Transient bending of a piezoelectric circular plate

Thin, piezoelectric circular plates are frequently used as active components in transducer and smart materials applications. This paper reports on the exact, explicit solution for the transient motion of a piezoelectric circular plate, built-in or simply supported on the edge and electrically grounded over the entire surface. Expressed by elementary Bessel functions and obtained via exact inverse Laplace transforms, the solution enables the efficient calculation of accurate system parameters.     

A new approach for bending analysis of thin circular plates with large deflection

This paper is concerned with bending analysis of an axisymmetric simply supported circular plate with large deflection. Based on the linear theory of thin plates, the incremental load technique is developed for solving the bending problem of a thin circular plate with large deflection. In the proposed method, the total applied load is divided into various small load steps. In each load step, the plate stress behavior is simplified to be linear. The incremental formulations are presented for the deflection and stresses of the plate when external loads increase. A numerical example is given to show simplicity and accuracy of the present method. It is found that the proposed method can be an alternative useful tool for engineering applications.     

On the rotating elastic–plastic solid disks of variable thickness having concave profiles

In this paper, an analytical solution for the elastic–plastic stress distribution in rotating variable thickness solid disks is presented. The analysis is based on Tresca's yield criterion, its associated flow rule and linear strain hardening material behavior. It is shown that depending on the shape of the disk profile, the radial stress in the central region may exceed the circumferential stress. The plastic zone which develops away from the axis of the disk consists of three annular regions governed by different mathematical forms of the yield criterion. The propagation of these plastic regions with increasing angular velocity is obtained together with the distributions of stresses and deformations in nondimensional forms.     

Post-failure behaviour of impulsively loaded circular plates

The dynamic plastic response of a simply supported circular plate is analysed. Emphasis is given to the plate behaviour after it has broken free from the supports due to a local material failure. The theoretical rigid plastic analysis predicts various features of the response such as the time to failure, residual kinetic energy and the critical velocity at failure. The residual kinetic energy of the plate could be significant enough to cause secondary impact damage. It is shown that the shape of the plate changes after breaking free from the supports, which is important for forensic investigations. The solution for various cases were proven to be exact in the context of the upper and lower bounds theorems of the theory of plasticity.     

Vibrations of microscale circular plates induced by ultra-fast lasers

In this study, the vibration phenomena during pulsed laser heating of a microscale circular plate are investigated. The circular plate is made of silicon and is heated uniformly on the upper surface by a non-Gaussian laser beam with a pulse duration of 2 ps, which incites vibration due to the thermoelastic coupling effect. The coupling between the temperature field and stress field induces energy dissipation and converts mechanical energy into heat energy, which is irreversible. An analytical-numerical technique based on the Laplace transform is utilized to calculate the vibration of the deflection and thermal moment. The size effect is analyzed. Finally, the vibration behaviors of the circular plate under different environmental temperatures are compared.     

中厚板弯曲过程中板厚变化的研究及数值模拟

以中厚钢板为研究对象,采用数学公式推导和实验相结合的方法,在弯曲过程中分析应力和应变中性层内移的基础上,根据弯曲前后体积不变、内外边层应变绝对值的增量与它们到应力中性层的距离成正比这两个条件,推导板厚变化与相对弯曲半径的关系式.比较实验值与公式推导的板厚变化值,得出板厚变化值的经验修正系数,并通过Abaqus软件对选定材料的弯曲进行数值模拟,验证计算方法的正确性.     

Three-dimensional free vibration of variable thickness thick circular and annular isotropic and functionally graded plates on Pasternak foundation

This paper describes a study of three-dimensional free vibration analysis of thick circular and annular isotropic and functionally graded (FG) plates with variable thickness along the radial direction, resting on Pasternak foundation. The formulation is based on the linear, small strain and exact elasticity theory. Plates with different boundary conditions are considered and the material properties of the FG plate are assumed to vary continuously through the thickness according to power law. The kinematic and the potential energy of the plate-foundation system are formulated and the polynomial-Ritz method is used to solve the eigenvalue problem. Convergence and comparison studies are done to demonstrate the correctness and accuracy of the present method. With respect to geometric parameters, elastic coefficients of foundation and different boundary conditions some new results are reported which may be used as benchmark solutions for future researches.     

Analytical investigation on axisymmetric free vibrations of moderately thick circular functionally graded plate integrated with piezoelectric layers

In this paper, a free vibration analysis of moderately thick circular functionally graded (FG) plate integrated with two thin piezoelectric (PZT4) layers is presented based on Mindlin plate theory. The material properties of the FG core plate are assumed to be graded in the thickness direction, while the distribution of electric potential field along the thickness of piezoelectric layers is simulated by sinusoidal function. The differential equations of motion are solved analytically for two boundary conditions of the plate: clamped edge and simply supported edge. The analytical solution is validated by comparing the obtained resonant frequencies with those of an isotropic host plate. The emphasis is placed on investigating the effect of varying the gradient index of FG plate on the free vibration characteristics of the structure. Good agreement between the results of this paper and those of the finite element analyses validated the presented approach.     

