Thermal Postbuckling of Imperfect Shear-Deformable Laminated Plates on Two-Parameter Elastic Foundations

Thermal postbuckling analysis is presented for a simply supported, shear-deformable composite laminated plate subjected to uniform or nonuniform parabolic temperature loading and resting on a two-parameter (Pasternak-type) elastic foundation. The initial geometric imperfection of the plate is taken into account. Reddy's third-order shear-deformation plate theory with von Karman nonlinearity is used. The governing equations also include the plate-foundation interaction and thermal effects. The analysis uses a mixed Galerkin-perturbation technique to determine thermal buckling loads and postbuckling equilibrium paths. Numerical examples are presented that relate to the performances of perfect and imperfect, symmetric cross-ply laminated plates resting on Pasternak-type elastic foundations from which results for Winkler elastic foundations are obtained as a limiting case. The influence played by a number of effects, among them foundation stiffness, transverse shear deformation, plate aspect ratio, fiber orientation, thermal load ratio, and initial geometric imperfections, is studied. Typical results are presented in dimensionless graphical form.     

Finite Element Multi-mode Approach to Thermal Postbuckling of Functionally Graded Plates

Postbuckling analysis of functionally graded ceramic-metal plates under temperature field is presented using finite element multi-mode method. The three-node triangular element based on the Mindlin plate theory is employed to account for the transverse shear strains, and the von-Karman nonlinear strain-displacement relation is utilized considering the geometric nonlinearity. The effective material properties are assumed to vary through the thickness direction according to the power law distribution of the volume fraction of constituents. The temperature distribution along the thickness is determined by one dimensional Fourier equations of heat conduction. The buckling mode shape solved from eigen-buckling analysis is adopted as the assumed mode function to reduce the degrees of freedom of nonlinear postbuckling equilibrium equations. The postbuckling response is obtained by solving the nonlinear equilibrium equations, and compared with the Newton- Raphson numerical results. The effects of boundary conditions, material gradient index and temperature distribution on postbuckling behavior are examined.     

弹性基础上矩形板热后屈曲分析

本文给出双参数弹性基础上矩形板在均匀和非均匀（抛物型）热分布作用下后屈曲分析。采用摄动－Ｇａｌｅｒｋｉｎ混合法给出完善和非完善矩形板热屈曲载荷和热后屈曲平衡路径。本文同时给出数值算例并讨论各种参数变化的影响。     

Postbuckling Analysis of Shear-Deformable Composite Laminated Plates on Two-Parameter Elastic Foundations

Postbuckling analysis is presented for a simply supported, shear-deformable, composite laminated plate subjected to uniaxial compression and resting on a two-parameter (Pasternak-type) elastic foundation. The initial geometric imperfection of the plate is taken into account. Two cases of in-plane boundary conditions are considered. The formulations are based on Reddy’s higher-order shear-deformation plate theory, including plate–foundation interaction. The analysis uses a deflection-type perturbation technique to determine buckling loads and postbuckling equilibrium paths. Numerical examples are presented that relate to the performance of perfect and imperfect, antisymmetric angle-ply and symmetric cross-ply laminated plates resting on Pasternak-type elastic foundations from which results for Winkler elastic foundations are obtained as a limiting case. The effects played by foundation stiffness, transverse shear deformation, the character of the in-plane boundary conditions, plate aspect ratio, total number of plies, fiber orientation, and initial geometric imperfections are studied.     

