Bi-axial buckling behavior of composite rectangular plates

Buckling behavior of composite plates subjected to bi-axial loading was experimentally determined and numerically analyzed. Modified rectangular specimens were introduced to overcome one of the experimental obstacles in which the loading grips interfere with each other's motion at each corner during the continuous bi-axial compression process. To determine the effects of modifications of the plate specimen, finite element analysis was performed in which the large deflection but small strain conditions were considered. In this paper, three different types of results which were determined from theoretical, numerical and experimental approaches are presented.     

Thermomechanical buckling of hybrid cross-ply laminated rectangular plates

A thermomechanical buckling analysis is presented for simply supported rectangular symmetric cross-ply laminated composite plates that are integrated with surface-mounted piezoelectric actuators and are subjected to the combined action of in-plane compressive edge loads, two types of thermal loads, and constant applied actuator voltage. The formulation of equations is based on the classical laminated plate theory and the von-Karman non-linear kinematic relations. The analysis uses an exact method to obtain closed-form solutions for the buckling load. The effects of applied actuator voltage, thermal and mechanical loads, plate geometry, and lay-up configuration of the laminated plates are investigated. The novelty of the present work is to obtain closed-form solutions for electro-thermomechanical buckling of hybrid composite plates, and to cover non-uniform temperature distribution loading. The results for various states are verified with known data in the literature.     

Thermal buckling behavior of composite laminated plates

Thermal buckling behavior of composite laminated plates was studied by making the use of finite element method. The thermal buckling mode shapes of cross-ply and angle-ply laminates with various E₁/E₂ ratios, aspect ratios, fiber angle, stacking sequence and boundary condition were studied in detail. The results indicate that the high E₁/E₂ and α₂/α₁ ratios of AS4/3501-6 and T 300/5208 laminates produce higher bending rigidity along the fiber direction and higher in-plane compressive force in a direction perpendicular to the fiber direction. Therefore, the higher thermal buckling mode shapes are formed. The thermal buckling mode that composite laminated plate will buckle into is mainly dependent on the E₁/E₂ ratio, α₂/α₁ ratio, fiber orientation and aspect ratio of the plate.     

Thermal buckling of cross-ply laminated composite beams

Summary Thermal buckling of thick, moderately thick and thin cross-ply laminated beams subjected to uniform temperature distribution are analyzed. Exact analytical solutions of refined beam theories are developed to obtain the critical buckling temperature of cross-ply beams with various boundary conditions. The state space concept in conjunction with Jordan canonical form will be used to solve exactly the governing equations of the thermal buckling problems. The effects of length to thickness ratio, modulus ratio, thermal expansion coefficients ratio, various boundary conditions and number of layers on the critical buckling temperature are investigated.     

Non-linear bending of antisymmetric cross-ply plates

The bending of antisymmetric cross-ply plates, based on Von-Karman plate theory, is investigated in this paper with one term approximations for the in-plane and transverse displacements. Rayleigh-Ritz solutions are presented for the non-linear response of cross-ply laminates with various modular and aspect ratios and subjected to sinusoidal transverse loading.     

Thermal buckling behavior of laminated composite plates with temperature-dependent properties

The thermal buckling behavior of composite laminated plates subjected to a uniform temperature field is investigated by the finite element method. Temperature-dependent elastic and thermal properties are considered. The stiffness and geometry matrices are derived based on the principle of minimum potential energy. The assumed displacement state over the middle surface of the plate element is expressed as the product of one-dimensional, first-order Hermitian polynomials. An iterative method is employed to determine the thermal buckling load. It is shown by numerical results that the influence of temperature-dependent mechanical properties on the thermal buckling behavior is significant.     

Thermal buckling of cross-ply laminated composite and sandwich plates according to a global higher-order deformation theory

A two-dimensional global higher-order deformation theory is presented for thermal buckling of cross-ply laminated composite and sandwich plates. By using the method of power series expansion of continuous displacement components, a set of fundamental governing equations which can take into account the effects of both transverse shear and normal stresses is derived through the principle of virtual work. Several sets of truncated Mth-order approximate theories are applied to solve the eigenvalue problems of a simply supported multilayered plate. Modal transverse shear and normal stresses can be calculated by integrating the three-dimensional equations of equilibrium in the thickness direction, and satisfying the continuity conditions at the interface between layers and stress boundary conditions at the external surfaces. Numerical results are compared with those of the published three-dimensional layerwise theory in which both in-plane and normal displacements are assumed to be C⁰ continuous in the continuity conditions at the interface between layers. Effects of the difference of displacement continuity conditions between the three-dimensional layerwise theory and the global higher-order theory are clarified in thermal buckling problems of multilayered composite plates.     

