非线性弹性基础上矩形板热后屈曲分析

给出非线性弹性基础上矩形板在均匀和非均匀（抛物型）热分布作用下的后屈曲分析。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。数值计算结果表明，非线性弹性基础上矩形板具有不稳定的热后屈曲平衡路径，且对初始几何缺陷是敏感的     

Thermomechanical Postbuckling of Imperfect Moderately Thick Plates on Nonlinear Elastic Foundations*

ABSTRACT

A postbuckling analysis is presented for a moderately thick rectangular plate subjected to combined axial compression and uniform temperature loading, and resting on a softening nonlinear elastic foundation. The cases of (1) thermal postbuckling of initially compressed plates and (2) compressive post-buckling of initially heated plates are considered. The initial geometrical imperfections of the plates are taken into account. Formulations are based on Reissner-Mindlin plate theory, considering first-order shear deformation effects, and including plate-foundation interaction and thermal effects. The analysis uses a deflection-type perturbation technique to determine buckling loads and postbuckling equilibrium paths. Numerical examples include the performance of perfect and imperfect, moderately thick plates resting on softening nonlinear elastic foundations. Typical results are presented in dimensionless graphical form.     

Perturbation analysis for the postbuckling of rectangular orthotropic plates

In this paper, applying perturbation method to von Kármán-type nonlinear large deflection equations of orthotropic plates by taking deflection as perturbation parameter, thé postbuckling behavior of simply supported rectangular orthotropic plates under inplane compression is investigated. Two types of in-plane boundary conditions are now considered and the effects of initial imperfections are also studied. Numerical results are presented for various cases of orthotropic composite plates having different elastic properties. It is found that the results obtained are in good agreement with those of experiments.     

考虑剪切变形的各向同性,正交各向异性矩形板的屈曲和后屈曲

本文讨论考虑横向剪切变形的各向同性、正交各向异性矩形板的屈曲和后屈曲性态。应用Reissner理论,采用文[1]提供的摄动方法,给出了完善和非完善各向同性、正交各向异性矩形板的后屈曲平衡路径,并与薄板理论结果作了比较。     

非完善板屈曲路径的有限元增量摄动法

本文以Thompson一般稳定性理论为基础,提出非完善结构(有初始几何缺陷)屈曲平衡路径分析的有限元增量摄动法,它克服了增量迭代法及摄动法各自的缺点,利用增量摄动法,还建立了非完善板屈曲平衡路径的数学分析模型,对非完善矩形板在各种边界条件下的屈曲路径实现了数值程序分析,得到了符合实验的结果。     

Thermal postbuckling analysis of moderately thick plates

A thermal postbuckling analysis is presented for a moderately thick rectangular plate subjected to (1) uniform and non-uniform tent-like temperature loading; and (2) combined axial compression and uniform temperature loading. The initial geometrical imperfection of plate is taken into account. The formulations are based on the Reissner-Mindlin plate theory considering the effects of rotary inertia and transverse shear deformation. The analysis uses a deflection-type perturbation technique to determine the thermal buckling loads and postbuckling equilibrium paths. Numerical examples are presented that relate to the performances of perfect and imperfect, moderately thick rectangular plates and are compared with the results predicted by the thin plate theory.     

Thermomechanical postbuckling of unilaterally constrained shear deformable laminated plates with temperature-dependent properties

This paper presents a study on the postbuckling responses of shear deformable laminated plates resting on a tensionless foundation of the Pasternak-type and subjected to combined axial and thermal loads. Two different postbuckling cases are considered, namely (1) the compressive postbuckling of initially heated plates and (2) the thermal postbuckling of initially compressed plates. The postbuckling analysis of laminated plates is based on the higher order shear deformation plate theory with a von Kármán-type of kinematic non-linearity. It is assumed that the foundation reacts in compression only. The thermal effects are also included and the material properties are assumed to be temperature dependent. The initial geometric imperfection of the plates is taken into account. The analysis uses a two-step perturbation technique to determine the postbuckling response of the plates. An iterative scheme is developed to obtain numerical results without using any assumption on the shape of the contact region. Numerical solutions are presented in tabular and graphical forms to study the postbuckling behavior of antisymmetric angle-ply and symmetric cross-ply laminated plates resting on tensionless elastic foundations of the Pasternak-type, from which results for conventional elastic foundations are obtained as comparators. The results reveal that the unilateral constraint has a significant effect on the postbuckling response of the plates subjected to combined axial and thermal loads when the foundation stiffness is sufficiently large. The results also confirm that the postbuckling responses are significantly influenced by temperature dependency and initial membrane stress as well as initial thermal stress.     