基于三维等效弹性模量的复合材料中厚层合板稳定性分析

通过对复合材料层合板刚度矩阵的转换,将中厚板等效为3D各向异性板,并将得到的等效弹性模量运用到有限元模型中,对轴压载荷作用下的中厚层合板进行稳定性分析。结果表明：有限元模拟得到的屈曲载荷与工程经验公式得到的屈曲载荷相差很小,简支情况下相差5.86%,固支情况下相差6.47%。证明这种等效方法是可行的,且可以提高复合材料中厚板的三维建模效率。     

非线性弹性地基上矩形薄板的非线性振动与奇异性分析

研究非线性弹性地基上小挠度矩形薄板的非线性振动，应用弹性力学理论建立非线性弹性地基上小挠度矩形薄板受简谐激励作用的动力学方程，利用Galerkin方法将其转化为非线性振动方程。根据非线性振动的多尺度法求得系统主参数共振-主共振情况的一次近似解，并进行数值计算。分析了阻尼系数、地基系数、激励参数等对系统主参数共振-主共振的影响。系统主参数共振-主共振曲线均具有跳跃现象。随着阻尼、地基系数的改变，系统响应曲线具有“类软刚度特征”。随着参数激励幅值的改变，系统响应曲线具有“类硬刚度特征”。应用奇异性理论得到系统主参数共振-主共振稳态响应的转迁集和分岔图。     

考虑地基耦合效应的矩形中厚板的非线性静力分析

基于能量变分原理,考虑板的横向剪切和地基耦合效应,建立了双参数地基上弹性中厚板的非线性控制方程。应用伽辽金法对双参数地基上四边自由矩形中厚板的非线性弯曲问题进行了探讨。数值计算中考虑了系统各种参数变化对弯曲问题的影响。     

Bending of Circular Sandwich Plate on Elastic Foundation

Bending of elastic circular sandwich plate with light filler, which is on an elastic foundation, is considered. To describe the kinematics of plate bending that is nonsymmetric in sandwich thickness, broken normal hypotheses are accepted. The foundation reaction is described by the Winkler model. The load is local symmetrical. A set of equilibrium equations and their exact solution in displacements have been obtained. Numerical results for a metal-polymeric sandwich plate are given. __________ Translated from Problemy Prochnosti, No. 6, pp. 68 – 78, November – December, 2005.     

Influence of Membrane Stresses on Postbuckling of Rectangular Plates Using a Nonlinear Elastic 3-D Cosserat Brick Element

This paper has two main objectives. The first is to examine the influence of membrane stresses on postbuckled deformations of nonlinear elastic isotropic rectangular plates. The second is to further examine the accuracy of a new 3-D Cosserat eight noded brick element (Nadler and Rubin in Int J Solids Struct 40: 4585–4614, 2003) which was developed within the context of the theory of a Cosserat point. The equations of the Cosserat element include both material and geometric nonlinearities. A number of example problems are considered which examine predictions of the Cosserat element for beams and plates and comparison has been made with results from the commercial codes ANSYS and ADINA. Also, the approximate nonlinear postbuckling solution described in Timoshenko and Gere (Theory of elastic stability, Mc Graw-Hill, New York) is shown to be more limited than originally expected. These results suggest that the Cosserat element is robust, can perform well under extreme conditions and is capable of modeling combinations of three-dimensional bodies with attached thin structures.     

Nonlinear Response of Imperfect Eccentrically Stiffened Ceramic-Metal-Ceramic Sigmoid Functionally Graded Material (S-FGM) Thin Circular Cylindrical Shells Surrounded on Elastic Foundations Under Uniform Radial Load

This article researches nonlinear response of imperfect eccentrically stiffened symmetric FGM thin circular cylindrical shells with ceramic-metal-ceramic layers, which are symmetric through the middle surface by Sigmoid-law distribution (S-FGM) and have stiffeners surrounded on elastic foundations under uniform radial load. The Donnell classical shell theory, stress function, and Galerkin method are used for investigation of the nonlinear stability of the S-FGM shell. The obtained results show the effects of the stiffeners, elastic foundations, mechanical load, and material parameters on the nonlinear buckling response of symmetric S-FGM circular cylindrical shells.     

