Sandwich Plate Theory Research Articles

Elastic Local Buckling Analysis of a Sandwich Corrugated Steel Plate Pipe-Arch in Underground Space

In underground spaces, corrugated steel plate (CSP) pipe-arches may experience local buckling instability, which can subsequently lead to the failure of the entire structure. Recently, sandwich CSP pipe-arches have been used to enhance the stability of embedded engineering outcomes, and their buckling behaviors require in-depth research. In this paper, we establish a theoretical model by simplifying soil support and using Hoff sandwich plate theory to focus on the local buckling stability of the straight segment in embedded sandwich CSP pipe-arches using the Rayleigh–Ritz method. Through stability analysis, the instability criteria for embedded sandwich CSP pipe-arches are analytically determined. Numerical calculations reveal that the critical buckling load of a sandwich CSP pipe-arch is affected by several factors, including the elastic modulus, thickness, Poisson’s ratio, rotational constraint stiffness, and the length of the straight segment. Specifically, increasing the thickness of the sandwich CSP pipe-arch can substantially enhance the critical buckling load. Meanwhile, the wavenumber is affected by the elastic modulus and the length of the straight segment. The analytical results are in agreement with those obtained from finite element analysis. These findings provide a theoretical basis and guidance for the application of sandwich CSP pipe-arches in fields such as subway stations, tunnel construction, underground passages, and underground parking facilities.

Isogeometric Analysis for Buckling and Wrinkling of Variable-Stiffness Sandwich Plates Under Compression

In this paper, an isogeometric analysis (IGA) framework based on the high-order sandwich plate theory is developed for the first time to deal with both buckling and wrinkling problems of variable-stiffness sandwich plates under compression. The present sandwich plate model is formulated based on the extended high-order sandwich plate theory (EHSAPT). The weak-form governing equations are firstly derived from the principle of virtual work, and afterward the IGA formulations based on the Non-Uniform Rational B-Splines (NURBS) are applied to predict the instability loads and the corresponding instability modes. Both the membrane and non-membrane conditions are integrated into the linear buckling analysis. The novelty of this work lies in that the employment of high-order continuous NURBS basis functions can directly fulfill the [Formula: see text] continuity requirement inherent in the EHSAPT theory, which enables the EHSAPT-based IGA model to be formulated with fewer degrees of freedom. Besides, the developed EHSAPT-based IGA model has also the ability to capture the overall buckling or wrinkling modes of the sandwich plates. The accuracy and effectiveness of the proposed EHSAPT-based IGA model are verified by comparison with previously published results and those obtained using ABAQUS. Effects of the core thickness and fiber angle on the buckling behaviors of the sandwich plates are also studied in numerical examples. It is observed that the non-uniform in-plane pre-stress over the skin layers is the main reason for the non-periodic wrinkling of constant-stiffness sandwich constructions, whereas the non-uniformity of both the in-plane pre-stress and out-of-plane bending stiffness is responsible for the non-periodic wrinkling of variable-stiffness sandwich constructions. The results presented herein may be beneficial for the design of variable-stiffness sandwich constructions under compression.

Compressive failure analysis of composite honeycomb sandwich panels with impact damage and stepped-scarf repairs

Composite honeycomb sandwich panels (CHSPs) have been widely used in the aerospace industry owing to their lightweight and superior mechanical properties. However, these CHSPs are susceptible to impact damage, leading to a significant reduction in compressive strength and potentially jeopardize aircraft safety. It is crucial to investigate repair methods for CHSPs with impact damage. This paper aims to evaluate the repair performance of CHSPs with impact damage through an analysis of their compressive failure behaviors. To accomplish this, both experimental tests and advanced numerical models are employed. The numerical models for the intact, damaged and stepped-scarf repaired CHSPs are established using the progressive failure analysis model, cohesive zone model and sandwich plate theory. A good agreement is observed between the experimental results and numerical predictions of compressive failure behaviors. Moreover, the validated numerical models are successfully utilized for determining optimum repair parameters by parametric analysis of the repaired CHSPs. The establishment of these numerical models offers an accurate and cost-effective evaluation of repair performance for CHSPs with impact damage, highlighting the novelty and main contribution of this paper.

