Corrugated Core Sandwich Plates Research Articles

Dynamic performance of ultralight corrugated sandwich plate with FML face-sheets impacted by FSP-foam composite projectile

Ultralight corrugated sandwich constructions have shown great promise as multifunctional structures capable of simultaneous load-bearing, shock mitigation and ballistic resistance, yet little is known about the synergetic effects of combined shock and fragment loadings on their performance. This study presented a combined experimental and numerical investigation of corrugated-core sandwich plate with ultra-high molecular weight polyethylene (UHMWPE) fiber metal laminate (FML) face-sheets subjected to combined shock and fragment impact. The combined loading was achieved using a laboratory-based experimental technique previously proposed by the present authors, i.e., the impact of fragment-foam composite projectile fired from a light gas gun. Corrugated-core sandwich plates with both FML face-sheets and metallic face-sheets were prepared, and their ballistic/blast resistances and deformation/failure modes were characterized experimentally. Three-dimensional finite element simulations were performed and validated to provide further insight into the underlying mechanisms of dynamic responses under combined loading. Compared with the reference sandwich plate with metallic face-sheets, stacking UHMWPE composite sheets into the face-sheets not only maintained the blast-induced deflection but also improved the ballistic limit against the fragment simulation projectile (FSP). The synergetic effect of combined loading could weaken the penetration resistance and increase the permanent deflection, but the tearing cracks caused by combined loading could be significantly inhibited by the use of FML face-sheets. In addition, the impact sequence of foam and fragment affected the ballistic resistance of corrugated-core sandwich plate with FML face-sheets.

Buckling analysis of corrugated-core sandwich plates using a FSDT and a meshfree Galerkin method

A meshfree Galerkin method is proposed for the buckling analysis of corrugated-core sandwich plates (CSP). A CSP is a composite structure composed of three parts — one corrugated sheet in the middle of the structure which can be approximated by an orthotropic plate that has different elastic properties along the two perpendicular directions. The displacement fields of the component are given with the moving-least squares (MLS) approximation and the first-order shear deformation theory (FSDT). The equations governing the elastic buckling behaviors of the three components are derived and superposed to present the meshfree governing equation of the entire CSP. A technique that was originally used to enforce essential boundary conditions in meshfree methods is developed to treat the governing equations before the superposition according to the displacement compatibility. The program is compiled on the C++ platform, and several numerical examples are employed to demonstrate the convergence and accuracy of the proposed method. The results show that the proposed method has high accuracy for the stability analysis of CSP under certain conditions.

Static and dynamic response analysis of corrugated core sandwich plates under patch loading

Static and dynamic response analysis of sandwich plates having corrugated core under patch loading is presented in this paper. In this work, the problem formulation is made using finite element-based higher shear deformation theory. The influence of various parameters like aspect ratio, corrugated plate thickness, core thickness, corrugation angle, boundary conditions, ratio of face thickness to corrugation plate thickness on transverse deflection, stresses, and dynamic bending responses are revealed. In the present investigation, a MATLAB program is developed with nine nodded seven degrees of freedom per node of element. The obtained results are verified with available results in the literature to check the program’s efficiency. It is found that transverse deflection increases with increase in corrugation angle, and maximum rotation about the ‘x’ and y-axis increases with increase in the area of the plates exposed to patch loading. Edge constraints have a significant effect on transverse deflection and stress.

Vibration behavior analysis of novelty corrugated-core sandwich plate structure by using first-order shear deformation plate and shell theories

Vibration behavior analysis of novelty corrugated-core sandwich plate structure by using first-order shear deformation plate and shell theories

Dynamic stability of different kinds of sandwich plates using third order shear deformation theory

In this paper dynamic buckling of different kinds of sandwich plates under harmonic axial load is analyzed by using combination of numerical finite strip analysis and Bolotin’s solution which offer a kind of method to find the regions of dynamic instability for dynamic stability of plates. The sandwich plates which are considered here consist of homogeneous core sandwich plates, functionally graded sandwich plates, trapezoidal corrugated core sandwich plates, Z and C form corrugated core sandwich plates and truss core sandwich plates. Third order shear deformation theory is used as numerical method to study stability regions of sandwich plates. The effect of damping is neglected and the effect of length to thickness ratio, different boundary conditions, number of face sheet layers and different geometry and material properties of core is studied. According to the results the dynamic buckling should also be investigated in sandwich plate. Also, according to the results, it is observed that the finite strip method has an acceptable accuracy in investigating the dynamic buckling of sandwich plates.

