Porous Sandwich Research Articles

Re-examination of nonlinear vibration and nonlinear bending of porous sandwich cylindrical panels reinforced by graphene platelets

Abstract This article re-examines the nonlinear vibration and nonlinear bending responses of porous sandwich cylindrical panels reinforced by graphene platelets resting on elastic foundations in thermal environments. The graphene platelet-reinforced composite (GPLRC) core is assumed to be of multilayers, and each layer may have different porosity coefficient values to achieve a piece-wise functionally graded pattern. By introducing an inhomogeneous model instead of the equivalent isotropic model (EIM), the Young’s moduli along with the shear modulus of the porous GPLRC core are predicted through a generic Halpin–Tsai model in which the porosity is included. The thermomechanical properties of metal face sheets and the porous GPLRC core are assumed to be temperature-dependent. Governing equations of motion for sandwich cylindrical panels with porous GPLRC core are formulated based on Reddy’s third-order shear deformation theory coupled with von Kármán nonlinear strain–displacement relationships. In the modeling, the panel–foundation interaction and the thermal effects are also considered. The analytical solutions for the nonlinear vibration and nonlinear bending problems are obtained by applying a two-step perturbation approach. Numerical studies are performed to compare the results obtained from the present model and the EIM. The results confirm that the EIM is not suitable for linear free vibration analysis of sandwich cylindrical panels with the porous GPLRC core, but the EIM may be valid for the cases of nonlinear vibration and nonlinear bending analyses of the same panel resting on Pasternak elastic foundations.

Re-examination of thermo-mechanical buckling and postbuckling responses of sandwich plates with porous FG-GPLRC core

The current study re-examines compressive postbuckling and thermal postbuckling responses of porous sandwich plates resting on an elastic foundation. The core of the sandwich plates is made of porous graphene platelets reinforced composite (GPLRC). Compressive postbuckling of the porous sandwich plates under uniaxial compression at elevated temperature and thermal postbuckling of the same plates under uniform thermal loading are studied. The GPLRC core is made of multilayers, and each layer may have different values of porosity coefficient to obtain a piecewise functionally graded (FG) pattern. The Young’s moduli along with the shear modulus of the porous GPLRC core are estimated through a generic Halpin–Tsai model in which the porous nature of the material is taken into consideration. The material properties of the metal face sheets and the porous GPLRC core are assumed to be temperature dependent. The governing equations for the postbuckling of the porous sandwich plates reinforced by GPLs are established based on the Reddy’s third order shear deformation theory (TSDT). In the modeling, we also consider the von Kármán nonlinear strain–displacement relationships, the plate-foundation interaction and the thermal effect. A two-step perturbation approach is utilized in solving the postbuckling problem. Numerical studies are performed to compare the results obtained from the present model and the equivalent isotropic model (EIM). The results confirm that the EIM is not suitable for analyzing buckling and postbuckling of porous plates.

Highly efficient mesh-free approach to simulate the non-linear bending analysis of FG porous beams and sandwich beams with FG face sheets

The main objective of the present work is to propose a coupling of the Radial Point Interpolation Method (RPIM) with variable shape parameter to High Order Continuation Method (HOCM) for analyzing the geometrically non-linear behavior of porous Functionally Graded (FG) isotropic and sandwich Timoshenko beams by taking into account the non-linear shear deformation. The FG and FG Sandwich Beams (FGSB) effective material properties are assumed to vary continuously in the thickness direction according to a power-law index. The porosity is modeled as the stiffness reduction criteria and included in the mixture rule. The strong form of the non-linear equations governing porous FG and FGSB beams are obtained using the principle of virtual displacements in the framework of First-Order Shear Deformation Theory (FOSDT). The HOCM is used to compute the solution of the non-linear problem by a transformation to recursive succession of linear problems using Taylor series expansion. The continuation technique is used to obtain the complete solution path in a step by step manner. The effectiveness and accuracy of the proposed coupling is brought out through numerical examples which concern porous FG isotropic and FG sandwich beams. The optimal parameters have been defined according to the stability analysis of the proposed solver, and then used to investigate the effect of boundary conditions, showing the effect of the power-law index, effect of geometric imperfections, and face sheet-core-face sheet thickness ratios on deflections. The validation is done by comparing the obtained results to those available in the literature and/or those computed using Finite Element Method (FEM).