Study the Effect of Face Sheets Material on Strength of Sandwich Plates with Circular Hole

This study aims to investigate the effect of changing skins material on the strength of sandwich plates with circular hole when subjected to mechanical loads. Theoretical, numerical and experimental analyses are done for sandwich plates with hole and with two face sheet materials. Theoretical analysis is performed by using sandwich plate theory which depends on the first order shear deformation theory for plates subjected to tension and bending separately. Finite element method was used to analyse numerically all cases by ANSYS program.
 The sandwich plates were investigated experimentally under bending and buckling load separately. The relationship between stresses and the ratio of hole diameter to plate width (d/b) are built, by studying the effect of hole size on strength of sandwich plates. The maximum stress were developed at the hole region in sandwich plates clarified the dropped in their strength. So, the experimental maximum stress was found by means of multiplying the experimental nominal stress obtained from Stress-strain curve by the stress concentration factor.
 All results which obtained, theoretically, numerically and experimentally are compared to find that the hole weaken the strength of sandwich plates because of the stress concentration and that weakness is depending on the hole size and the face sheets materials.

A Three-Dimensional Vibration Theory for Ultralight Cellular Sandwich Plates Subjected to Linearly Varying In-Plane Distributed Loads.

Thin structural elements such as large-scale covering plates of aerospace protection structures and vertical stabilizers of aircraft are strongly influenced by gravity (and/or acceleration); thus, exploring how the mechanical behaviors of such structures are affected by gravitational field is necessary. Built upon a zigzag displacement model, this study establishes a three-dimensional vibration theory for ultralight cellular-cored sandwich plates subjected to linearly varying in-plane distributed loads (due to, e.g., hyper gravity or acceleration), with the cross-section rotation angle induced by face sheet shearing accounted for. For selected boundary conditions, the theory enables quantifying the influence of core type (e.g., close-celled metal foams, triangular corrugated metal plates, and metal hexagonal honeycombs) on fundamental frequencies of the sandwich plates. For validation, three-dimensional finite element simulations are carried out, with good agreement achieved between theoretical predictions and simulation results. The validated theory is subsequently employed to evaluate how the geometric parameters of metal sandwich core and the mixture of metal cores and composite face sheets influence the fundamental frequencies. Triangular corrugated sandwich plate possesses the highest fundamental frequency, irrespective of boundary conditions. For each type of sandwich plate considered, the presence of in-plane distributed loads significantly affects its fundamental frequencies and modal shapes.

Natural Frequencies of Soft-Core Composite Sandwich Plates Reinforced by FG Graphene Platelets

Superior mechanical properties such as ultrahigh stiffness and strength along with amazing physical properties have led to the use of nano graphene platelets (GPLs) as a reinforcement in polymer composite structures such as sandwich plates. In this research, free vibration analysis of rectangular sandwich plates with functionally graded (FG) GPL-reinforced face sheets and a soft core is investigated. A high-order three-layer accurate sandwich plate theory is employed to model the soft-core sandwich structure. Third order shear deformable plate theory is applied for functionally graded graphene nano-composite face sheets while second and third order polynomials are used for displacements of the soft core. In this theory, the transverse flexibility of the core as well as the continuity conditions of transverse shear stresses are assumed. Hamilton’s principle is applied to extract the motion equations and the corresponding analytical solutions are presented. The effects of materials properties and geometrical parameters on the natural frequencies of the sandwich plates are studied. A comparison of the present results in particular cases with those of published studies confirms the accuracy of the present analysis. Results show that the natural frequencies of the sandwich plates are enhanced by reinforcing the face sheets with GPLs.