Development of an analytical framework for viscoelastic corrugated-core sandwich plates and validation against FEM

In this study, an analytical procedure for the bending problem of a viscoelastic sandwich plate with a corrugated core is presented. Reissner–Mindlin plate theory and N-termed Prony series are employed to define the elastic and time-dependent contributions of the governing equations, respectively. Three different corrugation patterns, i.e., rectangular, trapezoidal, and triangular, are examined. Moreover, the structure is analyzed under both simply support and clamp boundary conditions. The calibrated material parameters of polymethyl methacrylate (PMMA) for the Generalized Maxwell rheological model are employed to show the viscoelastic response of the structure. A 3D finite element simulation of the problem is also conducted to confirm the accuracy of the analytical formulation. The two well-known creep and stress relaxation phenomena of the viscoelastic materials are examined for the mentioned corrugation cores and both boundary conditions analytically and numerically. The time-dependent dimensionless deflection and resultant von Mises stress distributions are provided. Besides, the variation of the results with various rise-times and applied load are studied in detail. The von Mises stress contours of the upper surface of the structure at the end of the creep test are also presented. The finite element method outcomes verify the analytical results with excellent compatibility. The proposed analytical procedure can be used as an efficient tool to study the effects of various parameters such as material, geometrical constants, and corrugation pattern on bending of viscoelastic sandwich plates with corrugated core problems for design and optimization, which involves a high number of simulations.

A parametric study on the mechanical and thermal stability of corrugated-core sandwich plates

Mechanical and thermal buckling of corrugated-core sandwich plates is investigated in this study. To consider the effect of shear deformations, the first-order shear deformation theory is applied to the finite strip method. The validity of the proposed method is evaluated by comparing the results with those presented by previous research. Various boundary conditions and different loading types, as well as the geometric parameters affecting the buckling loads and critical temperatures are explored and evaluated. To the authors' best knowledge, investigation of the effective geometric parameters, convergence process and different boundary conditions are discussed for the first time using finite strip method.

Static and dynamic analysis of corrugated-core sandwich plates using finite strip method

Free and forced vibration and static analysis of corrugated-core sandwich plates are investigated in this study by employing the classic finite strip method. The 3D corrugated-core plate is converted to a 2D orthotropic continuum model by considering some equivalent elastic constants. Various boundary conditions and different features of these plates are explored and the geometric and mechanical factors influencing their responses, such as displacements, rotations, moments and shear forces, are evaluated. Because of the significant effect of the shear stiffness on the behavior of corrugated-core sandwich plates, the first order shear deformation theory (FSDT) is used to analyze the plate. Due to the comparatively low shear to flexural stiffness ratio of these plates compared to ordinary plates, the convergence of the results is relatively slow. Therefore, a fast numerical technique such as finite strip method which yields effective reduction of calculation cost is employed. A MATLAB program is developed to obtain the results and the validity of the proposed method is evaluated by comparing the results with those presented by previous researches.

Dynamic Compressive Response of Sinusoidal Corrugated Core Sandwich Plates

In this paper, the dynamic compressive response of metal sinusoidal corrugated core sandwich plates is investigated. The analytical model for the reaction forces of top and bottom face sheets subjected to constant velocity are developed. Finite element (FE) method is carried out to predict the dynamic collapse of metal sinusoidal corrugated cores. Several collapse modes of cores are found in terms of different impact velocity and relative core density. The analytical predications are compared with numerical results, and the analytical model captures numerical results for reaction forces reasonably. The collapse mechanism maps are constructed for sinusoidal corrugated cores with elastic-perfectly plastic material and strain hardening plastic material. The effect of strain rate sensitive on the collapse response is discussed. It is demonstrated that the strain hardening of the metal material increases the dominant deformation mode of the collapse mechanism maps.

