Quasi-isotropic bending responses of metallic sandwich plates with bi-directionally corrugated cores

In order to reduce anisotropic behaviors of sandwich plates with open channel cores under the bending load, bi-directionally corrugated cores were introduced. Bi-directionally corrugated core has two additional design parameters related with a corrugation pass than uni-directionally corrugated core, so that its properties with respect to core orientations can be controlled. Sandwich plate with bi-directionally corrugated core is designed optimally so that beam buckling of face sheets is reduced drastically and anisotropic buckling behavior in the face sheets is minimized. The cores fabricated by a sectional forming process were bonded with face sheets by adhesive bonding. Three-point bending experiments were carried out with respect to core orientations. It has been shown from the experiments that sandwich plates with bi-directionally corrugated cores exhibit quasi-isotopic bending behaviors and structural performances in sandwich plates.     

双向梯形夹芯板柱面弯曲成形回弹分析

整体弯曲成形是制造曲面夹芯板高效且经济的方法,其成形特点与回弹预测是重点研究方向。采用结合有限元的半解析法对双向梯形夹芯的力学参数进行推导,获得夹芯等效弹性常数,分析上、下面板不等厚夹芯板柱面弯曲成形时面板与夹芯的变形特点及应力中性层的变化,在此基础上建立夹芯板平面应变弯曲回弹理论计算模型,预测夹芯板弯曲成形的应力分布与回弹,并与数值模拟及多点弯曲成形实验结果进行对比。结果表明:夹芯板回弹量与中厚板十分接近,回弹量较小,易于控制成形精度;理论预测的横截面切向应力与回弹都偏大,其中上面板应力相对误差在2.9%以内,下面板应力相对误差在6.5%以内,下面板纵向中心截面线误差在1.0mm范围内,各项误差均在很小范围内,验证了本工作回弹计算模型的准确性。     

Analysis of cylindrical bending thermoelastic deformations of functionally graded plates by a meshless local Petrov–Galerkin method

We analyze plane strain static thermoelastic deformations of a simply supported functionally graded (FG) plate by a meshless local Petrov–Galerkin (MLPG) method. Material moduli are assumed to vary only in the thickness direction. The plate material is made of two isotropic randomly distributed constituents and the macroscopic response is also modeled as isotropic. Displacements and stresses computed with the MLPG method are found to agree very well with those obtained from the analytical solution of the problem. The number of nodes required to obtain an accurate solution for a FG plate is considerably more than that needed for a homogeneous plate.The work was partially supported by the Office of Naval Research grant N00014-98-1-0300 to Virginia Polytechnic Institute and State University with Dr. Y. D. S. Rajapakse as the program manager. L. F. Qian was also supported by the China Scholarship Council.     

Vibration analysis of sandwich plates with lattice truss core

An effective methodology is developed to investigate the vibration of the sandwich plate with pyramidal lattice core. Equation of motion of lattice sandwich plate is established by Hamilton's principle. Displacement fields are expressed with a simple method, and the natural frequencies of the lattice sandwich plate are conveniently calculated. The correctness of the analytical method is verified by comparing the present results with published literatures. The effects of structural and material parameters on the vibration characteristics of lattice sandwich plate are analyzed. The present method will be useful for vibration analysis and design of lattice sandwich plates.     

Underwater blast response of free-standing sandwich plates with metallic lattice cores

The underwater blast response of free-standing sandwich plates with a square honeycomb core and a corrugated core has been measured. The total momentum imparted to the sandwich plate and the degree of core compaction are measured as a function of (i) core strength, (ii) mass of the front face sheet (that is, the wet face) and (iii) time constant of the blast pulse. Finite element calculations are performed in order to analyse the phases of fluid–structure interaction. The choice of core topology has a strong influence upon the dynamic compressive strength and upon the degree of core compression, but has only a minor effect upon the total momentum imparted to the sandwich. For both topologies, a reduction in the mass of the front (wet) face reduces the imparted momentum, but at the expense of increased core compression. Conversely, an increase in the time constant of the blast pulse results in lower core compression, but the performance advantage over a monolithic plate in terms of imparted momentum is reduced. The sandwich panel results are compared with analytical results for monolithic plates of mass equal to that of (i) the sandwich panel and (ii) the front face alone. (Case (i) represents a rigid core while (ii) represents a core of negligible strength.) For most conditions considered, the sandwich results lie between these limits reflecting the coupled nature of core deformation and fluid–structure interaction.     

