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.     

Nonlinear flexural analysis of laminated composite plates using RBF based meshless method

The paper presents the nonlinear flexural response of laminated composite plates. The mathematical formulation of the actual physical problem of the laminated composite plate subjected to mechanical loading is presented utilizing higher order shear deformation theory and von-Karman nonlinear kinematics. These nonlinear governing differential equations of equilibrium are linearized using quadratic extrapolation technique. A meshfree technique based on multiquadric RBFs is used for analysis of the problems. Isotropic, orthotropic and laminated composite plates with immovable simply supported and clamped edges are analyzed.     

Fast analytical method describing the postbuckling behavior of long,symmetric, balanced laminated composite plates under biaxial compression and shear

The present work deals with the postbuckling behavior of an infinitely long plate consisting of laminated composites with symmetrical, balanced lay-up. Along the longitudinal edges the plate is elastically clamped with torsional springs. As loading situation combinations of biaxial compression and shear are accounted for. Aiming at high computational efficiency the problem is solved by variational methods employing a shape function with only few variables. Inserting the shape function into the compatibility condition of in-plane strains, a closed-form solution for the Airy stress function can be obtained. The resulting equilibrium condition is then used to derive the load–deflection relationship by means of the Galerkin procedure. All other state variables such as displacements and stresses can then be calculated. Comparative finite element analyses reveal that apart from the cases involving transversal compression, where the application should be handled with care, the present solution procedure can serve to obtain good approximations of the stability behavior in the early postbuckling region with negligible computational effort.     

Nonlinear analysis of doubly curved shells: An analytical approach

Dynamic analogues of von Karman-Donnell type shell equations for doubly curved, thin isotropic shells in rectangular planform are formulated and expressed in displacement components. These nonlinear partial differential equations of motion are linearized by using a quadratic extrapolation technique. The spatial and temporal discretization of differential equations have been carried out by finite-degree Chebyshev polynomials and implicit Houbolt timemarching techniques respectively. Multiple regression based on the least square error norm is employed to eliminate the incompatability generated due to spatial discretization (equations>unknowns). Spatial convergence study revealed that nine term expansion of each displacement inx andy respectively, is sufficient to yield fairly accurate results. Clamped and simply supported immovable doubly curved shallow shells are analysed. Results have been compared with those obtained by other numerical methods. Considering uniformly distributed normal loading, the results of static and dynamic analyses are presented. A list of symbols is given at the end of the paper     

A geometrically exact formulation for thin multi-layered laminated composite plates: Theory and experiment

A geometrically exact approach is employed to formulate the equations of motion of thin multi-layered isotropic and laminated composite plates subject to excitations that cause large strains, displacements, and rotations. The linearization of the obtained semi-intrinsic theory leads to the Mindlin–Reissner theory while an ad hoc truncated kinematic approximation delivers, as a by-product, the Föppl–von Kármán theory of plates. An experimental validation is sought for fully clamped plates which are either of the isotropic single-layered type or of the multi-layered laminated composite type. To this end, nonlinear equilibrium paths are constructed both theoretically and experimentally when the plates are subject to a quasi-statically increasing central point load. The comparisons between the experimentally obtained results and those furnished by the geometrically exact theory as well as by the Föppl–von Kármán (FVK) theory show the high accuracy of the proposed nonlinear theory while the FVK theory becomes increasingly inaccurate at deflection amplitudes of the order of the plates thickness.     

An analytical method for 3-D analysis of circular laminated composite plates

Summary In this paper, an analytical method is presented for 3-D (three-dimensional) researches of laminated composite plates. Using this method, the linear and nonlinear analytical 3-D solutions of high accuracy are obtained for circular laminated composite plates with rigidly clamped edges and under uniform transverse loading. Galerkin's method and the perturbation technique are used to obtained the solutions which satisfy the basic differential equations of linear and nonlinear 3-D problems. The geometric nonlinearity from a moderately large deflection is considered. Many numerical results of displacements and stresses are shown in figures. In the analytical method, there are not any restrictions regrading the stacking sequence of laminated composite plates, so the method may be used to analyze the 3-D problems of unsymmetrical laminated plates.     