A novel Gaussian higher-order plate theory for dynamic response of porous sandwich plates with different geometries

With the wide application of lightweight structures, it is necessary to precisely and efficiently predict dynamic response of sandwich plates for the dynamic safety of sandwich structures in service life. Due to the weak normal stiffness of the core, the used higher-order shear deformation theories (HSDTs) are required to consider the transverse normal strain. To the best knowledge of authors, the most efficient and accurate higher-order theory including transverse normal strain merely contains six independent unknowns. However, the existing six-unknown higher-order theories may be incapable of accurately forecasting the dynamic response of the soft-core sandwich plates attributing to the huge mismatches of mechanical properties. Therefore, a novel Gaussian higher-order plate theory (NGHPT) with six independent variables has been developed for the free and forced vibration of sandwich plates, where the transverse shear function is defined by Gaussian function and Fourier transformation to approximately fulfill the continuity requirement of transverse shear stresses at the interfaces. Meanwhile, the isogeometric analysis (IGA) is utilized to handle complex geometries. Compared to the existing HSDTs with six unknowns, the NGHPT can more accurately predict the dynamic behaviors of sandwich plates, which is verified by several experimental tests. Furthermore, a comprehensive parametric study on various sandwich plates including square, circular, elliptical and annular shapes, has been carried out to evaluate the influence of fiber orientation, distribution of internal pores and porosity coefficient on the dynamic response, which can provide suggestions for the future designs of porous sandwich plates to meet specific dynamic requirements.

Dynamic vibration analysis of double-layer auxetic FGP sandwich plates under blast loads using improved first-order shear plate theory

In this study, the characteristics of static bending and free and forced vibration of double-layer auxetic functionally graded porous (FGP) sandwich plates with shear connectors under blast load are explored comprehensively, where the structure of the plate comprises two layers joined by shear connectors. Each layer comprises auxetic FGM sandwich material, containing a core component made of auxetic honeycomb with a negative Poisson's ratio, while the upper and bottom two components are made from FGP materials. The whole plate is supported by a two-parameter Winkler-Pasternak elastic foundation. The key innovation of the proposed theory is that the transverse shear stresses are zero at the two free surfaces of each layer. In contrast to previous first-order shear deformation theories, no shear correction factor is required. To solve the plate issue when the boundary condition was entirely supported, Navier's exact solution was devised. On the other hand, in order to address the plate behavior in the event that the boundary condition was altered in any way, a plate element with nine nodes was used. Besides, to determine whether or not these results are accurate, a complete comparison approach that makes use of reliable claims has been used. The problem model's special case situations are used in order to accomplish this goal. When the object being developed is exposed to explosive loads, the findings that were derived from this research have the potential to be used to the construction of both military and civil works.

Thermoelectric nonlinear vibration and buckling analysis of the smart porous core sandwich plate (SPCSP) resting on the elastic foundation

This paper analyses the vibration and buckling responses analysis of the smart porous core sandwich plate (SPCSP) resting on the elastic foundation under thermoelectric and thermomechanical loading. The plate is a constraint with conventional and unconventional boundary conditions. The thermo-mechanical properties of the plate are graded through the thickness direction with the sigmoid and exponential laws. The sandwich plate considered geometrical nonlinearity and assumed quadratic electric potential function across the thickness direction. The Hamilton principle derives the formulation with the first-order shear deformation theory (FSDT) displacement field. A nine-node quadratic element-based higher-order finite element method with seven degrees of freedom (DOFs) is used to convert the governing equation into a set of algebraic forms and solve it computationally (using MATLAB) with a modified Newton-Raphson scheme. Buckling and vibration responses are analysed under varying plate parameters like material exponent N, thickness ratio (a/h), porous exponent with different porosity dispersion, conventional and unconventional conditions, applied electric voltage V and temperature change [Formula: see text]. It is found that the presence of the Pasternak parameter gives additional stability to structures and overcomes the instability due to porosity. Also, the proposed work is not only precise but also simple in predicting the vibration and buckling response of smart sandwich porous plates under thermo-electric mechanical loading.