Multi-scale modelling of sandwich structures using hierarchical kinematics

The aim of this paper is to present a multi-scale method for the mechanical modelling of sandwich structures. Low- and high-order sandwich elements are formulated on the basis of Carrera’s Unified Formulation (CUF) and bridged within the Arlequin framework. According to CUF, an N-order polynomials approximation is assumed on the beam cross-section for the unknown displacements, being N a free parameter of the formulation. Low-order, computationally cheap elements are used to describe the global mechanical response. High-order, computationally demanding elements are used to capture the local effects in the boundary layers. CUF framework is here enhanced by the assumption of the Constrained Variational Principle (CVP) in order to derive a new class of layered beam finite elements with an independent kinematic field for each lamina. Results are assessed towards two- and three-dimensional finite element solutions. The numerical results show that, in the context of CUF, the Arlequin method effectively couples sub-domains modelled via variable order finite elements. The proposed coupled models yield accurate results, being able to predict both the global solution and the local effects, with a reduced computational cost.     

Buckling of the CCFF orthotropic rectangular plates under in-plane pure bending

Solution of the buckling problem for the CCFF orthotropic plate subjected to in-plane pure bending is presented. The two parallel clamped edges of the plate are loaded by linearly distributed in-plane loads statically equivalent to the in-plane bending moments. The problem is solved using method of lines for partial differential equations and Galerkin’s method. The buckling problems are solved for isotropic, orthotropic and multilayered CFRP composite plates with various aspect ratios. Results of calculations of critical loads are compared with those based on finite-element modelling and analyses. The comparisons demonstrate efficiency of the proposed approach to the buckling analysis of composite CCFF plates with various dimensional and stiffness parameters.     

Vibrations of and sound radiation from sandwich plates in heavy fluid loading conditions

A problem of forced vibrations of a sandwich plate submerged in a fluid (an acoustic medium) is formulated as a coupled problem of structural acoustics. Two-dimensional (plane) formulation relevant to cylindrical bending of a plate is explored. Dynamics of a sandwich beam (a sandwich plate in cylindrical bending) is described in the framework of the sixth-order theory of multi-layered plates. Asymptotic analysis of the dispersion polynomial is performed in the low frequency and the low module limits for an isolated infinitely long beam. Green's functions for flexural vibrations are obtained analytically and thus explicitly contain the principal parameters of beam's composition. Forced vibrations of a fluid-loaded beam in a rigid baffle are considered. Both the interaction between an acoustic medium and a plate and the interaction between a plate and its boundaries are described by boundary integral equations assembled in a two-level system. Eigenfrequencies of a fluid-loaded beam are detected by maximum of the radiated acoustic power. A semi-analytical sensitivity analysis of the objective function selected as a radiated acoustic power to the parameters of beam's composition is performed.     

Static and low-velocity impact behavior of sandwich beams with closed-cell aluminum-foam core in three-point bending

In this paper, the response and failure of sandwich beams with aluminum-foam core are investigated. Quasi-static and low-velocity impact bending tests are carried out for sandwich beams with aluminum-foam core. The deformation and failure behavior is explored. It is found that the failure mode and the load history predicted by a modified Gibson's model agree well with the quasi-static experimental data. The failure modes and crash processes of beams under impact loading are similar to those under quasi-static loading, but the force-displacement history is very different. Hence the quasi-static model can also predict the initial dynamic failure modes of sandwich beams when the impact velocity is lower than 5 m/s.     

Experimental investigation of local bending effects in the vicinity of a junction between a straight sandwich beam and a curved sandwich beam

The junction between a curved and a straight sandwich beam is investigated experimentally using electronic speckle pattern interferometry. This technique facilitates a whole field measurement of the displacements through the thickness of the sandwich beam. The experimental results are compared with results obtained using a high order sandwich theory model. The results generally show good agreement within the accuracy of the measurements, thus indicating that the gross response of the model is predicted accurately by the high order sandwich theory, while the localised bending effects in the vicinity of curvature change in sandwich panels have not been verified experimentally.     

Collapse of clamped and simply supported composite sandwich beams in three-point bending

Composite sandwich beams, comprising glass–vinylester face sheets and a PVC foam core, have been manufactured and tested quasi-statically. Clamped and simply supported beams were tested in three-point bending in order to investigate the initial collapse modes, the mechanisms that govern the post-yield deformation and parameters that set the ultimate strength of these beams. Initial collapse is by three competing mechanisms: face microbuckling, core shear and indentation. Simple formulae for the initial collapse loads of clamped and simply supported beams along with analytical expressions for the finite deflection behaviour of clamped beams are presented. The simply supported beams display a softening post-yield response, while the clamped beams exhibit hardening behaviour due to membrane stretching of the face sheets. Good agreement is found between the measured, analytical and finite element predictions of the load versus deflection response of the simply supported and clamped beams. Collapse mechanism maps with contours of initial collapse load and energy absorption are plotted. These maps are used to determine the minimum mass designs of sandwich beams comprising woven glass face sheets and a PVC foam core.     