Thermal buckling and postbuckling behavior of functionally graded carbon nanotube-reinforced composite plates

Thermal buckling and postbuckling behavior is presented for functionally graded nanocomposite plates reinforced by single-walled carbon nanotubes (SWCNTs) subjected to in-plane temperature variation. The material properties of SWCNTs are assumed to be temperature-dependent and are obtained from molecular dynamics simulations. The material properties of functionally graded carbon nanotube-reinforced composites (FG-CNTRCs) are assumed to be graded in the thickness direction, and are estimated through a micromechanical model. Based on the multi-scale approach, numerical illustrations are carried out for perfect and imperfect, geometrically mid-plane symmetric FG-CNTRC plates and uniformly distributed CNTRC plates under different values of the nanotube volume fractions. The results show that the buckling temperature as well as thermal postbuckling strength of the plate can be increased as a result of a functionally graded reinforcement. It is found that in some cases the CNTRC plate with intermediate nanotube volume fraction does not have intermediate buckling temperature and initial thermal postbuckling strength.     

Shear buckling of rectangular composite plates composed of concentric layups

The buckling load of rectangular composite plates consisting of concentric rectangular layups under shear is determined using energy minimization and an out-of-plane displacement function based on sinusoids. By construction, the present method recovers the classical solution for buckling of anisotropic plates with one layup. Also, for the case of two concentric layups where only the thickness is varied, the present method was found to be in excellent agreement with finite element results. Using the results of the present method, combinations of multiple concentric layups were found that increased the buckling load of a single layup panel by 26% without increasing the weight.     

Vibration and buckling of rectangular composite plates with variable fiber spacing

This is a summary of the first known work which analyzes the structural behavior of composite plates having nonuniformly spaced fibers. The present investigation is limited to single layer composites having parallel fibers. This results in a plate which is macroscopically orthotropic, but nonhomogeneous. The free vibrations and buckling of such plates subjected to inplane boundary loadings are studied. A plane elasticity problem must first be solved to determine the inplane stresses caused by the applied boundary loading, and these stresses become input to the vibration and buckling problem. Both problems are dealt with by the Ritz method. Numerical results are obtained for six nonuniform distributions of E-glass, graphite and boron fibers in epoxy matrices in simply supported, square plates. The redistributions are seen to increase the buckling load by as much as 38%, and the fundamental frequency by as much as 21%.     

Finite strip buckling and free vibration analysis of stepped rectangular composite laminated plates

A general spline finite strip method is presented which allows the spline knots to be located arbitrarily along the plate strip and also facilitates the use of analytical integration in evaluating strip properties. The development takes place in the contexts of first‐order shear deformation plate theory and of classical plate theory, and encompasses composite laminated material. The prediction of natural frequencies and buckling stresses of stepped rectangular plates is considered using the new approach in which refinement of knot spacings is used local to a step change. The superstrip concept is used as part of an efficient solution procedure. A number of applications demonstrate the validity and practicability of the developed method. Copyright © John Wiley & Sons, Ltd.     

Thermal buckling behaviour of composite laminated plates with a circular hole

Thermal buckling of antisymmetric cross-ply laminates having central circular holes subjected to uniform or non-uniform temperature distribution are analysed by the finite element method. To account for the transverse shear deformation, the thermo-elastic Mindlin plate theory is used. Numerical results show that significant reduction of the critical buckling temperature occurs for laminates having a central hole.     

