1.

Precracking and interfacial delamination in a bimaterial structure:Static and dynamic loadings





Barbara Gambin Jordanka Ivanova Varbinka Valeva Gergana Nikolova《Acta Mechanica Sinica》,2011年第27卷第1期


The behavior of a precracked bimaterial structure interface under given static and dynamic axial loading is an interest object in the present paper.Firstly,it is shown that the shearlag model is a proper tool to analyze a delamination process in a precracked bimaterial structure undergoing static loading.Secondly,the"shearlag model"is applied to the structure under dynamic loading.To solve the problem for an interface delamination of the structure and to determine the debond length along the interface,our own 2D boundary element method(BEM)code is proposed in the case of static loading,and the shearlag model together with the Laplace transforms and halfanalytical calculations are used in the case of dynamic loading.The interface layer is assumed as a very thin plate compared with the other two.The parametric(geometric and elastic)analysis of the debond length and interface shear stress is done. The results from the 2D BEM code proved the validity of analytical solutions to the shearlag model.In the dynamic case,the influence of loading characteristics,i.e.,frequencies and amplitude fluctuations on the shear stress and the value of debond length for an interval of time,is discussed. The analysis of the obtained results is illustrated by an example of the modern ceramicmetal composite,namely cermet, and depicted in figures.

2.

Highprecision solution to the moving load problem using an improved spectral element method





ShuRui Wen ZhiJing Wu NianLi Lu《Acta Mechanica Sinica》,2018年第34卷第1期


In this paper, the spectral element method(SEM)is improved to solve the moving load problem. In this method, a structure with uniform geometry and material properties is considered as a spectral element, which means that the element number and the degree of freedom can be reduced significantly. Based on the variational method and the Laplace transform theory, the spectral stiffness matrix and the equivalent nodal force of the beamcolumn element are established. The static Green function is employed to deduce the improved function. The proposed method is applied to two typical engineering practices—the onespan bridge and the horizontal jib of the tower crane. The results have revealed the following. First, the new method can yield extremely highprecision results of the dynamic deflection, the bending moment and the shear force in the moving load problem.In most cases, the relative errors are smaller than 1%. Second, by comparing with the finite element method, one can obtain the highly accurate results using the improved SEM with smaller element numbers. Moreover, the method can be widely used for statically determinate as well as statically indeterminate structures. Third, the dynamic deflection of the twinlift jib decreases with the increase in the moving load speed, whereas the curvature of the deflection increases.Finally, the dynamic deflection, the bending moment and the shear force of the jib will all increase as the magnitude of the moving load increases.

3.

NONLINEAR DYNAMIC ANALYSIS OF A LAMINATED HYBRID COMPOSITE PLATE SUBJECTED TO TIMEDEPENDENT EXTERNAL PULSES





Mehmet Senyer Zafer Kazanci《Acta Mechanica Solida Sinica》,2012年第6期


Nonlinear dynamic responses of a laminated hybrid composite plate subjected to timedependent pulses are investigated. Dynamic equations of the plate are derived by the use of the virtual work principle. The geometric nonlinearity effects are taken into account with the von Kármán large deflection theory of thin plates. Approximate solutions for a clamped plate are assumed for the space domain. The single term approximation functions are selected by considering the nonlinear static deformation of plate obtained using the finite element method. The Galerkin Method is used to obtain the nonlinear differential equations in the time domain and a MATLAB software code is written to solve nonlinear coupled equations by using the Newmark Method. The results of approximatenumerical analysis are obtained and compared with the finite element results. Transient loading conditions considered include blast, sine, rectangular, and triangular pulses. A parametric study is conducted considering the effects of peak pressure, aspect ratio, fiber orientation and thicknesses.

4.

Structuralacoustic topology optimization analysis based on evolutionary structural optimization approach





《Chinese Journal of Acoustics》,2009年第4期


The continuum structuralacoustic topology optimization with external loading is investigated herein. Finite element method （FEM） is used to obtain the structural frequency response and boundary element method （BEM） is adopted to perform exterior acoustic radiation analysis. The evolutionary structural optimization （ESO） is served as an optimization method in structuralacoustic radiation topology analysis. The acoustic radiation optimization of a plate under harmonic excitation is given for example. The numerical results show that using ESO solution to analyze structuralacoustic topology optimization is feasible and effective.