Effective elastic constants of corrugated core sandwich plate microstructure considering imperfection in adhesive bonding

Imperfection of adhesive bonding in the corrugated core sandwich plate microstructure is commonly occured due to inaccuracies in fabrication process or environmental effect. Considering the geometrical changed due to the adhesive imperfection, it could influence the mechanical properties of sandwich plate structure. Hence, this paper was caried out to predict the effective elastic constants of corrugated core sandwich plate microstructure by considering the effect of adhesive imperfecction. Unit cell of corrugated core microstructure with variation of adhesive imperfection was developed using multiscale finite element software named Voxelcon. Homogenization method was integrated with probability function to predict the effective elastic constants of corrugated core sandwich plate structure. The proposed method could potentially be extended to other types of periodic microstrostructure in predicting the reliable homogenized properties of heterogeneous materials.

Stochastic multi-scale analysis of homogenised properties considering uncertainties in cellular solid microstructures using a first-order perturbation

Randomness in the microstructure due to variations in microscopic properties and geometrical information is used to predict the stochastically homogenised properties of cellular media. Two stochastic problems at the micro-scale level that commonly occur due to fabrication inaccuracies, degradation mechanisms or natural heterogeneity were analysed using a stochastic homogenisation method based on a first-order perturbation. First, the influence of Young's modulus variation in an adhesive on the macroscopic properties of an aluminium-adhesive honeycomb structure was investigated. The fluctuations in the microscopic properties were then combined by varying the microstructure periodicity in a corrugated-core sandwich plate to obtain the variation of the homogenised property. The numerical results show that the uncertainties in the microstructure affect the dispersion of the homogenised property. These results indicate the importance of the presented stochastic multi-scale analysis for the design and fabrication of cellular solids when considering microscopic random variation.

Free vibration analysis of corrugated-core sandwich plates using a meshfree Galerkin method based on the first-order shear deformation theory

This paper focuses on free vibration analysis of corrugated-core sandwich plates (CSP) via a meshfree Galerkin method based on a first-order shear deformation theory (FSDT). A CSP is considered as a composite structure of three members — two face sheets at the top and the bottom, and one corrugated sheet in the middle of the structure. The face sheets are taken as isotropic plates, and the corrugated sheet is approximated by an orthotropic plate that has different elastic properties along the two perpendicular directions. Dynamic equations of the members are given by the meshfree Galerkin method based on the FSDT. After overcoming the difficulty to implement the displacement compatibility conditions among the members, the governing equation for the entire CSP is obtained by superposing the dynamic equations of the members. The meshfree characteristic of the proposed method guarantee that no meshes are used in deriving the dynamic equations, therefore the proposed method is more flexible in studying problems for which remeshing is inevitable with the finite element methods. The approximation of the corrugated sheet with an orthotropic plate also simplifies the analysis without much loss of precision. A few selected examples are studied to demonstrate the accuracy and convergence of the proposed method. The results obtained for these examples are compared with the ANSYS solutions. Good agreement is evident for all cases.

An analytic homogenisation model for shear–torsion coupling problems of double corrugated core sandwich plates

The homogenisation of shear–torsion behaviours for orthotropic sandwich plates such as corrugated cardboards is a difficult task, even numerically. We decompose the plate torsion into two beam torsions in order to analytically calculate its torsion rigidity. A simple but fairly accurate model based on Bredt theory is proposed for the torsion rigidity of double corrugated core plates. The in-plane shear rigidity is also analytically determined using beam theory. For non-symmetric plate sections, an analytical formulation is developed for the shear–torsion coupling problem. Very good agreement is obtained between the three-dimensional shell simulations and our fast H-model for a non-linear buckling problem coupling the membrane-shear-bending-torsion effects.