双向压缩简支矩形板的后屈曲性态

本文从Karman板大挠度方程出发,以挠度为摄动参数,采用直接摄动法,研究了简支矩形板在面内双向压缩作用下的后屈曲性态.本文同时考虑了板初始几何缺陷的影响.计算结果与实验结果的比较表明二者是一致的.     

Postbuckling of rectangular plates under uniaxial compression combined with lateral pressure

Based on the nonlinear large deflection equations of von Kármán plates, the lateral pressure is first converted into an initial deflection by Galerkin method, the postbuckling behavior of simply supported rectangular plates under uniaxial compression combined with lateral pressure is then studied applying perturbation method by taking deflection as perturbation parameter. Two types of in-plane boundary conditions and the effects of initial geometric imperfection are also considered. It is found that the theoretical results are in good accordance with experiments.     

Perturbation analyses for the postbuckling of simply supported rectangular plates under uniaxial compression

In this paper, applving perturbation method to von Kármán nonlinear large deflection equations of plates by taking deflection as perturbation parameter, the posibuckling behavior of simply supported rectangular plates under uniaxial compresion is investigated. Two types of in-plane boundary conditions are now considered and the effects of initial imperfections are also studied. It is found that the theoretical results are in good agreement with experiments. The method suggested in this paper which has not been found in previous papers is rather simple and easy for the postbuckling analysis of rectangular plates.     

Non-linear analysis of functionally graded plates under transverse and in-plane loads

Large deflection and postbuckling responses of functionally graded rectangular plates under transverse and in-plane loads are investigated by using a semi-analytical approach. 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 plate is assumed to be clamped on two opposite edges and the remaining two edges may be simply supported or clamped or may have elastic rotational edge constraints. The formulations are based on the classical plate theory, accounting for the plate-foundation interaction effects by a two-parameter model (Pasternak-type), from which Winkler elastic foundation can be treated as a limiting case. A perturbation technique in conjunction with one-dimensional differential quadrature approximation and Galerkin procedure are employed in the present analysis. The numerical illustrations concern the large deflection and postbuckling behavior of functional graded plates with two pairs of constituent materials. Effects played by volume fraction, the character of boundary conditions, plate aspect ratio, foundation stiffness, initial compressive stress as well as initial transverse pressure are studied.     

Postbuckling of piezoelectric FGM plates subject to thermo-electro-mechanical loading

In this paper, we examine the postbuckling behavior of functionally graded material FGM rectangular plates that are integrated with surface-bonded piezoelectric actuators and are subjected to the combined action of uniform temperature change, in-plane forces, and constant applied actuator voltage. A Galerkin-differential quadrature iteration algorithm is proposed for solution of the non-linear partial differential governing equations. To account for the transverse shear strains, the Reddy higher-order shear deformation plate theory is employed. The bifurcation-type thermo-mechanical buckling of fully clamped plates, and the postbuckling behavior of plates with more general boundary conditions subject to various thermo-electro-mechanical loads, are discussed in detail. Parametric studies are also undertaken, and show the effects of applied actuator voltage, in-plane forces, volume fraction exponents, temperature change, and the character of boundary conditions on the buckling and postbuckling characteristics of the plates.     

Ultimate strength of postbuckling for simply supported rectangular composite thin plates under compression

1.IntroductionAsiswellthnown,thepostbucklingmetalplatescanbesuccessivelysubjectedtotheload.Forsomemetalplates,theultimatestrengthcanreachthirtytimesofthebucklingstressll].Inordertostudythebearingcapacityofthecompositeplatesthroughtestsandtheoreticalanalysis,f'ttiluretestsofthe283specimensofGFRPthinrectangularplatesundercompres.sionarecarriedout.ItisprovedthattheGFRPplatesinpostbucklingstillhavehigherbearingcapacity,forthetestedspecimensshowedultimatestrengthwhichisfourtotwenty-livetiniesth…     

含基体横向损伤的黏弹性板的蠕变后屈曲分析

基于Schapery三维黏弹性损伤本构关系,引入沈为和Kachanov损伤演化方程,建立了基体横向损伤的纤维单一方向铺设黏弹性板的损伤模型;应用von Karman板理论,导出了考虑损伤效应的具初始挠度的纤维单一方向铺设黏弹性矩形板的非线性压屈平衡方程. 对未知变量在空间上采用差分法离散,时间上采用增量算法和Newton-Cotes积分法离散,控制方程被迭代求解. 算例中讨论了损伤以及有关参数对黏弹性复合材料板后屈曲行为的影响,且与已有文献的结果进行了比较. 数值结果表明：随着外载荷或者初始挠度的增大,板后屈曲趋于稳定时的挠度就愈大,损伤的影响愈明显;而随着长宽比的增大,板后屈曲趋于稳定时的挠度愈小,损伤的影响却随之增大.     