The stress and strain concentrations of out-of-plane bending plate containing a circular hole

The elastic stress and strain fields of a finite thickness plate containing a circular hole subjected to out-of-plane bending are systematically investigated using the finite element method. It is found that the stress and strain concentration factors of the finite thickness plate are different except at the notch root of the free surface even if the plate is in elasticity state. The through-thickness distributions of strain components are not linear with the distance from the mid-plane in the stress concentration region. The nonlinearity of these distributions is very severe near the free surface especially in thick plate. The Euler-Bernoulli hypothesis and Kane-Mindlin's plate theory may not be reasonable to be used in the stress concentration region especially near the free surface. The maximum stress and strain do not always occur on the free surface and their locations depend on the moment ratio and the plate thickness. The maximum stress and strain concentration factors occur on the free surface only in thin plates of small moment ratio. The differences between the maximum value and surface value of stress concentration factor increase with the plate thickness and the moment ratio. This relation of strain concentration factor is similar to the one of stress concentration factor. But the difference magnitude of stress concentration factor is larger than that of strain concentration factor in same plate.     

Free transverse vibration of elliptical plates of variable thickness with half of the boundary clamped and the rest free

First four frequencies have been computed for an elliptical plate half of whose boundary (y0) is clamped and the other half is free. The thickness of the plate is taken varying linearly with space coordinates. The Rayleigh–Ritz method has been used to obtain successive approximations utill convergence is achieved up to at least four significant figures. Results are tabulated for various values of the taper parameters. Three-dimensional mode shapes and the associated contour lines have been plotted in some selected cases. A table showing the rate of convergence with increasing order of approximation is given. Comparison has been made with known results in special cases. For the sake of completeness, results for the cases when the entire boundary is clamped or completely free are also reported.     

Three-dimensional vibration, buckling and bending analyses of thick rectangular plates based on discrete singular convolution method

The main objective of this study is to give a numerical solution of three-dimensional analysis of thick rectangular plates. The analysis uses discrete singular convolution (DSC) method. Free vibration, bending and buckling of rectangular plates have been studied in this paper. Regularized Shannon's delta (RSD) kernel is selected as singular convolution to illustrate the present algorithm. In the proposed approach, the derivatives in both the governing equations and the boundary conditions are discretized by the method of DSC. The obtanied results are compared with those of other numerical methods. It is found that the convergence of the DSC approach is very good and the results agree well with those obtained by other researchers.     

Three-dimensional static solutions of rectangular plates by variant differential quadrature method

An endeavor to exploit three-dimensional elasticity solutions for bending and buckling of rectangular plates via the differential quadrature (DQ) and harmonic differential quadrature (HDQ) methods is performed. Unlike other works, the priority of this paper is to examine the computational characteristics of the two methods; therefore, we focus our studies only on the simply supported and clamped rectangular plates. To start with, we first outline the basic equations and boundary conditions describing the bending and buckling of rectangular plates followed by normalizing and discretizing them according to the DQ and HDQ algorithms. The resulting algebraic equation systems are then solved to obtain the solutions. Based on these solutions, the computational characteristics of the DQ and HDQ methods are investigated in terms of their numerical performances. It is found that the DQ method displays obvious superior convergence characteristics over the HDQ method for the three-dimensional static analysis of rectangular plates.     

Analysis of stiffened corrugated plates based on the FSDT via the mesh-free method

The elastic bending of unstiffened and stiffened corrugated plates is studied in this paper, and a mesh-free Galerkin method is presented for the analyses. A corrugated plate is treated as an orthotropic plate that has different flexure properties in two perpendicular directions. The equivalent flexure properties are estimated by applying constant curvature conditions to the corrugated sheet. The stiffened corrugated plate is considered as a composite structure of an orthotropic plate with beams. By superimposing the strain energy of the orthotropic plate and the beams, and imposing the displacement compatibility conditions between the plate and the beams, the stiffness matrix of the structure is obtained. Because no mesh is needed in the proposed method, there is no limitation to the position of the stiffeners (beams). Changes in the positions of the stiffeners do not require the re-meshing of the plate. Several numerical examples are employed to show the accuracy and convergence of the proposed method. The computation results demonstrate good agreement with the solutions given by ANSYS, and different profiles of corrugated plates are considered.     

Stress distribution in a linear hardening annular disk of variable thickness subjected to external pressure

The subject of investigation is a linear hardening annular disk of variable thickness subjected to external pressure. The variation of thickness is considered for two different cases: (1) h = h_o (1 − tr)^k and (2) h = h_o (1 − tr^k), where h₀, t and k are real constants. The analysis is based on Tresca's yield condition and its associated flow rule. The governing differential equations are presented in terms of radial displacement. Exact elastic—plastic solutions are obtained in terms of hypergeometric functions for the radial displacement and stress distributions. Numerical results showing the influence of the thickness variation on the stress distribution for different values of the hardening parameter are presented graphically. It can be seen from the present analysis that the thickness variation influences the radial stress and displacement distributions significantly. The present investigation may provide useful information for structural designers and engineers working in these scopes.     