Free vibration analysis of symmetric laminated skew plates by discrete singular convolution technique based on first‐order shear deformation theory

In this study, free vibration of laminated skew plates was investigated. Discrete singular convolution (DSC) method is used for numerical solution of vibration problems. The straight‐sided quadrilateral domain is mapped into a square domain in the computational space using a four‐node element by using the geometric transformation. Typical results are presented for different geometric parameters and boundary conditions. It is concluded from the results that the skew angle have considerable influence on the variations of the frequencies with fibre orientation angle and number of layers in the laminate. The results obtained by DSC method are compared with those obtained by analytical and numerical approaches. It is shown that reasonable accurate results are obtained. Present work also indicates that the method of DSC is a promising and potential approach for computational mechanics. Copyright © 2009 John Wiley & Sons, Ltd.     

Thermal postbuckling analysis of laminated composite plates

The thermal postbuckling behavior of graphite/epoxy multi-layered rectangular plates of various boundary conditions is studied using the finite element method. Temperature dependent thermal and elastic properties of the material are used in the analysis. The nonlinear finite element equations are solved as a sequence of linear eigenvalue problems to trace the thermal postbuckling paths of 15-layered symmetric angle-ply plates. The presence of secondary instability with an unsymmetric deformation mode has been identified for symmetric laminates under uniform temperature rise. In the case of linearly varying temperature rise through the thickness of the plate, the nonlinear equilibrium equations are solved by the modified Newton–Raphson technique to get the temperature-displacement curves.     

Classical coupled thermoelasticity in laminated composite plates based on third-order shear deformation theory

A new mixed finite element formulation is proposed to analyze transient coupled thermoelastic problems. Coupled model of dynamic thermoelasticity is selected for a laminated composite and a homogeneous isotropic plate. For the particular finite element developed here, there are 15 degrees of freedom at each node. Two simply supported plates are considered subjected to sinusoidally distributed mechanical and thermal loading. It is seen, by comparing the present results with results from the NISA II FEM code, that they are in good agreement.     

Isogeometric analysis for flexural behavior of composite plates considering large deformation with small rotations

A large deformation theory, so-called Green strains with small rotations, is proposed and employed for flexural analysis of composite plates. Isogeometric analysis cooperated with first-order shear deformation theory is used to derive finite element models. Strain-displacement relations in the sense of von-Kármán theory and the proposed theory are formulated. Shear locking phenomenon is avoided by using reduced integration technique. Newton–Raphson method is employed for nonlinear analysis procedure. Numerical examples, including isotropic and laminated composite plates under different boundary conditions, are investigated. The results have been verified with those available in the literature and show the advantages of the proposed strain theory.     

Panel flutter analysis of general laminated composite plates

The problem of nonlinear aeroelasticity of a general laminated composite plate in supersonic air flow is examined. The classical plate theory along with the von-Karman nonlinear strains is used for structural modeling, and linear piston theory is used for aerodynamic modeling. The coupled partial differential equations of motion are derived by use of Hamilton’s principle and Galerkin’s method is used to reduce the governing equations to a system of nonlinear ordinary differential equations in time, which are then solved by a direct numerical integration method. Effects of in-plane force, static pressure differential, fiber orientation and aerodynamic damping on the nonlinear aeroelastic behavior of the plate are studied. Results show that the fiber orientation has significant effect on dynamic behavior of the plate and the asymmetric properties, changes the behavior of the limit cycle oscillation.     