5.

SOLUTION OF BENDING OF CANTILEVER RECTANGULAR PLATES UNDER UNIFORM SURFACELOAD BY THE METHOD OF TWODIRECTION TRIGONOMETRIC SERIES





林小松 袁文伯《应用数学和力学(英文版)》,1985年第6卷第8期


The bending of a cantilever rectangular plate is a very complicated problem in thetheory of plates.For a long time,there have been only approximate solutions for thisproblem by energy methods and numerical methods.since 1979,Prof.F.V.Chang of Tsing Hua University obtained,by the method ofsuperposition,a series of analytic solutions for cantilever rectangular plates under uniformload and concentrated load.In this paper,the twodirection trigonometric series is used to obtain the solution forthe bending of cantilever rectangular plates under uniform load.The obtained results arecompared with the results by the method of superposition.The comparison shows that theresults of these two methods are in good agreement,hence they are mutually confirmed to becorrect.

6.

Kármántype equations for a higherorder shear deformation plate theory and its use in the thermal postbuckling analysis





Shen Huishen《应用数学和力学(英文版)》,1997年第18卷第12期


Kármántype nonlinear large deflection equations are derived occnrding to the Reddy’s higherorder shear deformation plate theory and used in the thermal postbuckling analysis The effects of initial geometric imperfections of the plate areincluded in the present study which also includes th thermal effects.Simply supported,symmetric crossply laminated plates subjected to uniform or nomuniform parabolictemperature distribution are considered. The analysis uses a mixed GalerkinGolerkinperlurbation technique to determine thermal buckling louds and postbucklingequilibrium paths.The effects played by transverse shear deformation plate aspeclraio, total number of plies thermal load ratio and initial geometric imperfections arealso studied.

7.

ANALYTICAL SOLUTIONS TO STRESS CONCENTRATION PROBLEM IN PLATES CONTAINING RECTANGULAR HOLE UNDER BIAXIAL TENSIONS 被引次数：2





Yi Yang Jike Liu Chengwu Cai《Acta Mechanica Solida Sinica》,2008年第21卷第5期


The stress concentration problem in structures with a circular or elliptic hole can be investigated by analytical methods. For the problem with a rectangular hole, only approximate results are derived. This paper deduces the analytical solutions to the stress concentration problem in plates with a rectangular hole under biaxial tensions. By using the Utransformation technique and the finite element method, the analytical displacement solutions of the finite element equations are derived in the series form. Therefore, the stress concentration can then be discussed easily and conveniently. For plate problem the bilinear rectangular element with four nodes is taken as an example to demonstrate the applicability of the proposed method. The stress concentration factors for various ratios of height to width of the hole are obtained.

8.

AN EFFECTIVE BOUNDARY ELEMENT METHOD FOR ANALYSIS OF CRACK PROBLEMS IN A PLANE ELASTIC PLATE 被引次数：3





闫相桥《应用数学和力学(英文版)》,2005年第26卷第6期


A simple and effective boundary element method for stress intensity factor calculation for crack problems in a plane elastic plate is presented. The boundary element method consists of the constant displacement discontinuity element presented by Crouch and Starfield and the cracktip displacement discontinuity elements proposed by YAN Xiangqiao. In the boundary element implementation the left or the right cracktip displacement discontinuity element was placed locally at the corresponding left or right each crack tip on top of the constant displacement discontinuity elements that cover the entire crack surface and the other boundaries. Test examples (i. e. , a center crack in an infinite plate under tension, a circular hole and a crack in an infinite plate under tension) are included to illustrate that the numerical approach is very simple and accurate for stress intensity factor calculation of plane elasticity crack problems. In addition, specifically, the stress intensity factors of branching cracks emanating from a square hole in a rectangular plate under biaxial loads were analysed. These numerical results indicate the present numerical approach is very effective for calculating stress intensity factors of complex cracks in a 2D finite body, and are used to reveal the effect of the biaxial loads and the cracked body geometry on stress intensity factors.

9.

The bending of a thick rectangular plate with three clamped edges and one free edge





Cheng Changjun Yang Xiao《应用数学和力学(英文版)》,1990年第11卷第6期


The exact solution of the bending of a thick rectangular plate with three clamped edges and one free edge under a uniform transverse load is obtained by means of the concept of generalized simplysupported boundary^{[1]} in Reissner’s theory of thick plates. The effect of the thickness h of a plate on the bending is studied and the applicable range of Kirchhoffs theory for bending of thin plates is considered.

