Buckling and postbuckling response of sandwich panels under non-uniform mechanical edge loadings

The buckling and postbuckling responses of cylindrical sandwich panels, subjected to non-uniform in-plane loadings are investigates in this paper by analytical method. A fourth and fifth order expansions are used respectively for the transverse and tangential displacement of the core to model the core compressibility effect. The stress distribution within the panels due to the applied non-uniform in-plane edge loadings are determined by prebuckling analysis. The governing partial differential equations describing the buckling and postbuckling behavior of cylindrical sandwich panels are derived using the principle of minimum total potential energy. Galerkin’s method is used to reduce the governing partial differential equations to a set of non-linear algebraic equations. Newton–Raphson method in conjunction with Riks approach is employed to solve the algebraic equations. Numerical results are presented for both flat and cylindrical sandwich panels subjected to various non-uniform in-plane edge loadings. The sandwich panels used in the present investigation are made up of isotropic and composite materials.     

Nonlinear closed-form high-order analysis of curved sandwich panels

Closed-form high-order theory of sandwich panels, including transverse flexibility and shear rigidity of a core, as well as geometrical nonlinearity of unsymmetric faces is generalized for sandwich panels of constant curvature. Variational calculus is used to derive the set of governing equations describing a stress-deformation response of the panel to arbitrary loads. Boundary conditions are presented both in the local and global formulations. The procedure for the numerical solution of the governing nonlinear differential equations is based on the finite-difference method with deferred corrections. The solution technique is illustrated through numerical examples. Influence of the geometrical nonlinearity on the overall behaviour of the sandwich panel and localized effects are demonstrated.     

Nonlinear dynamical analysis of eccentrically stiffened functionally graded cylindrical panels

Based on the classical shell theory with the geometrical nonlinearity in von Karman–Donnell sense and the smeared stiffeners technique, the governing equations of motion of eccentrically stiffened functionally graded cylindrical panels with geometrically imperfections are derived in this paper. The characteristics of free vibration and nonlinear responses are investigated. The nonlinear dynamic buckling of cylindrical panel acted on by axial loading is considered. The nonlinear dynamic critical buckling loads are found according to the criterion suggested by Budiansky–Roth. Some numerical results are given and compared with the ones of other authors.     

Linear and nonlinear parametric instability behavior of cylindrical sandwich panels subjected to various mechanical edge loadings

Linear and nonlinear dynamic instability behavior of cylindrical sandwich panels subjected to combined static and dynamic nonuniform in-plane loadings is studied in this article. The core compressibility effects are considered in the model by assuming fourth and fifth order expansions for the transverse and tangential displacement of the core. The exact stress distributions within the panel are determined by panel prebuckling analysis for the applied parabolic and partial edge loadings. Galerkin's method is used to reduce the governing partial differential equations of the shell panel into a set of nonlinear ordinary differential equations. Dropping the nonlinear term, dynamic instability regions are obtained by solving the Mathieu-type differential equation by the method of Fourier series. The characteristics feature of the stable and unstable regions are investigated by linear and nonlinear time history responses and phase plots of the shell panel in those regions using Newmark's time integration. Incremental harmonic balance (IHB) method is used to study the nonlinear frequency amplitude responses of the cylindrical sandwich panels.     

Investigation on the square cell honeycomb structures under axial loading

To investigate into the collapse of a sandwich panel or beam with a square cell honeycomb, the novel plate model and beam model are developed according to the cross-sectional symmetry of the cell. The treble series solution of buckling mode is presented, and the formulas of critical compressive stress on skins are derived. The honeycomb sandwich panels are classified as thin, medium and thick plates based on their failure forms. It is found that the different kinds of cells have different buckling modes and different parameter governing equations. A new iterative optimization design method for a square honeycomb sandwich panel is developed and the curves of critical compressive stresses with geometrical parameters are provided in details. Finally, the 3D finite element numeric simulations have validated the formulas presented by this paper. Our study reveals some mechanical characteristics of the square honeycomb sandwich structures.     