An exact solution for the bending of thin rectangular plates with uniform, linear, and quadratic thickness variations

In this paper, the analysis of the titled problem is based on classical thin-plate theory, and its numerical solution is carried out by using the small parameter method and Lévy-type approach. The thin rectangular plate considered herein is simply supported on two opposite edges. The boundary conditions at the other two edges may be quite general, and between these two edges the plate may have varying thickness. Closed-form solutions have been developed for the static response of isotropic rectangular plates with non-uniform thickness variation and subjected to arbitrary loading. The accuracy of the present model is demonstrated via problems for which the exact solutions and numerical results are available, and results are also compared with those obtained by using the finite-difference method.     

变截面涡旋盘高速铣削仿真加工与实验研究

为减小变截面涡旋盘涡旋齿的变形,提高加工精度,需确定合理的铣削参数。开展了变截面涡旋盘高速铣削仿真与实验研究以确定铣削参数的合理取值范围;选用HT250变截面涡旋盘为研究对象,研究了更接近实际的材料本构模型、刀-屑摩擦模型和热传导控制方程等关键技术;建立了变截面涡旋盘几何模型和简化后的二维铣削模型,利用ABAQUS软件仿真切屑成形过程及不同的铣削参数对铣削力、铣削热影响的变化曲线;通过多因素正交实验加工变截面涡旋盘。结果表明:当主轴转速为3500 r/min、每齿进给量为0.1 mm以及切削深度为2.5 mm时进行铣削更加合理。铣削变截面涡旋盘的研究为加工参数的选择提供了依据和参考;依据实验后所得的铣削参数进行铣削可减小铣削力、铣削温度及齿变形,提高了变截面涡旋盘的加工效率和质量。     

Axisymmetric response of circular plates with piezoelectric layers: an exact solution

Electromechanical responses of symmetric circular laminates consisting of piezoelectric layers are studied, and the influence of surface and interlayer electrodes are involved. The laminates are traction-free on the top and bottom surfaces, but may be subjected to external forces at the lateral edge and to voltages applied across certain layers. Under axisymmetric deformation conditions, an approximate model which employs Kirchhoff hypothesis and incorporates the charge equation of electrostatic is established. Then, a closed-form three-dimensional solution of the laminates is generated in a very straightforward manner by the solution of the approximate model. The three-dimensional solution fulfills all field equations and interface or surface conditions as well as the specified electric edge boundary conditions; the only restriction is that the mechanical edge boundary conditions are satisfied in an average manner, rather than point by point. Thus, according to Saint-Venant's principle the proposed solution is exact in the interior region of the laminates.     

Nonlinear cylindrical bending analysis of shear deformable functionally graded plates under different loadings using analytical methods

An exact solution is presented for the nonlinear cylindrical bending and postbuckling of shear deformable functionally graded plates in this paper. A simple power law function and the Mori–Tanaka scheme are used to model the through-the-thickness continuous gradual variation of the material properties. The von Karman nonlinear strains are used and then the nonlinear equilibrium equations and the relevant boundary conditions are obtained using Hamilton's principle. The Navier equations are reduced to a linear ordinary differential equation for transverse deflection with nonlinear boundary conditions, which can be solved by exact methods. Finally, by solving some numeral examples for simply supported plates, the effects of volume fraction index and length-to-thickness ratio are studied. It is shown that there is no bifurcation point for simply supported functionally graded plates under compression. The behavior of near-boundary areas predicted by the shear deformation theory and the classical theory is remarkably different.     

Influence of stiffener location on the stability of stiffened plates under compression and in-plane bending

The elastic behaviour of stiffened plates under non-uniform edge compression is investigated. As a first stage, an energy formulation, in which the structure is modelled as assembled plate and beam elements, is presented. A Sequential Quadratic Programming (SQP) algorithm is then used to evaluate the buckling load and the associated buckling mode for given plate/stiffener geometric properties. Results are presented showing the influence of the stiffener location on the stability of the structure under combined compression and bending. Then, a strategy is presented for optimum location of the stiffener. The proposed methodology can be used to develop an improved design procedure for efficient design of stiffened plates under this type of loading.     

可变地球张角圆锥扫描式地球模拟器结构设计

地球模拟器是红外地球敏感器地面模拟试验与标定的重要设备,针对现有的圆锥扫描式地球模拟器无法提供可变地球张角的问题,提出了一种可变地球张角圆锥扫描式地球模拟器的设计方案,对冷板、热板等主要组成部分进行了详细的结构设计。根据两块活动冷板尺寸大且不易控制转动精度的特点,采用一个电动推杆通过两个连杆机构带动两片活动冷板同时转动的结构,建立三维仿真模型,并应用有限元ANSYS软件对支架进行应力分析和对冷板和热板进行热分析。经实验验证:该结构设计合理,能满足红外地球敏感器的测试与标定要求。