10.

THE BENDING OF A THICK RECTANGULAR PLATE WITH THREE CLAMPED EDGES AND ONE FREE EDGE





程昌钧 杨骁《应用数学和力学(英文版)》,1990年第6期


The exact solution of the bending of a thick rectangular plate with three clamped edgesand one free edge under a uniform transverse load is obtained by means of the concept ofgeneralized simplysupported boundary in Reissner’s theory of thick plates.The effect ofthe thickness h of a plate on the bending is studied and the applicable range of Kirchhoffstheory for bending of thin plates is considered.

11.

Thermal buckling of axisymmetrically laminated cylindrically orthotropic shallow spherical shells including transverse shear





朱永安 王璠 刘人怀《应用数学和力学(英文版)》,2008年第29卷第3期


The nonlinear thermal buckling of symmetrically laminated cylindrically orthotropic shallow spherical shell under temperature field and uniform pressure including transverse shear is studied. Also the analytic formulas for determining the critical buckling loads under different temperature fields are obtained by using the modified iteration method. The effect of transverse shear deformation and different temperature fields on critical buckling load is discussed.

12.

BENDING OF THICK PLATES WITH A CONCENTRATED LOAD





程昌钧《应用数学和力学(英文版)》,1981年第5期


In this paper,according to the simplified theory of[1].the bending of rectangular plates withtwo opposite edges simply supported and other two opposite edges being arbitrary under the action of aconcentrated load is treated by means of propertiesof twovariablefunction and the method of series[2].The effect of transverse shearing forces onthe bending of plates is considered.When the thickness h of plates is small.and the term,whose ordersare more than order of h~2 are neglected.then theresults agree with the solutions corresponding to theproblem of thin plates[3].At the end,the solutionsof the bending problem of plates with arbitrary lineardistributed load are also obtained.

13.

BENDING OF THICK PLATES WITH A CONCENTRATED LOAD





程昌钧《应用数学和力学(英文版)》,1981年第5期


In this paper,according to the simplified theory of[1].the bending of rectangular plates withtwo opposite edges simply supported and other two opposite edges being arbitrary under the action of aconcentrated load is treated by means of propertiesof twovariablefunction and the method of series[2].The effect of transverse shearing forces onthe bending of plates is considered.When the thickness h of plates is small.and the term,whose ordersare more than order of h~2 are neglected.then theresults agree with the solutions corresponding to theproblem of thin plates[3].At the end,the solutionsof the bending problem of plates with arbitrary lineardistributed load are also obtained.

14.

NONLINEAR THREEDIMENSION ANALYSIS FOR AXIALLY SYMMETRICAL CIRCULAR PLATES AND MULTILAYERED PLATES





江晓禹 张相周《应用数学和力学(英文版)》,1993年第14卷第8期


Analytic nonlinear threedimension solutions are presented for axially symmetrical homogeneous isotropic circular plates and multilayered plates with rigidly clamped boundary conditions and under transverse load.The geometric nonlinearily from a moderately large deflection is considered.A developmental perturbation method is used to solve the complicated nonlinear threedimension differential equations of equilibrium.The basic idea of this perturbation method is using the twodimension solutions as a basic form of the corresponding threedimension solutions,and then processing the perturbation procedure to obtain the threedimension perturbation solutions.The nonlinear threedimension results in analytic expressions and in numerical forms for ordinary plates and multilayered plates are presented.All of the plate stresses are shown in figures.The results show that this perturbation method used to analyse nonlinear threedimension problems of plates is effective.

15.

ELASTIC INSTABILITY OF AN ORTHOTROPIC ELLIPTIC PLATE





程昌钧 宁建国《应用数学和力学(英文版)》,1991年第12卷第4期


On the basis of von Kármán equations and using the general bifurcation theory,theelastic instability of an orthotropic elliptic plate whose edge is subjected to a uniform planecompression is discussed.Following the wellknown LiapunovSchmidt process theexistance of bifurcation solution at a simple eigenvalue is shown and the asymptoticexpression is obtained by means of the perturbation expansion with a small parameter.Finally,by using the finite element method,the critical loads of the plate are computed andthe postbuckling behavior is analysed.And also the effect of material and geometric parameters on the stability is studied.