Assessment of equivalent methods effectiveness used for honeycomb plate structure

Honeycomb plates are commonly used in aerospace structures for their lightweight and rigidity characteristics. However, for modeling honeycomb structure many equivalent methods are established to represent the behavior of detailed model. In the present paper, we focus on the equivalent methods precision compared to the miso-scale model. Therefore, we compare two equivalent assumptions regarding the detailed design of a honeycomb plate (miso-scale). Then, we perform modal analysis and microvibration assessments to verify the effectiveness of methods accuracy regarding modes values and microvibration transmissibility. It can be noticed that each method has the advantage to be a candidate to represent the honeycomb plate behavior due to the lower error percentage. The sandwich plate theory gives minimal difference error for both modal analysis and the measurement of disturbance transmissibility from the reaction wheel to the structures. Hence, the sandwich theory is more or less accurate for representing a detailed model for structural analysis of honeycomb plates.

Vibration analysis of a composite elastic metamaterial plate based on a semi-analytical method

A semi-analytical vibration analyzing process is presented for a kind of finite composite elastic metamaterial plate by combining the effective medium theory and the first-order shear deformation sandwich plate theory, and the natural and steady-state vibration characteristics of such complex composite structure are investigated by means of equivalent analysis. The effectiveness of the semi-analytical analyzing process is demonstrated and some extraordinary vibration behaviors of such composite structure are revealed, such as there is no natural frequency in the bandgap, the modal density consistently increases around the bandgap's starting frequency, and the modes of the appropriate orders before and after the bandgap are consistent at the macroscopic level. The semi-analytical analyzing process and the special vibration behaviors may provide useful reference for relevant investigation and design of composite elastic metamaterial plate structures in the field of vibration control and isolation.

Global buckling and wrinkling of variable angle tow composite sandwich plates by a modified extended high-order sandwich plate theory

The advanced Automated Fibre Placement (AFP) manufacturing technologies make the synthesis of Variable Angle Tow (VAT) composites, which enable the design of lightweight sandwich structures to possess variable stiffness facesheets. However, both global and local instability phenomena of VAT sandwich plates under in-plane compressive loads are rarely explored till now. The objective of this article is to fill this gap by developing a Rayleigh–Ritz procedure based on a modified extended high-order sandwich plate theory (EHSAPT). The original two-dimensional EHSAPT proposed by Phan et al. (2012) is extended to a three-dimensional case with a minor modification that the first-order shear deformation theory instead of the classical Kirchhoff–Love hypothesis is adopted for each facesheet, which brings several merits such as the conciseness in derivation process and the easiness in program implementation. The Rayleigh–Ritz approach combined with the principle of minimum potential energy is employed to derive the eigenvalue equation that governs the instability problem of VAT sandwich plates under in-plane compressive loads. Both global buckling and wrinkling patterns of VAT sandwich plates can be captured under this proposed analytical model framework. Before instability analysis, the nonuniform prebuckling stresses over the entire sandwich plate are determined under the assumption of membrane prebuckling state. The usage of Lagrange multiplier method in the prebuckling regime removes the restrictions inherent in conventional Rayleigh–Ritz formulation and thus provides a general way to model in-plane boundary conditions. The accuracy and effectiveness of the developed Rayleigh–Ritz procedure are validated by comparing with previously published results and FE solutions given by ABAQUS. Effects of core thickness, core orthotropy, and fibre orientation angle of the facesheets on the instability behaviour of VAT sandwich plates are investigated. Finally, the mechanism of steering the fibre trajectory over the facesheets to improve the buckling resistance for the sandwich plate is studied and discussed.

Semi-active control for the nonlinear vibration suppression of square-celled sandwich plate with multi-zone MRE filler core

A semi-active controller is designed for the nonlinear vibration suppression of a novel square-celled sandwich plate with a multi-zone magnetorheological elastomers (MRE) filler core that can spontaneously generate a magnetic field using the embedded spiral coil. First, the nonlinear dynamic model of the square-celled sandwich plate with multi-zone MRE filler core is constructed by employing the nonlinear MRE model, the equivalent theory of material mechanics, the sandwich plate theory, the virtual spring technology, the eigenvalue increment method, and the modified Fourier-Ritz method. Next, based on the Newmark-Beta approach, the displacement and acceleration responses of the dynamic system are obtained. Afterwards, the high-order differential equation of the dynamic system is derived based on the relation of input and output of the dynamic system. A reference state of the dynamic response is predefined, and then the transfer function with respect to current can be identified. Furthermore, the verifications of the proposed model and controller are conducted. With the validated model, the optimal design of the semi-active controller is provided, and the feasibility of various control strategies is also discussed in detail.