Postbuckling analysis of axially-loaded functionally graded cylindrical shells in thermal environments

A postbuckling analysis is presented for a functionally graded cylindrical thin shell of finite length subjected to compressive axial loads and in thermal environments. 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 governing equations are based on the classical shell theory with von Kármán–Donnell-type of kinematic nonlinearity. The nonlinear prebuckling deformations and initial geometric imperfections of the shell are both taken into account. A boundary layer theory of shell buckling, which includes the effects of nonlinear prebuckling deformations, large deflections in the postbuckling range, and initial geometric imperfections of the shell, is extended to the case of functionally graded cylindrical shells. A singular perturbation technique is employed to determine the buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling response of axially-loaded, perfect and imperfect, cylindrical thin shells with two constituent materials and under different sets of thermal environments. The effects played by temperature rise, volume fraction distribution, shell geometric parameter, and initial geometric imperfections are studied.     

Thermo-mechanical load interactions in foam cored axi-symmetric sandwich circular plates – High-order and FE models

This work presents analytical and finite element analysis (FEA) results of the thermo-mechanical non-linear response of an axi-symmetric circular sandwich plates with a compliant foam core. The study investigates the load–thermal interaction response of a sandwich panel where the properties of the core are temperature dependent and degrade as the temperatures are raised. It presents briefly the governing equations for a sandwich plate based on the principles of the high-order sandwich panel theory (HSAPT) which incorporates the effects of the vertical flexibility of the core material as well as the effects of temperature independent/dependent mechanical properties of the foam core. The effects of the thermal degradation of core material on the thermo-mechanical non-linear response of a simply supported circular sandwich plate are studied through the analytical and FE models. The difficulties involved in non-linear geometrical FE modeling of sandwich panels with a compliant “soft” core with temperature-dependent mechanical properties are discussed. The HSAPT model predictions are compared very well with FE result. An important conclusion of the study is that the interaction between mechanical loads, temperature induced deformations, and degradation of the mechanical properties due to elevated temperatures, may seriously affect the structural integrity of foam cored sandwich plates.     

Buckling Analysis of Composite Sandwich Plates with Flexible Core Using Improved High-Order Theory

A new improved high-order theory is presented for global and local buckling analysis of sandwich plates with soft orthotropic core. Continuity conditions for transverse shear stresses at the interfaces as well as the conditions of zero transverse shear stresses on the upper and lower surfaces of plate are satisfied. Overall buckling loads, as well as wrinkling loads, are obtained for various sandwich plates. Effect of geometrical parameters and material properties of face sheets and core are studied on the overall buckling and face wrinkling of sandwich plates.     

Nonlocal and surface effects on the buckling behavior of flexoelectric sandwich nanobeams

In this article, an analytical approach is presented to study the surface and flexoelectric effects on the buckling characteristics of an embedded piezoelectric sandwich nanobeam. According to the nonlocal elasticity theory, the flexoelectricity is believed to be authentic for size-dependent properties in nanostructures. The boundary conditions and the governing equations are derived by Hamilton's principle and are solved by Navier method. The results obtained from the present work show that the nonlocal term has an important reduction on the critical load and also the flexoelectricity shows an increasing influence on the buckling loads of the sandwich nanobeam, especially at lower thicknesses.     

Precise bending stress analysis of corrugated-core,honeycomb-core and X-core sandwich panels

A semi-analytical method for bending analysis of corrugated-core, honeycomb-core and X-core sandwich panels is presented. The real displacement of sandwich panels is divided into the global displacement field and local displacement field. The discrete geometric nature of the core is taken into account by treating the core sheets as beams and the sandwich panel as composite structure of plates and beams with proper displacement compatibility. In the global displacement field, the governing equations of these sandwich panels are derived using energy variation principle and solved by employing Fourier series and the Galerkin approach. In the local displacement field, the face sheets under external loads are taken as a multi-span thin plate and the local bending response are then computed. Then the real bending responses are obtained by superposing these bending responses calculated in the two displacement fields and the structural stress fluctuation can be captured. Results from the proposed method agree well with available results in the literature and those from detailed finite element analysis. Furthermore, the mechanical properties of the three kinds of sandwich panels have been compared.     