双稳定矩形非对称复合材料层板的跳变研究

对双稳定矩形非对称复合材料层合板两种稳定构型的跳变行为进行了实验和数值研究。通过实验测得中心加载下层合板两种稳定构型跳变的临界载荷, 建立了两种稳定构型的非线性有限元分析模型, 成功预报了层合板固化后的两种稳定构型, 并进一步预报了两种稳定构型的跳变临界载荷, 预报结果与实验结果吻合良好。实验和有限元模拟结果表明, 中心加载下矩形非对称层合板两种构型的临界载荷相差较大, 并且跳变的过程有所差异。      

Thermal buckling of laminated cylindrical plates

Thermal buckling of a laminated cylindrical plate subjected to a temperature change is studied. The governing differential equations for Donnell-type laminated cylindrical shells are used and Galerkin's method is employed to determine the critical buckling temperature. Clamped and simply supported boundary conditions are both considered. The effects of various parameters on thermal buckling are examined.     

含分层损伤的复合材料格栅(AGS)板的非线性热屈曲分析

采用基于复合材料一阶剪切效应理论的有限元法分别研究了含分层损伤的复合材料层合光板、 单向加筋板和格栅加筋(AGS)板的热屈曲性态。在分析中考虑材料热物理性质与温度相关特性, 同时在分层前缘采用了位移约束条件以保证分层区域的各子板的变形相容要求。3种结构的典型算例分析和结果的比较表明, 复合材料格栅(AGS)板具有很强的抗热屈曲的能力, 但是, 分层损伤将使其临界温度降低, 同时还会导致热屈曲的模态发生改变。本文中提出的方法和所得结论对AGS结构的热承载能力预测和损伤容限设计将具有参考价值。      

Study of critical buckling loads and modes of cross-ply laminated annular plates

Buckling of composite annular plates under uniform internal and external radial edge loads have been investigated using energy method. Trefftez rule is used in the stability equations. The symmetric buckling of symmetric cross-ply laminates is considered. In this paper, buckling behavior for the three laminates (90/0)_2s, (90/0₂/90)_s and (90₂/0₂)_s are studied. Influence of some parameters such as thickness, stacking sequence, type of supports and the ratio of hole to sheet radius on buckling loads and modes are investigated. The results of the energy method are compared with the results of numerical method. Based on the results, in the plates with clamped boundary conditions the symmetric buckling assumption is not accurate, contrary to other boundary conditions.     

Unilateral buckling of elastically restrained rectangular mild steel plates

 This paper considers the elastic unilateral buckling of rectangular mild steel plates that are restrained elastically and subjected to bending and axial actions. A variational formulation of the Ritz method using linear combinations of harmonic functions for the buckling deformations is used to establish an eigenproblem to determine the plate local buckling coefficients. The motivation for the study is the retrofit of reinforced concrete beams by gluing and then bolting steel plates to the sides of the beam. Such plates, when acting compositely with the concrete beam, are subjected to predominantly bending and axial actions which may cause unilateral local buckling. Whereas the bolts provide complete restraint against buckling at discrete points, the glue may also inhibit local buckling between these nodal points since it acts as a continuous elastic restraint. The influence of the glue stiffness, support conditions and plate proportions on the unilateral buckling of such plates are assessed.     

Free vibration of composite rectangular plates with rectangular cutouts

A simple numerical method based on the Rayleigh principle is presented for predicting the natural frequencies of composite rectangular plates which exhibit special and general orthotropy. The method is illustrated for simply-supported rectangular plates having central rectangular cutouts and double square cutouts. The results are compared with the reported finite element and analytical results.     

Three-dimensional exact elasticity solutions for antisymmetric angle-ply laminated composite plates

International Journal of Mechanics and Materials in Design - This paper is concerned with the derivation of the benchmark three-dimensional exact solutions for the static analysis of rectangular...     

Elastic-plastic buckling analysis of rectangular plates subjected to biaxial loads

In order to calculate the buckling load of a rectangular plate, the analytical approach is used in this study. The plate is assumed to be simply supported on four edges and loaded by uniform stresses along the edges. If the plate is slender, the buckling is elastic. However, if the plate is sturdy, it buckles in the plastic range. Then, the instantaneous moduli in the constitutive equations depend on the external loading. In this study, the elastic and plastic buckling equations are derived for rectangular plates under biaxial loading, and the corresponding interaction curves are presented. The influences of aspect ratios, load ratios and hardening factors on the buckling stresses are investigated for rectangular plates. From the plastic buckling analysis, the optimal combination of loads is given for the buckling strength.