The dynamic response of clamped rectangular Y-frame and corrugated core sandwich plates

The dynamic response of fully clamped, monolithic and sandwich plates of equal areal mass has been measured by loading rectangular plates over a central patch with metal foam projectiles. All plates are made from AISI 304 stainless steel, and the sandwich topologies comprise two identical face-sheets and either Y-frame or corrugated cores. The resistance to shock loading is quantified by the permanent transverse deflection at mid-span of the plates as a function of projectile momentum. At low levels of projectile momentum both types of sandwich plate deflect less than monolithic plates of equal areal mass. However, at higher levels of projectile momentum, the sandwich plates tear while the monolithic plates remain intact. Three-dimensional finite element (FE) calculations adequately predict the measured responses, prior to the onset of tearing. These calculations also reveal that the accumulated plastic strains in the front face of the sandwich plates exceed those in the monolithic plates. These high plastic strains lead to failure of the front face sheets of the sandwich plates at lower values of projectile momentum than for the equivalent monolithic plates.

Bending behavior of corrugated-core sandwich plates

In this paper, the comprehensive analysis for the linear behavior of a corrugated-core sandwich plate is presented. A closed-form solution based on the Mindlin–Reissner plate theory is presented to describe the behavior of corrugated-core sandwich plate bending with various boundary conditions. A three-dimensional sandwich panel is reduced to an equivalent two-dimensional structurally orthotropic thick plate continuum. Some new phenomena observed in experimental investigations but not found in previous numerical analyses have been confirmed and reported, herein. The present numerical analysis agrees well with the reported experimental investigations of deflections and moments. Furthermore, the effects of several geometric parameters of a corrugated-core sandwich plate on its rigidity and state of stress are investigated.

Natural frequency for rectangular orthotropic corrugated-core sandwich plates with all edges simply-supported

Natural frequency for rectangular orthotropic corrugated-core sandwich plates with all edges simply-supported

NATURAL FREQUENCY FOR RECTANGULAR ORTHOTROPIC CORRUGATED-CORE SANDWICH PLATES WITH ALL EDGES SIMPLY-SUPPORTED

A simple approach to reduce the governing equations for orthotropic corrugated-core sandwich plates to a single equation containing only one displacement function is presented, and the exact solution of the natural frequencies for rectangular corrugated-core sandwich plates with all edges simply-supported is obtained. Furthermore, two special cases of practical interests are discussed in details.

均質化法による単層波状コアサンドイッチ板の解析 面内のみ周期性を有する複合構造への均質化法の適用について

The effectiveness of the homogenization method for the analysis of composite materials has been shown since it was firstly introduced in the 1970's. As this method is applicable to periodic problems only, however, some important engineering problems remain unsolved. Those problems are, for instance, honey-comb sandwich plates and panels with reinforcing ribs, which are not periodic in the thickness direction. In this paper, the application of the homogenization method to those problems is discussed. As a pratical example, stress analysis of single-layered corrugated core sandwich plates is presented. A method to homogenize its complicated geometry to a simple solid model, to get the homogenized material constants, and to calculate the microscopic stress is proposed.

STRESS ANALYSIS OF SANDWICH PLATE BY THE HOMOGENIZATION METHOD

The effectiveness of the homogenization method for analysis of composite materials has been shown since it was firstly introduced in 1970's. As this method is applicable to periodic problems only, however, some engineering problems remain unsolved. For instance, we could not apply it to honey-comb sandwich plates and panels with reinforcing ribs because these structures are not periodic in the thickness direction. In this paper, the application of the homogenization method to those composite structures is discussed. As a practical example, stress analysis of single-layered corrugated core sandwich plate is presented. A method to homogenize the complicated geometry to a simple solid model, to get the homogenized material constants, and to calculate the microscopic stress is proposed.

Transverse shear stiffness of structural core sandwich

Transverse shearing deformations in corrugated core sandwich plates cannot always be disregarded in the calculation of their strength and stability. This makes it necessary to accurately characterize the corresponding shear stiffnesses. In an effort towards this goal a theoretical study on how various core shapes influence the effective transverse shear moduli is presented. An upper limit of the transverse shear modulus across the corrugations is calculated assuming rigid facings. The reduction of the effective shear modulus across the corrugation due to deformations of the facings is quantified and the results are compared with classical theory and finite elements.