Nonlinear buckling and post-buckling of imperfect FG porous sandwich cylindrical panels subjected to axial loading on elastic foundation

This paper deals with the nonlinear buckling and post-buckling of sandwich cylindrical panels with non-uniform porous core and functionally graded face sheets. The imperfect sandwich cylindrical panels are subjected to axial loading on elastic foundation. Based on the Donnell shell theory, with von Kármán geometrical nonlinearity, the governing equations are derived. The effects of elastic foundation, various panel geometrical characteristics, porosity parameters, and the thickness of the porous core are investigated. The effects of foundation parameters, porosity parameters, the thickness of the porous core, and material parameters are investigated.

Influence of Porosity on the Free Vibration Response of Sandwich Functionally Graded Porous Beams

Functionally graded materials are composite materials used to build a variety of structures. These structures are used in ships industries, marine, automotive, high building structures, energy engineering applications, and many more. The porosity made in these materials may negatively affect some behavior aspects like stiffness, and strength, but it may provide superior performance in other fields like vibration reduction, thermal isolation, energy absorption, and others. In this paper, we will discuss the effect of porosity on the natural frequencies for functionally graded porous (FGP) sandwich beams. The mechanical properties of the FGP sandwich beams are changing with the porosity in the thickness direction. The free vibration of the beams is examined with the effect of porosity. The analysis is carried out for four different beam supporting types (hinged – hinged, fixed – fixed, fixed – free, fixed – hinged). Various porosity ratios are considered with a range from (0.1 – 0.9). Forty–four samples are analyzed for each type of core material distribution which is the symmetric material constitutive relationships (SMCR) and uniform core material. The results gained from the analysis show that the porosity constant has a significant effect on the natural frequencies of the FGP sandwich beams.

Research on the mechanical behaviour of functionally graded porous sandwich plates using a new C1 finite element procedure

This article develops a new C1 rectangular element based on Shi's third-order shear deformation plate theory (TSDT) for the static and dynamic analysis of functionally graded porous (FGP) sandwich plates. Although the plate theory is attractive, it cannot be exploited as expected in finite element analysis due to the difficulties associated with satisfying the zero shear stress boundary condition. In this work, the proposed element has four nodes with seven degrees of freedom (DOFs) per node. The performance of this element is confirmed by conducting various examples, showing its accuracy and range of applications. Then, some studies are performed to present the effects of input parameters on the static and dynamic response of FGP sandwich plates.

On the transient performance of agglomerated graphene platelets-reinforced porous sandwich plates

We in this work present an efficient and straightforward computational model to discover transient responses of agglomerated graphene platelets (GPLs)–reinforced porous sandwich plates subjected to various dynamic loads. To this end, a generalized three-variable high-order shear deformation plate theory within the NURBS-based isogeometric analysis framework is exploited to approximate the displacements of the sandwich plates. Furthermore, a novel advanced sandwich plate model made of a porous core layer and two face layers reinforced with GPLs is proposed in this work. Two dispersion patterns of internal pores in terms of the thickness direction in the core layer including symmetric and uniform distributions are considered. Herein, a number of numerical investigations are carried out to study the effect of a wide range of key parameters on transient responses of advanced sandwich plates under four different dynamic loadings including step, triangular, half-sine and explosive blast loadings. For the first time, a significant influence of the GPLs agglomeration phenomenon on transient responses of the proposed sandwich plate model is thoroughly presented. The findings of the current work can be considered as benchmarks as well as bring useful guides for the structural design process with exceptional features in the future.

A novel finite element formulation for static bending analysis of functionally graded porous sandwich plates

A novel finite element formulation for static bending analysis of functionally graded porous sandwich plates

Influence of circular cutouts and elastic foundation on vibration characteristics of porous sandwich FGM plates under hygro-thermal environments

The present article investigates the effect of cutouts, porosity inclusion, and hygro-thermal environment on the vibrational characteristics of sandwich functionally graded material (FGM) plates resting on Pasternak elastic foundation. The governing equations for the sandwich FGM plates have been developed using the finite element method (FEM) with the conjunction of non-polynomial-based higher-order shear deformation theory (HSDT). The trigonometric shear-strain shape function has been used for the first time for sandwich FGM plates. The effective material properties with porosity inclusions have been computed using modified power–law distribution. The present results have been acquired by employing a C0 continuity isoparametric finite element (FE), using 4-noded elements with 7-DOF's per node. The accuracy of the current solution has been confirmed by convergence and validation studies. The influence of circular cutout, elastic foundations, hygro-thermal conditions, and geometric and boundary conditions on the vibrational frequency of porous sandwich FGM plates have been discussed in detail.