Validation of the Rayleigh–Ritz method for the postbuckling analysis of rectangular plates with application to delamination growth

Postbuckling solutions of laminated rectangular plates are obtained by the Rayleigh–Ritz method using von Karman’s nonlinear strain displacement relations and high-order polynomial expansions of the displacements. The potential energy function and the nonlinear algebraic equations governing the undetermined coefficients are obtained by Mathematica. Reasonably accurate solutions for the membrane forces, the bending and twisting moments and the pointwise energy-release rates generally require more undeterminated coefficients. Such refined postbuckling solutions show significant non-uniformity of the in-plane forces and strains and certain boundary effects characterized by concentration of the curvatures and the bending moment.     

非完善正交异性复合矩形板在面内双向压缩作用下的后屈曲

本文是文[1,2]工作的继续,给出了非完善正交异性复合矩形板在面内双向压缩作用下后屈曲平衡路径渐近表达式。     

层合析参固支边界条件下的不稳定后屈曲分析

为了深入地研究复合材料层板所独具的后屈曲特性,利用能量变分原理和非线性几何方程建立了具有弹性约束的复合材料层板在面内载荷作用下的非线性稳定性控制方程组,并运用广义傅立叶级数法对其进行求解。重点分析了非对称层板在固支边界条件下的稳定性问题,发现层板在此条件下有可能存在非对称的失稳临界点和不稳定的后屈曲路径,进而构造了简化的物理模型进行解释,指出后屈曲的非对称性是由于结构关于Z轴不对称,而不稳定性是由于固支边界条件阻碍了前屈曲的发生。     

Non-linear analysis of functionally graded fiber reinforced composite laminated plates,Part I: Theory and solutions

This paper deals with the large amplitude vibration, non-linear bending and postbuckling of fiber reinforced composite laminated plates resting on an elastic foundation in hygrothermal environments. Two kinds of fiber reinforced laminated plates, namely, uniformly distributed and functionally graded reinforcements, are considered. The material properties of fiber reinforced laminated plates are estimated through a micromechanical model and are assumed to be temperature-dependent and moisture-dependent. The motion equations are based on a higher order shear deformation plate theory that includes plate-foundation interaction and the hygrothermal effect. A two-step perturbation technique is employed to determine the non-linear to linear frequency ratios of plate vibration, the load-deflection and load-bending moment curves of plate bending, and postbuckling equilibrium paths of laminated plates.     

Postbuckling of imperfect rectangular composite plates under inplane shear closed-form approximate solutions

In this paper, the postbuckling behavior of rectangular orthotropic laminated composite plates with initial imperfections under inplane shear load is investigated in a closed-form analytical manner. The plates under consideration are assumed to be infinitely long in the longitudinal direction. At the longitudinal edges, two different sets of boundary conditions are considered, specifically 1) simply supported edges and 2) fully clamped edges. Using Timoshenko-type shape functions for both the initial bifurcational buckling analysis and the subsequent Marguerre-type postbuckling studies, closed-form analytical solutions for the buckling loads and for the postbuckling state variables are derived. A comparison with geometrically non-linear finite element computations shows that the derived analysis approaches are suitable for postbuckling studies in load ranges not too far beyond bifurcational buckling as they are currently relevant for e.g., composite airframe structural analysis and design. Due to their strictly closed-form analytical nature, the presented analysis methods can be used conveniently in engineering practice for all application purposes where computational time is a crucial factor, especially for preliminary analysis and design or optimization procedures.     

Effect of elastic foundation on the vibration of orthotropic elliptic plates with varying thickness

Two-dimensional boundary characteristic orthonormal polynomials are used in the Rayleigh–Ritz method to study the free vibration of rectangular orthotropic elliptic plates resting on a Winkler elastic foundation. Two types of varying thickness are considered: (1) linearly varying with respect to the concentric ellipses, (2) linearly varying along both the principal axes simultaneously. Numerical results for frequencies are presented in tables. Nodal lines are shown in figures. Effects of stiffness of elastic foundation, aspect ratios of plates, degree of orthotropy, and types of thickness variation on vibration frequencies of elliptical plates are also discussed.