Thermal Buckling Analysis of Piezoelectric Functionally Graded Plates with Temperature-Dependent Properties

In this study, the thermal buckling analysis of hybrid laminated plates made of two-layered functionally graded materials (FGMs) that are integrated with surface-bonded piezoelectric actuators referred to as (P/FGM)_s are investigated. Material properties for both substrate FGM layers and piezoelectric layers are temperature-dependent. Uniform temperature rise as a thermal load and constant applied actuator voltage are considered for this analysis. By definition of four new analytic functions, the five coupled governing stability equations, which are derived based on the first-order shear deformation plate theory, are converted into fourth-order and second-order decoupled partial differential equations (PDEs). Considering a Levy-type solution, these two PDEs are reduced to two ordinary differential equations. One of these equations is solved using an accurate analytical solution, which is named as power series Frobenius method. The effects of parameters, such as the plate aspect ratio, ratio of piezoelectric layer thickness to thickness of FGM layer, gradient index, actuator voltage, and the temperature dependency on the critical buckling temperature difference, are illustrated and explained. The critical buckling temperatures of (P/FGM)_s with six various boundary conditions are reported for the first time and can be served as benchmark results for researchers to validate their numerical and analytical methods in the future.     

溶胶-凝胶法Pd／SiO2杂化材料的热稳定性和热分析动力学

采用溶胶-凝胶法,在甲基化改性SiO2溶胶中掺杂PdCl2,制备Pd／SiO2杂化材料,通过XRD、红外光谱、TG—DTG分析以及接触角测定,考察Pd／SiO2杂化材料在N2气氛中的热稳定性,用Coast—Redfern方程、Doyle方程,结合最概然机理函数的Malek推断法,求算Pd／Si02杂化材料在热分解过程中各阶段的热分析动力学三因子,结果表明,保持Pd／SiO2杂化材料疏水性的最适宜焙烧温度为350℃。在N2气氛中,Pd／SiO2杂化材料中-CH3的无机化过程包括4个阶段,各阶段具有不同的热分解动力学机理函数,其活化能分别为73．85、143．66、204．47和417．19kJ·mol-1,指前因子分别为1．20x10^12、2．27x10^13、8．50x10^11和1．03x10^20S-1。     

Nonlinear bending of FGM plates subjected to combined loading and resting on elastic foundations

A nonlinear bending analysis is presented for a simply supported, functionally graded plate resting on an elastic foundation of Pasternak-type. The plate is exposed to elevated temperature and is subjected to a transverse uniform or sinusoidal load combined with initial compressive edge loads. Material properties are assumed to be temperature-dependent, and graded in the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents. The formulations are based on a higher-order shear deformation plate theory and general von Kármán-type equation that includes the plate-foundation interaction and thermal effects. A two step perturbation technique is employed to determine the load–deflection and load–bending moment curves. The numerical illustrations concern nonlinear bending response of functional graded plates with two constituent materials resting on Pasternak elastic foundations from which results for Winkler elastic foundations are obtained as a limiting case. The results reveal that the characteristics of nonlinear bending are significantly influenced by foundation stiffness, temperature rise, transverse shear deformation, the character of in-plane boundary conditions and the amount of initial compressive load. In contrast, the effect of volume fraction index N becomes weaker when the plate is supported by an elastic foundation.     

Nonlinear Symmetric Free Vibration Analysis of Super Elliptical Isotropic Thin Plates

Nonlinear symmetric free vibration analyses are first presented for super elliptical isotropic thin plates with simply supported edge and clamped edge based on classical plate theory. Approximate solutions of super elliptical thin plates are obtained by Ritz method, and the validity can be confirmed by comparison with related researchers’ results. Numerical results confirm that the characteristics of nonlinear vibration behaviors are significantly influenced by different boundary conditions, vibration amplitudes, the power of the super ellipse, as well as ratio of major to minor axis.     