Buckling of porous FG sandwich plates subjected to various non-uniform compressions and resting on Winkler–Pasternak elastic foundation using a finite element model based on the high-order shear deformation theory

Buckling of porous FG sandwich plates subjected to various non-uniform compressions and resting on Winkler–Pasternak elastic foundation using a finite element model based on the high-order shear deformation theory

Multi-Objective Optimization for Curvilinearly Stiffened Porous Sandwich Plates Reinforced with Graphene Nanoplatelets

With the development of innovative manufacturing technology, multi-objective optimization algorithms for optimal design of advanced composite structures have gained increasing attention. An effective and high-accurate prediction on the mechanical behavior of structures is the basic core of optimization algorithms. Thus, a novel refined sinusoidal higher-order theory (NRSHT) combined with isogeometric analysis (IGA) is developed as the high-precision solver. A novel curvilinearly stiffened porous sandwich plate reinforced with graphene nanoplatelets (CSP-GPL) is proposed as the research object. Compared with previous higher-order theories, the proposed NRSHT can more accurately forecast the natural frequencies of CSP-GPL through several numerical and experimental tests. Subsequently, the shape and material distribution design of CSP-GPL are studied with multi-objective optimization. The random forest regression (RFR) is utilized as the high-fidelity surrogate model to construct the objective function in the improved Nondominated Sorting Genetic Algorithm (NSGA-II), which can significantly accelerate the integration of NRSHT-IGA and NSGA-II. Finally, the Pareto-optimal solutions, optimizing for fundamental frequency and total mass of CSP-GPL, are obtained from the present platform, which can give effective suggestions for the future designer to meet specific requirements.

Effect of thickness stretching and electro-mechanical loading on sandwich FGM plate with piezoelectric face sheet with different boundary conditions: A semi-analytical approach

Functionally graded material (FGM) belongs to the class of advanced composite materials with material properties that vary according to the volume fraction. FGM is the future material for smart structures, being used in place of conventional composite materials. The article aims at performing the static analysis of different types of sandwich FGM plates with a piezoelectric face sheet taking into consideration the porosity and thickness stretching effect. The problem is formulated using a variational approach and the bending solution is obtained for the first time using Galerkin Vlasov’s method. Three different types of porous sandwich plates are considered for the analysis when subjected to sinusoidally distributed mechanical and electrical loading. For the first time, a new uneven non-symmetric porosity model is put forward to capture the realistic bending behavior of the plate. The effect of boundary conditions, thickness stretching, and applied voltage on stress and deflection distribution along and across the porous plate’s surface is analyzed. It is observed that effect of the applied potential difference when assumed to be a function of position, the change in stresses and deflection are approximately 30%. This infers that voltage distribution plays a significant role in the distribution of stresses in the plate and cannot be neglected which is otherwise assumed as a constant by various researchers. To check the exactness and validity of the current formulation, various examples are discussed. The estimated results can be used as a validation study for the upcoming research on porous sandwich FGM plates with piezoelectric facesheets. Communicated by Francesco Tornabene

Finite Element Analysis for the Static Response of Functionally Graded Porous Sandwich Beams

In this paper, the finite element method is used to analyze the static response of the functionally graded porous (FGP) sandwich beams subjected to uniformly distributed loads along the beam span. The core of the beam is made up of functionally graded porous material while the top and bottom layers are made up of isotropic homogenous materials. Uniform distribution and symmetric distribution of pores are used as two different types of porous material. Shear deformation is considered in the analysis by utilizing BEAM189 in ANSYS which is a finite element package program. This element is based on the first-order shear deformation theory. The influence of porosity coefficient, boundary conditions, and type of the porous material on the static response of the considered structures is presented in detail. The results demonstrate that the porosity coefficient has an important impact on the static response of the FGP sandwich beams.