Experimental and numerical studies on buckling of laminated composite skew plates with circular holes under uniaxial compression

This article deals with experimental and finite element studies on the buckling of isotropic and laminated composite skew plates with circular holes subjected to uniaxial compression. The influence of skew angle, fiber orientation angle, laminate stacking sequence, and aspect ratio on critical buckling load are evaluated using the experimental method (using Methods I through V) and finite element method using MSC/NASTRAN. Method I yields the highest experimental value and Method IV the lowest experimental value for critical buckling load in the case of isotropic skew plates with circular holes. For all laminate stacking sequences considered, Method V yields the highest experimental value for critical buckling load for skew angle = 0° and Method IV yields the highest experimental value for critical buckling load for skew angles = 15° and 30°. For all laminate stacking sequences and skew angles considered, Method II yields the lowest experimental value for critical buckling load. The maximum discrepancy between the experimental values given by Method IV and the finite element solution is about 10% in the case of isotropic skew plates. The maximum discrepancy between the experimental values given by Method II and the finite element solution is about 21% in the case of laminated composite skew plates considered. The percentage of discrepancy between the numerical or finite element solution and experimental value increases as the skew angle increases. The critical buckling load decreases as the aspect ratio increases.     

Free vibration of moving laminated composite plates

Two-dimensional axially moving materials have a wide range of industrial applications such as papers, plastics and composites in producing lines, power transmission and conveyor belts, etc. In many of these instances, the moving material is not isotropic, but is a single-layer orthotropic material or consists of several orthotropic layers.

In this article, free vibration of axially moving symmetrically laminated plates subjected to in-plan forces is studied by classical plate theory. This category includes symmetric cross-ply and angle-ply laminates and anisotropic plates. Firstly, an exact method is developed to analyze vibration of multi-span traveling cross-ply laminates, and then a semi-analytical finite strip method is extended for moving symmetric laminated plates in general, with arbitrary boundary conditions. By the finite strip method intermediate elastic or rigid supports can also be added to the model of the moving plate. The supports may be in the form of point, line or local distributed supports.     

Large amplitude vibration analysis of functionally graded laminated skew plates in thermal environment

Large amplitude vibration analysis of functionally graded laminated skew plates in thermal environment has been studied. The mechanical properties are assumed to be temperature-dependent and graded in the thickness direction using power-law distribution in terms of the volume fractions of the constituents. The temperature field is uniformly distributed over the plate surface and varied in the thickness direction only. The nonlinear C⁰ finite element equations are obtained using Reddy’s HSDT with von-Karman’s strain assumptions. The convergence and comparison studies have been performed to prove the accuracy of the present model. Results with different design parameters have been presented.     

Buckling of symmetrically laminated rectangular plates with general boundary conditions – A semi analytical approach

A semi-analytical extended Kantorovich approach for the buckling analysis of symmetrically laminated rectangular plates with general boundary conditions is presented. The solution is derived as a multi-function expansion that allows the analysis of laminated plates characterized by a non-separable solution. Among these, the cases of buckling of angle-ply laminates under inplane compression and shear buckling of any type of plate are the most common ones. The formulation is based on the variational principal of total energy minimization and the iterative extended Kantorovich method. The exact element method is adopted for the solution of the resulting differential eigenvalue problem. The capabilities of the proposed approach and its applicability to buckling analysis of composite laminated plates that cannot be analyzed using the classical single-term extended Kantorovich method are demonstrated numerically. The results are compared with exact solutions (where available), and with approximate results from other numerical methods. The accuracy and convergence of the proposed approach are also discussed.     

Dynamic stability of laminated FGM plates based on higher-order shear deformation theory

This paper conducts a dynamic stability analysis of symmetrically laminated FGM rectangular plates with general out-of-plane supporting conditions, subjected to a uniaxial periodic in-plane load and undergoing uniform temperature change. Theoretical formulations are based on Reddys third-order shear deformation plate theory, and account for the temperature dependence of material properties. A semi-analytical Galerkin-differential quadrature approach is employed to convert the governing equations into a linear system of Mathieu–Hill equations from which the boundary points on the unstable regions are determined by Bolotins method. Free vibration and bifurcation buckling are also discussed as subset problems. Numerical results are presented in both dimensionless tabular and graphical forms for laminated plates with FGM layers made of silicon nitride and stainless steel. The influences of various parameters such as material composition, layer thickness ratio, temperature change, static load level, boundary constraints on the dynamic stability, buckling and vibration frequencies are examined in detail through parametric studies.This work was fully supported by grants from the Australian Research Council (A00104534) and from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. CityU 1024/01 E). The authors are grateful for this financial support.     