Fluid–structure–soil interaction effects on the free vibrations of functionally graded sandwich plates

This study investigates the effects of fluid–structure and soil–structure interaction on the free vibration response of functionally graded sandwich plates. To this aim, an exemplary problem is analyzed, whereas a metal/ceramic sandwich plate is placed at the bottom of a tank filled in with fluid. Two cases are considered: (i) soft core, i.e., a sandwich plate with metal core and ceramic skins, and (ii) hard core, i.e., a sandwich plate with ceramic core and metal skins. In both cases, the skins are modelled as suitable functionally graded materials (FGMs). The soil is modelled as a Pasternak foundation. The free vibration analysis is carried out according to the extended higher order sandwich plate theory (EHSAPT). The fluid is assumed to be inviscid, incompressible, and irrotational. Hamilton’s principle is exploited to deduce the governing equations and the corresponding boundary conditions. The Rayleigh–Ritz method with two-variable orthogonal polynomials is used to compute the natural frequencies of the sandwich plate. The adopted approach is first validated through comparison with results published in the literature. Then, the effects are studied of several parameters on the dynamic response of the system.

Free vibration analysis of a laminated composite sandwich plate with compressible core placed at the bottom of a tank filled with fluid

The paper addresses the free vibration problem of a laminated composite sandwich plate with compressible core, placed at the bottom of a tank filled in with fluid. The analysis is performed based on the extended higher order sandwich plate theory (EHSAPT). First-order shear deformation theory (FSDT) is used for the face sheets. Cubic and quadratic polynomials are used to describe the in-plane and transverse displacements of the core, respectively. The fluid is assumed inviscid, incompressible, and irrotational. To obtain the kinetic energy of the fluid, its velocity potential is expressed by using the compatibility and boundary conditions. The governing differential equations and corresponding boundary conditions are derived from Hamilton’s principle. A single series expansion is considered with two-variable orthogonal polynomials as a set of admissible functions satisfying the boundary conditions. The natural frequencies of the coupled sandwich plate-fluid system are calculated by using the Rayleigh-Ritz method. Convergence of the adopted strategy is first investigated. Then, comparisons are conducted with previous results reported in the literature. Also, the effects are investigated of several parameters, such as the plate side-to-thickness ratio, the core-to-face sheets thickness ratio, the face sheet-to-core flexural modulus ratio, the height and aspect ratio of the tank.

A novel finite element formulation based on extended higher-order theory for sandwich plates of arbitrary aspect ratio

The extended higher-order sandwich plate theory for plates with arbitrary aspect ratio was formulated for two-dimensional orthotropic sandwich plates. The novelty of the theory is that it considers five generalized co-ordinates in the core (two axial and one transverse displacements at centroid of the core, one rotation at the centroid of the core about x-axis and one rotation at the centroid of the core about y-axis). Theory is very accurate when compared with the exact elasticity solution in terms of stresses and displacement both. In the current paper, a novel two dimensional rectangular element is developed based on the extended higher-order sandwich plate theory. Elemental equations along with the procedure to derive these is given in the paper. Developed finite element model is validated by comparing the results with elasticity solution and the theory itself for two sandwich plate configurations. The comparison shows that results obtained from the proposed finite element are in very good agreement with elasticity in terms of displacements and stresses both. Thus the proposed element is a powerful analysis tool which can be used for accurately analyzing the real world structures involving sandwich plates at a low computational cost.