Ball milling synthesis of robust sandwich-structured C/Si@SnO2 anode with porous silicon buffer layer for fast charging lithium-ion battery

Aiming at enhancing cyclic stability and fast charging performance of lithium-ion batteries (LIBs), a sandwich structured composite with a buffer layer of porous silicon (Si) between the carbon layer and SnO2 layer (C/Si@SnO2) was developed by using ball milling. The results showed that the Si layer with plenty of mesoporous and cracks was coated successfully and the introduction of Si increased the disordered structure of SnO2, including the expansion of interlayer spacing, the emergence of Sn and SiOx indicated the reaction between Si and SnO2 occurred during the ball milling process, while the generation of Si-O-Sn and Si-O-C bonds formed by Si integration connected the three components with intimate interfaces. Used as an anode for LIBs, the C/Si@SnO2 electrode performed a favorable discharge capacity (919.21 mAh·g−1 at 0.1 A·g−1), the ultra-long cyclability after 1000 and 2000 cycles, impressive rate performance (269.87 mAh·g−1 at 5 A·g−1), and fast charging capability accompanying discharge capacity of 805.57 mAh·g−1 at 0.2 A·g−1 and charge capacity of 400.55 mAh·g−1 at 2 A·g−1. In addition, the electrochemical impedance spectroscopy analysis showed that the graphitic carbon layer and porous Si layer improved the rapid Li+ diffusion and transportation, which was beneficial to fast charging in LIBs. Our work provided a facile and green ball milling method to construct porous sandwich structured metal oxide/C composites with the introduction of Si, which can effectively increase the disordered structure of composite and also open up a new scheme of Si materials as an anode in the field of fast charging for LIBs.

A new design of metal supported micro-tubular solid oxide fuel cell with sandwich structure

Micro-tubular solid oxide fuel cell (MT-SOFC) is considered as a promising choice for portable applications. In this work, we developed a novel metal supported MT-SOFC with porous 430 stainless steel support| 430 stainless steel-SSZ| SSZ| porous SSZ sandwich structure by dip coating and one-step co-sintering technology. The metal supported MT-SOFC showed good connection between each function layer and exhibited a significant maximum power density of 271 mW cm−2 at 800 °C. Although the power density showed about 19.6% off after 14 thermal cycles between 600 °C and 800 °C, and about 5% per 100 h degradation rate during the 200 h long-term stability test at 700 °C and 0.7 V, the structure of the single cell could be maintained well and no crack and Sr diffusion was observed. As the result, the ohmic resistance of the cell kept unchanged during the thermal cycling and long-term test. The relatively fast degradation was attributed to the Ni and LSM particles coarsening and agglomeration, which will be improved in the further work. This work presented a low-cost and simple way to fabricate the metal supported MT-SOFCs with good electrochemical performance.

A refined quasi-3D theory for the bending of functionally graded porous sandwich plates resting on elastic foundations

An improved porosity distribution is introduced for the bending of a novel model of functionally graded (FG) sandwich plates via a refined quasi-3D shear and normal deformation theory. The sandwich plates are lying on Pasternak’s elastic foundation and exposed to sinusoidal mechanical loads. The shear and normal strains are both included, for that the shear correction factor is unnecessary. Depending on a specific function, the material properties of the sandwich plates vary continuously across the thickness direction. The equilibrium equations will be derived using the virtual work principle and solved using Navier’s method. The effects of the porosity parameter, inhomogeneity factor, elastic foundations parameters, length-to-thickness, and length-to-width ratios will be introduced. Comparison examples will be discussed to support the accuracy of the current theory. Further results will be introduced to provide benchmarks for comparison purposes.

The Post-Buckling Analysis of Porous Sandwich Cylindrical Shells with Shape Memory Alloy Wires Reinforced Layers Under Mechanical Loads

The main purpose of this paper is to analyze the nonlinear post-buckling behavior of three-layer porous sandwich cylindrical shells with shape memory alloy (SMA) wires reinforced outer layers under the mechanical loads. Considering the large deformations, the governing differential equations were extracted and then, using the Ritz energy method and considering the Airy function, the analytical expression for the critical stress of the system was extracted. Three types of porosity distributions were considered in the shell core and the mechanical properties of SMA-reinforced layers were determined using the law of mixtures. After validating the results, the effect of various parameters such as porosity distribution, volume fraction of SMA wires and geometric characteristics on nonlinear buckling loads and post-buckling behavior of these structures has been investigated. According to the results, it can be seen that the difference in critical buckling stress for three different porosity distribution types is significant, which reveals the need to determine the optimal porosity distribution for composite shells reinforced with SMA wires. The results show that the SMA wires increase the equivalent stiffness of the structure and their presence has a significant effect on improving the critical axial stress of the shells. According to the results, for the use of 1% volume fraction of SMA wires, the axial stress of sandwich shells can be increased up to about 51%. Therefore, the use of SMA wires is a good method to increase the load-bearing capacity of this type of structures.