functionally graded magneto-electro-elastic (FGMEE) cantilever beam, which is subjected to a uniform load on its upper surface, as well as the concentrated force and moment at the free end. This solution can be applied for any form of gradient distribution. For the basic equations of plane problem, all the partial differential equations governing the stress field, electric, and magnetic potentials are derived. Then, the expressions of Airy stress, electric, and magnetic potential functions are assumed as quadratic polynomials of the longitudinal coordinate. Based on all the boundary conditions, the exact expressions of the three functions can be determined. As numerical examples, the material parameters are set as exponential and linear distributions in the thickness direction. The effects of the material parameters on the mechanical, electric, and magnetic fields of the cantilever beam are analyzed in detail.     

Fracture behavior of a bonded magneto-electro-elastic rectangular plate with an interface crack

In this paper the anti-plane problem for an interface crack between two dissimilar magneto-electro-elastic plates subjected to anti-plane mechanical and in-plane magneto-electrical loads is investigated. The interface crack is assumed to be either magneto-electrically impermeable or permeable, and the position of the interface crack is arbitrary. The finite Fourier transform method is employed to reduce the mixed boundary-value problem to triple trigonometric series equations. The dislocation density functions and proper replacement of the variables are introduced to reduce these series equations to a standard Cauchy singular integral equation of the first kind. The resulting integral equation together with the corresponding single-valued condition is approximated as a system of linear algebra equations which can be easily solved. Field intensity factors and energy release rates are determined numerically and discussed in detail. Numerical results show the effects of crack configuration and loading combination parameters on the fracture behaviors of crack tips according to energy release rate criterion. The study of this problem is expected to have applications to the investigation of dynamic fracture properties of magneto-electro-elastic materials with cracks.     

The 3-D stress intensity factor for a half plane crack in a transversely isotropic solid due to the motion of loads on the crack faces

Three-dimensional analysis of a half plane crack in a transversely isotropic solid is performed. The crack is subjected to a pair of normal point loads moving in a direction perpendicular to the crack edge on its faces. Transform methods are used to reduce the boundary value problem to a single integral equation that can be solved by the Wiener-Hopf technique. The Cagniard-de Hoop method is employed to invert the transforms. An exact expression is derived for the mode I stress intensity factor as a function of time and position along the crack edge. Some features of the solution are discussed through numerical results. The project supported by the Guangdong Provincial Natural Science Foundation and the Science Foundation of Shantou University     

流体饱和弹性半空间裂隙对平面P_I波的衍射

采用间接边界元法,求解了饱和半空间裂隙对平面PI波的二维衍射问题。基于单层位势理论,将边界离散并直接在边界单元上施加虚拟荷载(水平作用力、竖向作用力和流量源的叠加)以构造散射波场,并由边界条件确定虚拟荷载密度,总波场由自由波场和散射波场共同组成。通过参数分析研究了入射波频率、入射倾角、埋深、孔隙率、边界渗透条件等因素对饱和半空间中裂隙对平面PI波衍射的影响规律。结果表明:裂隙随埋深增大,地表位移谱振荡加剧,峰值有所降低;随着入射频率增加,孔隙率影响逐渐增大;垂直入射时,水平位移的放大区域主要分布在裂隙两端,斜入射时,主要集中在裂隙正上方地表附近;透水和不透水两种情况下的地表位移幅值和相位差别较小,但干土情况与饱和情况下的位移幅值相差较大。     

Stress intensity factor in a contact problem for a plane crack under an antiplane shear wave

The frictional contact interaction of the finite edges of a plane crack under the action of a normally incident harmonic shear wave that produces antiplane deformation is studied. The influence of the forces of contact interaction on the stress intensity factor is analyzed Published in Prikladnaya Mekhanika, Vol. 43, No. 9, pp. 115–119, September 2007.     

Analyzing the viscoelastic state of a plate with elliptic or linear elastic inclusions

A method is proposed for studying the stress state of a viscoelastic multiply connected isotropic plate with aligned elastic inclusions. The viscoelastic state of a plate with a finite or infinite number of circular and linear inclusions is analyzed __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 2, pp. 88–98, February 2007. For the centenary of the birth of G. N. Savin.     

The growth of the void in a hyperelastic rectangular plate under a uniaxial extension

In the present paper, the finite deformation and stress analysis for a hyperelastic rectangular plate with a center void under a uniaxial extension is studied. In order to consider the effect of the existence of the void on the deformation and stress of the plate, the problem is reduced to the deformation and stress analysis for a hyperelastic annular plate and its approximate solution is obtained from the minimum potential energy principle. The growth of the cavitation is also numerically computed and analysed.Project supported by the National Natural Science Foundation of China     

Fredholm integral equation for the multiple circular arc crack problem in plane elasticity

Summary An elementary solution for the multiple circular arc problem is obtained in this paper. The elementary solution is defined as a particular case of the single circular arc crack problem, in which remote stresses are equal to zero, and two pairs of concentrated forces are applied at a prescribed point of crack face. By using the principle of superposition, Fredholm integral equation for the multiple circular arc problem in plane elasticity is obtained. The suggested approach is illustrated by several numerical examples. If a smaller arc crack is surrounded by a larger arc crack, the stress intensity factors for the former become rather small. The phenomenon of shielding is illustrated by examples. Accepted for publication 17 September 1996     

矩形板屈曲问题的一个小波解

利用Wavelet-Galerkin法分析了四边固支与四边简支矩形板的屈曲问题.以小波作为基函数表示板的挠度,推导出屈曲系数及屈曲模态的计算过程.数值计算给出了不同边长比的矩形板的屈曲系数及屈曲半波数.与传统的三角函数作基函数的Galerkin法及有限元法结果比较,结果表明在一定条件下小波可以作为试函数解决结构力学的屈...     

Stable Equilibrium of the Multilayer Lining of a Vertical Mine Opening in Elastoplastic Rock Mass

Based on the three-dimensional linearized theory of stability, the stability problem is solved for the multilayer lining of a vertical circular mine opening in rock mass under inelastic conditions. The effect of the geometric and physicomechanical parameters of the lining and rock on the critical contact pressures is evaluated