Elastic behavior of uniformly loaded circular corrugated plate with sine-shaped shallow waves in large deflection

By means of modified iteration method, this paper gives approximate solution of the large deflection equations of circular corrugated plate with sine-shaped shallow waves having a central platform under uniform lateral load. A formula of initial modification coefficient is given, and an integral is obtained for the simplification of modified iteration calculations. The results of present paper show better agreement with experimental data and larger applicable range than all other existing solutions of corrugated plates.     

用能量法研究双模量大挠度圆板的轴对称弯曲

双模量圆板在外载荷作用下发生轴对称弯曲变形时,会形成各向同性的拉伸区和压缩区.此种情况下,可把双模量圆板看成两种各向同性材料组成的层合板,采用弹性理论建立了双模量圆板在外载荷作用下的静力平衡方程,利用静力平衡方程确定了双模量圆板的中性面位置.在此基础上,采用能量法研究了双模量大挠度圆板轴对称弯曲变形问题,将该方法计算结...     

Optimal design of minimax deflection of an annular plate

The optimal design of minimax deflection of an annular plate is studied in this paper. The annular plate is subjected to an arbitrary axisymmetric loading. The problem can be posed as a standard nonlinear programming problem with equality constraints by means of the stepped reduction method. Some examples are also given to illustrate the method which has many advantages.Project Supported by the Science Fund of the National. Education Committee.     

On the jumping problems of a circular thin plate with initial deflection

In this paper, the jumping problems of a circular thin plate with initial deflection are studied by using the method of two variables^[3],[4] proposed by Jiang Fu-ru and the method of the normal perturbation (in this paper (1.1), (1.2)). We obtain Nth-order uniformly valid asymptotic expansion of the solution of this problem ((1.66), (1.67)). When the initial deflection vanishes the solution of a circular thinplate with initial deflection is reduced to the solution of the problems of the nonlinear bending of a circular thin plate^[6]. If the initial deflection is largish and the signs of the initial deflection with the intensity of the transverse load are opposite, when the intensity of the transverse load reaches a certain value, the circular thin plate with initial deflection should produce the jumping phenomenon^[8].     

Elasto-plastic bending of an annular plate at large deflection

Summary The elasto-plastic bending of a simply supported annular plate with a free inner edge upon which an uniformly distributed lateral load acts is theoretically investigated, taking into account the influence of the membrane forces. A homogeneous and isotropic elasto-perfectly-plastic material satisfying the Mises' yield condition and the Hencky's stess-strain relation is assumed. The theoretical results are discussed and compared with experimental results obtained with a plate of mild steel; the relation between the real behavior of the actual material and the usual assumptions used in the analysis is emphazised. The theoretical result is also compared with the result of an analysis in which the membrane forces were neglected; in this manner the influence of these forces is shown.

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Übersicht Das elastisch-plastische Biegen einer einfach gelagerten Ringplatte wird theoretisch untersucht, wobei der Einfluß der Membrankräfte berücksichtigt wird. Der innere Rand der Platte ist frei gelagert und trägt eine stetig verteilte Querlast. Es wird ein homogenes, isotropes und ideal elastisch-plastisches Material vorausgesetzt, das der v. Misesschen Fließbedingung und dem Henkyschen Spannungs-Dehnungs-Gesetz genügt. Die Rechenergebnisse werden diskutiert und mit entsprechenden Versuchsergebnissen verglichen, wobei besonderen Wert auf die Beziehung zwischen dem wirklichen Materialverhalten und den üblicherweise in der Theorie verwendeten Annahmen gelegt wird. Die Ergebnisse werden außerdem mit entsprechenden Berechnungsergebnissen verglichen, bei denen die Membrankräfte vernachlässigt wurden, so daß der Einfluß dieser Kräfte deutlich wird.

     

Elastic instability of an orthotropic elliptic plate

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 well-known Liapunov-Schmidt 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 post-buckling behavior is analysed.And also the effect of material and geometric parameters on the stability is studied.     

Post-buckling analysis of a thin stiffened plate with uncertain initial deflection via interval analysis

The post-buckling behavior of the thin stiffened plates with uncertain initial deflection under uni-direction compression load is investigated based on Von-Karman large deflection theory. The uncertain initial deflections are considered to be unknown except that they belong to a given set in the interval range. Interval analysis model for computing the bounds of curves of the post-buckling deflection versus load of the plate is presented. Interval analysis model is compared with the stochastic model, which is taken as the benchmarks of accuracy for judgment. The results indicate that the non-probabilistic and stochastic methods will produce similar results for a large deviation of uncertainty. If the probabilistic information is unavailable, one should not propose the probabilistic method based on an arbitrary assumption on the distribution of the deflection coefficients. Rather, one should use the non-probabilistic method to uncertainty.     