Vibro-acoustic characteristics of sigmoid functionally graded sandwich plates with temperature-dependent materials

The vibro-acoustic characteristics of the sandwich plate with temperature-dependent parameters in thermal environment is analyzed and discussed in the present study, in which the material properties of the sigmoid function-based functionally graded material (S-FGM) plate are assumed to vary according to the two-power law distributions of the volume fractions of the constituents. Based on the first-order shear deformation theory, the vibration and vibro-acoustic coupling control equations for S-FGM sandwich plates with simply supported edges are established. Here, the thermal stress induced by the temperature distribution along the thickness direction is involved. By Navier method and fluid-solid coupling conditions, the natural frequency and the sound transmission loss are obtained, which are compared with that computed by the finite element simulation to verify the accuracy of the theoretical results. The natural frequencies for several kinds of structures are compared, and the effects of the temperature variations on the vibration and the sound transmission loss are analyzed. Then the influences of the parameters including the gradient index, core thickness and the top panel thickness on the vibro-acoustic characteristics are investigated by the fundamental frequency and the sound transmission loss. The research results provide a theoretical basis for the optimal design of the sandwich structures.

Free vibration analysis of rectangular sandwich plates with compressible core and various boundary conditions

Extended higher-order sandwich plate theory is used to analyze the free vibrations of rectangular sandwich plates with compressible core. Accordingly, first-order shear deformation theory is used to model the laminated face sheets. Besides, the in-plane and transverse displacements of the core are assumed to be cubic and quadratic functions of the thickness coordinate, respectively. To deduce the governing equations, Hamilton’s principle is used. Then, based on the Rayleigh-Ritz method, single series expansions with two-variable orthogonal polynomials – namely, the orthogonal plate functions – are considered to approximate the displacement components. Lastly, a generalized eigenvalue problem is solved to obtain the free vibrational characteristics of sandwich plates with both symmetric and anti-symmetric lay-ups subjected to various boundary conditions. The method is validated against the results obtained by different methods in the literature. Finally, the effects of the plate side-to-thickness ratio, in-plane aspect ratio, and core-to-face sheets thickness ratio on the natural frequencies are discussed.

Hygrothermal modeling of the buckling behavior of sandwich plates with nanocomposite face sheets resting on a Pasternak foundation

In this work we investigate the buckling response of sandwich plates with a polymeric core and two face sheets reinforced by carbon nanotubes (CNTs). The problem is tackled analytically by means of a higher-order sandwich plate theory, where the face sheets are modeled according to a classical plate theory and modified strain gradient theory with temperature-dependent and moisture-dependent material properties. A Mori–Tanaka method is applied to determine the mechanical properties associated with the face sheets, while considering the agglomeration effect of CNTs. The governing equations of the problem are derived from the Hamilton’s principle, whose solutions are recovered by means of a Navier–Stokes method. A thorough sensitivity study of the structural response to different parameters includes the agglomeration and volume fraction of CNTs, the material length scale parameter, the side and aspect ratios, together with the temperature variation and humidity conditions. The sandwich plates are assumed to be immersed within an orthotropic Pasternak foundation, whose normal and shear moduli can affect the overall buckling response of the structure. Numerical experiments show that sandwich plates with nanocomposite face sheets, resting on orthotropic elastic foundations, feature an increased stiffness, where the proposed formulation yields accurate results, due to the possibility of considering the variation in temperature, humidity and agglomeration of the reinforcing CNTs within the solution.

Free vibration analysis of sandwich plates with compressible core in contact with fluid

In this paper, the extended higher-order sandwich plate's theory (EHSAPT) is used to analyze the free vibration of the sandwich plate with compressible core and different boundary conditions in contact with fluid. First-order shear deformation theory is adopted for the top and bottom face sheets, while the in-plane and transverse displacements of the core are considered to be cubic and quadratic functions of the transverse coordinate, respectively. A single series is considered with two-variable orthogonal polynomials as a set of admissible functions satisfying the boundary conditions. Besides, the fluid is considered to be irrotational, inviscid and incompressible. By taking into account the boundary conditions and compatibility conditions, the fluid velocity potential is acquired. The natural frequencies of the system are calculated by the Rayleigh-Ritz method. An excellent accuracy is obtained between the results in the available literature and the present method. Finally, the effects of various parameters including boundary conditions, side-to-thickness ratio, thickness of the core to thickness of the face sheets ratio, face sheet to core flexural modulus ratio, dimensions of the container, and aspect ratios on the natural frequencies of the sandwich plate are presented and discussed in detail.