Failure analysis of adhesive surface damage in sandwich plates under compressed loads

Abstract

Failures of honeycomb sandwich plates are analyzed using experiments and three-dimensional (3D) finite element simulations to understand the failure mechanism. Meanwhile, correlations of the critical load and various physical parameters (e.g., height and thickness of the core) are investigated. The results demonstrated that the core height and skin thickness have significant effects on the compressed load buckling of the honeycomb sandwich plates, the core density is a sub-critical sensitive factor, while wall thickness and spacing of the cell, and the sandwich modulus have negligible effects. Cracking on the adhesive surface is the dominant factor to reduce the buckling critical load of the laminated plate, which leads to failures of sandwich plates. The ultimate failure of the sandwich panel is attributed to severe deformations that lead to local cracking of the entire cemented adhesive surface. Due to the bonding of the adhesive surface defects, the actual loads related to the core height are large enough to cause compressions with local buckling. Hence, the actual loads cannot reflect the performance of the sandwich panels. It is recommended to use panels with appropriate thicknesses below the sandwich and moderate grid density in the design.     

Dynamic buckling of FGM truncated conical shells subjected to non-uniform normal impact load

Dynamic buckling of functionally graded materials truncated conical shells subjected to normal impact loads is discussed in this paper. In the analysis, the material properties of functionally graded materials shells are assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. Geometrically nonlinear large deformation and the initial imperfections are taken into account. Galerkin procedure and Runge–Kutta integration scheme are used to solve nonlinear governing equations numerically. From the characteristics of dynamic response obtain critical loads of the shell according to B-R criterion. From the research results it can be found that gradient properties of the materials have significant effects on the critical buckling loads of FGM shells.     

Compressive and shear buckling analysis of metal matrix composite sandwich panels under different thermal environments

Combined inplane compressive and shear buckling analysis was conducted on flat rectangular sandwich panels using the Rayleigh-Ritz minium energy method with a consideration of transverse shear effect of the sandwich core. The sandwich panels were fabricated with titanium honeycomb core and laminated metal matrix composite face sheets. The results show that slightly slender (along the unidirectional compressive loading axis) rectangular sandwich panels have the most desirable stiffness-to-weight ratios for aerospace structural applications; the degradation of buckling strength sandwich panels with rising temperature is faster in shear than in compression; and the fiber orientation of the face sheets for optimum combined-load buckling strength of sandwich panels is a strong function of both loading condition and panel aspect ratio. Under the same specific weight and panel aspect ratio, a sandwich panel with metal matrix composite face sheets has a much higher buckling strength than one having monolithic face sheets.     

A high-order theory for the analysis of circular cylindrical composite sandwich shells with transversely compliant core subjected to external loads

A new model based on the high order sandwich panel theory is proposed to study the effect of external loads on the free vibration of circular cylindrical composite sandwich shells with transversely compliant core, including also the calculation of the buckling loads. In the present model, in contrast to most of the available sandwich plate and shell theories, no prior assumptions are made with respect to the displacement field in the core. Herein the displacement and the stress fields of the core material are determined through a 3D elasticity solution. The performance of the present theory is compared with that of other sandwich theories by the presentation of comparative results obtained for several examples encompassing different material properties and geometric parameters. It is shown that the present model produce results of very high accuracy, and it is suggested that the present model, which is based on a 3D elasticity solution for the core material, can be used as a benchmark in future studies of the free vibration and buckling of circular cylindrical composite sandwich shells with a transversely compliant core.     