Buckling Analysis of Plates Stiffened by Parallel Beams

In this paper a general solution for the elastic buckling analysis of plates stiffened by arbitrarily placed parallel beams of arbitrary doubly symmetric cross section subjected to an arbitrary inplane loading is presented. According to the proposed model, the stiffening beams are isolated from the plate by sections in the lower outer surface of the plate, taking into account the arising tractions in all directions at the fictitious interfaces. These tractions are integrated with respect to each half of the interface width resulting two interface lines, along which the loading of the beams as well as the additional loading of the plate is defined. The unknown distribution of the aforementioned integrated tractions is established by applying continuity conditions in all directions at the two interface lines, while the analysis of both the plate and the beams is accomplished on their deformed shape. The method of analysis is based on the capability to establish the elastic and the corresponding geometric stiffness matrices of the stiffened plate with respect to a set of nodal points. Thus, the original eigenvalue problem for the differential equation of buckling is converted into a typical linear eigenvalue problem, from which the buckling loads are established numerically. For the calculation of the elastic and geometric stiffness matrices six boundary value problems are formulated and solved using the Analog Equation Method (AEM), a BEM-based method. Numerical examples with practical interest are presented. The accuracy of the results of the proposed model compared with those obtained from a 3-D FEM solution is remarkable.     

爆炸冲击震动下柔性基础上浮放设备的抛离分析

核武器或常规武器爆炸冲击作用将会引起地下工程结构底板振动，强烈的振动可能导致搁置在结构底板上的没备发生抛离、倾倒和损坏，这是爆炸冲击隔震设计中需要研究解决的一类问题。本文将地下工程结构底板简化为单向板，分析其受到冲击震动时的弹性动力反应，推导结构底板的振动加速度同冲击作用时间、峰值、结构自振特性之间的关系，根据抛离条件分析了浮放设备的抛离规律，结果表明：冲击荷载峰值越大，浮放设备越容易抛离；浮放设备位置离侧墙越远越容易抛离，其中底板中点处为最易抛离点；结构的自振周期越小，浮放设备越易抛离；冲击波升压时间越小，浮放设备越容易抛离；冲击波持续时间越小，浮放设备越容易抛离。     

有限长弹性地基梁地基系数的识别

本文通过实测弹性地基梁的固有频率，以传递矩阵法为基础，利用计算机代数语言，导出以支承刚度为未知数的高次方程，从而识别出地其系数，并通过实验验证该方法的正确性。     

Analysis of nonlinear dynamic stability for carbon nanotube-reinforced composite plates resting on elastic foundations

This article studies nonlinear dynamic stability of carbon nanotube-reinforced composite (CNTRC) plates resting on an elastic foundation. The single-walled carbon nanotubes (SWCNTs) are aligned and distributed in the form of uniformly distributed (UD) and functionally graded (FG) reinforcements. The governing equations are established based on classic plate theory, which is converted to a Mathieu-type equation by using a two-step perturbation technique, and then solved by adopting an incremental harmonic balanced (IHB) method. In numerical results, the effects of nonlinear geometric factor, distribution and fraction volume of CNTs, and foundation stiffness on principle dynamic unstable regions are discussed.     

弹性地基上间断中厚矩形板的非线性振动

研究了弹性地基上带传力杆的间断中厚矩形板结构的非线性振动特性。荷载在传力杆中的传递由竖向弹簧模拟，其弹簧刚度取决于传力杆的特性以及杆与板间的相互作用。根据能量变分原理，考虑地基耦合效应，建立了双参数地基上带传力杆的间断矩形中厚板的非线性运动控制方程。应用伽辽金法和谐波平衡法对该组非线性方程进行了求解。在算例中，讨论了传力杆参数、板的结构参数以及地基参数对中厚矩形板的非线性自由振动特性的影响。     

Nonlinear response of a shear deformable S-FGM shallow spherical shell with ceramic-metal-ceramic layers resting on an elastic foundation in a thermal environment

This article presents an analytical approach to investigate the nonlinear stability of thick, functionally graded material (FGM) shallow spherical shells resting on elastic foundations, subjected to uniform external pressure and exposed to thermal environments. Material properties are assumed to be temperature dependent and graded in the thickness direction according to a Sigmoid power law distribution (S-FGM) in terms of the volume fractions of constituents. Using the first-order shear deformation theory and the Galerkin method, the effects of materials, geometry, elastic foundation parameters, and temperature on the nonlinear response of the thick S-FGM shells are analyzed and discussed in detail.