Multi-objective genetic algorithm optimization of composite sandwich plates using a higher-order theory

The main purpose of this paper is multi-objective optimization of soft-core composite sandwich plates using a known accurate high-order sandwich plate theory. In this three-layer theory, high-order kinematic assumptions are dedicated to each face sheet and the core layer. This theory considers the transverse flexibility of the soft core and satisfies transverse shear stresses continuity conditions and zero transverse shear stresses conditions at the upper and lower surfaces of the plate. The governing equations for bending and buckling analyses are derived using Hamilton’s principle, and their analytical solutions are presented for cross-ply plates. Two multi-objective optimization problems consist of weight/deflection optimization and weight/buckling load optimization of the unidirectional and cross-ply sandwich plates being studied. The thicknesses of the core and the face sheet layers are set as problems variables. The genetic algorithm is employed to find the optimal solutions for the problems, and the results are presented in form of the Pareto front. The accuracy of the present modeling and optimization method is evaluated for special case of buckling load maximization of laminated composite plates. For each problem, the optimization process is continued for more than 200 generations, but the results don’t change after 100 generations and the optimized results are obtained. The results confirm that there is no significant difference between the optimal solutions of unidirectional and cross-ply sandwich plates in both optimization problems. The process statistics show that cross-ply layup optimization takes about 25% more time than the unidirectional layup.

On inefficiency of the shape memory alloys in dynamically loaded sandwich plates with structural damping: New 3D zigzag-viscoelasticity theory and asymmetric transformations

Abstract The important claim that the presence of the structural damping considerably lessens or even eliminates the effectiveness of the embedded shape memory elements in the dissipation of the vibration/impact energies of the structures, is stated and proven here for the first time. The finite-element-based governing equations of thick composite sandwich plates with homogeneous/FG soft viscoelastic cores and embedded SMA wires are derived based on a new hyperbolic SMA-zigzag sandwich plate theory that considers the transverse flexibility. The tension-compression asymmetry of the SMA behavior and Zener-viscoelasticity-based zigzag nonlinear corrections are implemented to guarantee the transverse stress continuity at the interfaces between layers and updating the relation between the describing parameters of the displacement field, and the stiffness and even mass matrices of the elements within each time step. For the first time, the phase-based rather than the mixture-based stresses are considered in tracing the phase transformations. The resulting time-dependent nonlinear integro-differential equations are solved by a special algorithm. Results confirm, for the first time, that the stress-strain hysteresis loops of the SMAs may shrink or even disappear in presence of the structural damping; so that, the belief that the phase-transformation-based damping and the structural damping directly add to each other, is quite wrong.

Temperature-Dependent Buckling Analysis of Functionally Graded Sandwich Cylinders

This study is limited to study of buckling analysis of a sandwich cylindrical shell with functionally graded face sheets and homogenous core. High-order sandwich plate theory is improved by considering the in-plane stresses of the core that usually are ignored in the analysis of sandwich structures. Assume that all properties of the face sheets and the core are temperature dependent. Strain components are obtained by using the nonlinear Von-Karman type relations. The equilibrium equations are derived via principle of minimum potential energy. Analytical solution for static analysis of simply supported sandwich conical shells with functionally graded face sheets under axial in-plane compressive loads and in the temperature environments is performed by using Navier’s solution. The results show the critical dimensionless static axial loads are affected by the configurations of the constituent materials, compositional profile variations, temperature and the variation of the sandwich geometry. The comparisons show that the present results are in the good agreement with the numerical results.