Parametric study of the post-buckling strength of structural core sandwich panels

Post-buckling strength of simply supported orthotropic corrugated board panels subjected to edge compressive loading has been investigated using geometrically non-linear finite element analysis (FEA). Adjustments of the transverse shear stiffnesses in the FEA were necessary and performed by comparing the critical buckling load calculated by FEA with a closed form solution. The collapse load of the sandwich plate was calculated based on material failure of the facings predicted from Tsai-Wu failure theory. Parametric studies were performed to investigate the sensitivity of the collapse load to changes in the transverse shear stiffnesses of the core, initial out-of-plane imperfections, asymmetry in board construction, slenderness ratio and eccentric loading of the plate. It was found that a reduction of the transverse shear stiffnesses of the core below a certain limit produces a significant reduction in the collapse load. Panels are said to be insensitive to imperfections and this holds true when the imperfections are the same as or lesser than the thickness of the panel, but a 40% reduction of the collapse load is observed for imperfections that are ten times the panel thickness. From a design point of view it is shown that a symmetrical board is preferred because an asymmetric board as well as eccentric loading of the panel significantly reduce the collapse load. It is also shown that the critical buckling load is directly related to the slenderness ratio of the panel whereas the collapse load is not.     

Mechanical behaviour of cellular core for structural sandwich panels

This paper deals with the analysis of the mechanical properties of the core materials for sandwich panels. In this work, the core is firstly a honeycomb and secondly tubular structure. This kind of core materials are extensively used, notably in automotive construction (structural components, load floors...). For this study, three approaches are developed: a finite element analysis, an analytical study and experimental tests. Structural members made up of two stiffs, strong skins separated by a lightweight core (foam, honeycomb, tube...) are known as sandwich panels. The separation of the skins by the core increases the inertia of the sandwich panel, the flexure and shear stiffness. This increase is obtained with a little increase in weight, producing an efficient structure to resist bending and buckling loads. A new analytical method to analyse sandwich panels core will be presented. These approaches (theoretical and experimental) are used to determine elastic properties and ultimate stress. A parameter study is carried out to determine elastic properties as a function of geometrical and mechanical characteristics of basic material. Both theoretical and experimental results are discussed and a good correlation between them is obtained.     

Vibration and buckling analysis of functionally graded sandwich beams by a new higher-order shear deformation theory

This paper proposes a new higher-order shear deformation theory for buckling and free vibration analysis of isotropic and functionally graded (FG) sandwich beams. The present theory accounts a new hyperbolic distribution of transverse shear stress and satisfies the traction free boundary conditions. Equations of motion are derived from Lagrange's equations. Analytical solutions are presented for the isotropic and FG sandwich beams with various boundary conditions. Numerical results for natural frequencies and critical buckling loads obtained using the present theory are compared with those obtained using the higher and first-order shear deformation beam theories. Effects of the boundary conditions, power-law index, span-to-depth ratio and skin-core-skin thickness ratios on the critical buckling loads and natural frequencies of the FG beams are discussed.     

Free vibration response of composite sandwich cylindrical shell with flexible core

This study deals with the free vibration analysis of composite sandwich cylindrical shell with a flexible core using a higher order sandwich panel theory. The formulation uses the classical shell theory for the face sheets and an elasticity theory for the core and includes derivation of the governing equations along with the appropriate boundary conditions. The model consists of a systematic approach for the analysis of sandwich shells with a flexible core, having high-order effects caused by the nonlinearity of the in-plane and the vertical displacements of the core. The behavior is presented in terms of internal resultants and displacements in the faces, peeling and shear stresses in the face–core interface and stress and displacement field in the core. The accuracy of the solution is examined by comparing the results obtained with the analytical and numerical results published in the literatures. The parametric study is also included to investigate the effect of geometrical properties such as radius of curvature, length and sector angle of the shell.     

Thermal buckling of bimodular sandwich beams

This paper presents a model that explores the thermal buckling of three-layer sandwich beams possessing thick facings and moderately stiff cores. Bimodular facings and core material are used. In contrast to conventional theory, the effects of transverse shear deformation in the facings as well as the effect of the stretching and bending action in the core on thermal buckling are considered. The governing equations are derived using the principle of minimum total potential energy and the fact that its second derivative is zero. The finite-element results are presented in order to investigate the effects of important parameters such as thickness, thermal expansion coefficients and moduli ratio on critical buckling temperatures.     

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.