16.

APPROXIMATE SOLUTION FOR BENDING OF RECTANGULAR PLATES KantorovichGalerkin’s Method





Wang Lei and Li Jiabao《应用数学和力学(英文版)》,1986年第7卷第1期


This paper derives the cubic spline beam function from the generalized beam differential equation and obtains the solution of the discontinuous polynomial under concentrated loads, concentrated moment and uniform distributed by using delta function. By means of Kantorovich method of the partial differential equation of elastic plates which is transformed by the generalized function (δ function and σ function), whether concentrated load, concentrated moment, uniform distributed load or smallsquare load can be shown as the discontinuous polynomial deformed curve in the xdirection and the ydirection. We change the partial differential equation into the ordinary equation by using Kantorovich method and then obtain a good approximate solution by using Glerkin’s method. In this paper there ’are more calculation examples involving elastic plates with various boundaryconditions, various loads and various section plates, and the classical differential problems such as cantilever plates are shown.

17.

ADHESIVE CONTACT PROBLEM OF AXISYMMETRIC MINIATURE CIRCULAR PLATES WITH CENTRAL RIGID BUMP





Fu Yiming Li Sheng Tian Yanping《Acta Mechanica Solida Sinica》,2006年第19卷第4期


Considering the adhesive effect and geometric nonlinearity, the adhesive contactbetween an elastic substrate and a clamped miniature circular plate with two different centralrigid bumps under the action of uniform transverse pressure and inplane tensile force in theradial direction was analyzed. And an analytical solution is presented by using the perturbationmethod. The relation of surface adhesive energies with critical load to detach the contacted surfacesis obtained. In the numerical results, the effects of adhesive energy, inplane tensile force, rigidbump size and contact radius on the critical load are discussed, and the relation of critical contactradius with the gap between the central rigid bump and the substrate for different adhesive energiesis investigated.

18.

GENERAL ANALYTIC SOLUTION OF DYNAMIC RESPONSE OF BEAMS WITH NONHOMOGENEITY AND VARIABLE CROSSSECTION





叶开沅 童晓华 纪振义《应用数学和力学(英文版)》,1992年第13卷第9期


In this paper, a new method, the stepreduction method, is proposed to investigate the dynamic response of the BernoulliEuler beams with arbitrary nonhomogeneity and arbitrary variable crosssection under arbitrary loads. Both free vibration and forced vibration of such beams are studied. The new method requires to discretize the space domain into a number of elements. Each element can be treated as a homogeneous one with uniform thickness. Therefore, the general analytical solution of homogeneous beams with uniform crosssection can be used in each element. Then, the general analytic solution of the whole beam in terms of initial parameters can be obtained by satisfying the physical and geometric continuity conditions at the adjacent elements. In the case of free vibration, the frequency equation in analytic form can be obtained, and in the case of forced vibration, a final solution in analytical form can also be obtained which is involved in solving a set of simultaneous algebraic equations with only

19.

Nonlinear vibration and buckling of circular sandwich plate under complex load





杜国君 马建青《应用数学和力学(英文版)》,2007年第28卷第8期


The nonlinear vibration fundamental equation of circular sandwich plate under uniformed load and circumjacent load and the loosely clamped boundary condi tion were established by von Karman plate theory,and then accordingly exact solution of static load and its numerical results were given.Based on time mode hypothesis and the variational method,the control equation of the space mode was derived,and then the amplitude frequencyload character relation of circular sandwich plate was obtained by the modified iteration method.Consequently the rule of the effect of the two kinds of load on the vibration character of the circular sandwich plate was investigated.When circumjacent load makes the lowest natural frequency zero,critical load is obtained.

20.

NONLINEAR ANALYSIS OF A CORRUGATED CIRCULAR PLATE UNDER COMBINED LATERAL LOADING





刘人怀《应用数学和力学(英文版)》,1988年第8期


In this paper, nonlinear bending of a corrugated circular plate with a plane central region under the combined action of uniformly distributed load and a concentrated load at the center has been investigated by using large deflection theories of isotropic and anisotropic circular plates. The quite accurate analytical solutions for rigidly as well as loosely clamped edge conditions have been obtained following the modified iteration method.