The large deflection problem of circular thin plate with variable thickness under uniformly distributed loads

In this paper, to begin with, the large deflection equation of variable thickness circular plates is given. By using small parameter method and revised iteration jointly a cubic approximate solution is obtained. A characteristic is also given for comparison with linear theory.     

Large deflection of a circular cantilever beam with uniformly distributed load

Summary In this paper, the bending of thin circular cantilever beam, convex downward, under a uniformly distributed load is discussedby the use of the Bernoulli-Euler equation. The solutions are obtained in the form of power series. Numerical results are also presented.The author wishes to thank Dr. S. Higuchi, Professor Emeritus of the Thoku University, for his suggestion and encouragement in the work. The author also wishes to thank Professor F. Numachi and Professor O. Tamate for their kind advice.     

Elastic compensation simulation of elastic/plastic axisymmetric circular plate bending using a deformation model

A deformation plasticity model is used to implement the elastic compensation (iterative use of linearly elastic models to approximate elastic/plastic response) simulation of small axisymmetric circular plate deformations by the finite element method. Representative numerical results are presented graphically and used to demonstrate the utility of the approach.     

The influence of a uniformly compressed floating elastic plate on the development of three-dimensional waves in a homogeneous fluid

A study is made in the linear formulation of the influence of a uniformly compressed floating elastic plate on the unsteady three-dimensional wave motion of a homogeneous fluid of finite depth. Waves are excited by a region of normal stresses which moves on the surface of the plate. Three-dimensional flexural-gravity waves were studied in [1, 2] without allowance for compressing forces. Plane waves under conditions of longitudinal compression were considered in [3, 4].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 78–83, November–December, 1984.     

Inviscid flow past a ducted axisymmetric body with annular elliptical region

The flow regime with an annular elliptical region between the shock wave and a ducted body is realized when the ratio of the duct diameter to the characteristic body thickness is sufficiently large and the backpressure is sufficiently low. In the present paper we consider the application of the method of integral relations in the first approximation to the calculation of such a flow. The examples were calculated on a computer.     

Effect of initial imperfections in geometry on the elastic-plastic stability of a thin annular plate

In this paper,Neale’S generalized variational principle aboutincremental boundarg-value problems is utilized to study theeffect of initial imperfections in geometry on tbe criticalloads of elasticoplastic buckling of thin annular plates.Thecalculations show that.if the effect of initial imperfectionsin geometrg is taken into account in the solutions by J_2 in-cremental theorg.the results are very close to the bifurca-tional buckling loads of the perfect annular Plates accordingto the plastic deformation theorg.     

铸铁均匀压缩破坏形式

通过灰铸铁试件的均匀轴向压缩实验,得到的实验结果为断口与试件轴线夹角在43度左右.对一些作者的不同结果的灰铸铁试件压缩实验提出质疑.     

Bending of a uniformly loaded clamped sector plate

The paper involves the expansion of the biharmonic deflection function in a series of non-orthogonal functions satisfying the condition of clamped edges. Each of these non-orthogonal functions is expanded in a series of orthogonal functions which satisfy a certain fourth order differential equation and the boundary conditions implied by the fact that the edges are clamped. This reduces the bending of a uniformly loaded clamped sector plate to the solution of a linear algebraic system of equations. Numerical results for the deflection of the central line are obtained when the semi-sector angle is 15 degrees.     

Analysis of multiple axisymmetric annular cracks in a piezoelectric medium

An axisymmetric annular electric dislocation is defined. The solution of axisymmetric electric and Volterra climb and glide dislocations in an infinite transversely isotropic piezoelectric domain is obtained by means of Hankel transforms. The distributed dislocation technique is used to construct integral equations for a system of co-axial annular cracks with so-called permeable and impermeable electric boundary conditions on the crack faces where the domain is under axisymmetric electromechanical loading. These equations are solved numerically to obtain dislocation densities on the crack surfaces. The dislocation densities are employed to determine field intensity factors for a system of interacting annular and/or penny-shaped cracks.