Large deformation of shear-deformable plates by the boundary-element method

Boundary-integral equations for large deformation of shear-deformable plates are presented. Two different methods are used to calculate the derivatives of the nonlinear terms in the domain integral. The first approach requires the evaluation of a hypersingular domain integral. The second approach avoids the calculation of a hypersingular integral by utilizing radial basis functions to approximate the integrand. Quadratic isoparametric boundary-elements are used to discretise the boundary, and constant cell elements are used to discretise the domain. For the solution of a nonlinear problem four methods are presented. They include: total incremental method, cumulative-load incremental method, Euler method and nonlinear system method. Several examples are presented and comparisons with analytical results and other numerical results are made to demonstrate the accuracy of the proposed methods.     

Vibration analysis of variable stiffness laminated composite sandwich plates

Abstract

This paper presents the free vibration analysis of a variable stiffness laminated composite sandwich plates. The fiber orientation angle of the face sheets (Skin) is assumed to vary linearly with the x-axis. The problem formulation is based on the higher-order shear deformation plate theory HDST C⁰ coupled with p-version of finite element method. The elements of the stiffness and mass matrices are calculated analytically. The sandwich plate is presented with a uniform mesh of four p-elements and the convergence properties are achieved by increasing the degree p of the hierarchical shape functions. A calculation program is developed to determine the fundamental frequencies for different physical and mechanical parameters such as plate thickness, core to face sheets thickness ratio, orientation angle of curvilinear fibers and boundary conditions. The results obtained show a good agreement with the available solutions in the literature. New comparison study of vibration response of laminated sandwich plate between the straight and curvilinear fibers is presented.     

Nonlinear behavior of functionally graded circular plates with various boundary supports under asymmetric thermo-mechanical loading

The equilibrium equations of the first-order nonlinear von Karman theory for FG circular plates under asymmetric transverse loading and heat conduction through the plate thickness are reformulated into those describing the interior and edge-zone problems of the plate. A two parameter perturbation technique, in conjunction with Fourier series method is used to obtain analytical solutions for nonlinear behavior of functionally graded circular plates with various clamped and simply-supported boundary conditions. The material properties are graded through the plate thickness according to a power-law distribution of the volume fraction of the constituents. The results are verified with known results in the literature. The load–deflection curves for different loadings, boundary conditions, and material constant in a solid circular plate are studied and discussed. It is shown that the behavior of FG plates with clamped or simply-supported boundary conditions are completely different. Under thermo-mechanical loading, snap-through buckling behavior is observed in simply-supported FG plates which are immovable in radial direction. Moreover, it is found that linear theory is inadequate for analyzing FG and also homogenous plates with immovable boundary supports in radial direction and subjected to thermal loading, even for deflections that are normally considered small.     

Finite element dynamic stability analysis of laminated composite skew plates containing cutouts based on HSDT

The finite element dynamic stability analysis of laminated composite skew structures subjected to in-plane pulsating forces is carried out based on the higher-order shear deformation theory (HSDT). The two boundaries of the instability regions are determined using the method proposed by Bolotin. The numerical results obtained for square and skew plates with or without central cutout are in good agreement with those reported by other investigators. The new results for laminated skew plate structures containing cutout in this study mainly show the effect of the interactions between the skew angle and other various parameters, for example, cutout size, the fiber angle of layer and thickness-to-length ratio. The effect of the magnitude of the periodic in-plane load on the dynamic instability index is also investigated.