Design of load-bearing antenna structures by embedding technology of microstrip antenna in composite sandwich structure

Electrically and structurally effective antenna structure is developed for the next generation of surface technology for communication, in which the structural surface itself becomes an antenna. The basic design concept is a sandwich structure composed of composite laminates and Nomex honeycomb, with which microstrip antenna is integrated. Composite materials with high electrical loss must not reduce antenna efficiency. Stacked-patch microstrip antenna is preferred for wideband performance. An open condition that defines a position of outer facesheet is exploited in order to allow an antenna into the sandwich structure without loss of antenna performances. Measured electrical performances of fabricated structure show that the gain is more improved than original antenna and the bandwidth is as wide as specified in our requirements. With the open condition, wideband antenna can be integrated with mechanical structures without reducing any electrical performances, as confirmed experimentally here.     

Optimum distribution of smart stiffeners in sandwich plates subjected to bending or forced vibrations

The problems of optimum distribution of active stiffeners manufactured from piezoelectric or shape memory alloy materials and bonded to or embedded within the facings of a sandwich plate are considered. The sandwich plate consists of thin composite or isotropic facings which are in the state of plane stress and a thick shear deformable core. The amplitude of forced vibrations of the plate is reduced using symmetric couples of piezoelectric stiffeners subjected to out-of-phase dynamic voltages. Shape memory alloy stiffeners are used to reduce bending deformations. In the latter case, a desirable effect is achieved by activating the stiffeners on one side of the middle surface. Optimum design is considered based on the requirement of minimal transverse static or dynamic deflections subject to a constraint on the volume of smart stiffeners. The variables employed in the process of optimization are the ratios of the cross-sectional areas of the stiffeners in each direction to their respective spacings. It is shown, that, dependent on the load, materials, and geometry, optimum design can significantly reduce deflections, i.e. enhance the strength, of sandwich plates.     

Static and dynamic analysis of plates in cylindrical bending through displacement and mixed approaches

This work analyzes the influence of edge-boundary conditions on the static and dynamic behavior of isotropic and cross-ply plates in cylindrical bending conditions. The main concern of the analysis is addressed to dynamic problems (free vibrations) along with certain boundary conditions that seem to be mainly responsible for a low convergence of the eigenvalues to the exact values. The interest on the static behavior comes from the inherent sensitivity of related quantities, which can both be compared with previous studies and can better elucidate such a low convergence. The analysis is carried out within the frame of the three-dimensional theory by using different variational formulations based both on assumed displacements and/or stresses along with the attempt to unify the comparison of the different formulations. The numerical results/performance of such formulations are also compared to those achieved through alternative models.     

泡沫铝层合梁的三点弯曲变形

研究了泡沫铝层合梁三点弯曲的载荷(P)-位移(δ)曲线、变形过程及面板破坏、夹芯剪切破坏、凹陷破坏等破坏模式。用极限载荷公式得到的计算值与实验值符合良好。实验所得的加载和卸载刚度(P/δ)与计算结果吻合较好。泡沫铝层合梁具有较低的密度((0.42～0.92)×10~3kg/m~3)和很高的弯曲比刚度(E~(1/2)/ρ)。利用极限载荷公式建立了破坏模式图。     

Stability of the face layer of sandwich beams with sub-interface damage in the foam core

This paper addresses the effect of local indentation/impact damage on the bearing capacity of foam core sandwich beams subjected to edgewise compression. The considered damage is in a form of through-width zone of crushed core accompanied by a residual dent in the face sheet. It is shown that such damage causes a significant reduction of compressive strength and stiffness of sandwich beams. Analytical solutions estimating the Euler’s local buckling load are obtained for two typical modes of damage. These solutions are validated through experimental investigation of three sandwich configurations. The results of the analytical analysis are in agreement with the experimental data.     

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.     

Finite element modelling of core thickness effects in aluminium foam/composite sandwich structures under flexural loading

This paper models the flexural behaviour of a composite sandwich structure with an aluminium foam core using the finite element (FE) code LS-DYNA. Two core thicknesses, 5 and 20 mm, were investigated. The FE results were compared with results from previous experimental work that measured full-field strain directly from the sample during testing. The deformation and failure behaviour predicted by the FE model compared well with the behaviour observed experimentally. The strain predicted by the FE model also agreed reasonably well with the distribution and magnitude of strain obtained experimentally. However, the FE model predicted lower peak load, which is most likely due to a size effect exhibited by aluminium foam. A simple modification of the FE model input parameters for the foam core subsequently produced good agreement between the model and experimental results.     

流场中填充吸声材料夹层板结构的声振耦合特性

采用等效流体模拟吸声材料,建立了外部流场作用下填充吸声材料夹层板结构的声振耦合模型,应用波动分析方法研究结构中声的透射特性,分析了入射声波入射角和方位角、流场流速和流向、夹层结构几何尺寸等参数对填充吸声材料夹层板结构声振耦合特性的影响。仿真计算表明吸声材料提高了双层板结构的隔声性能;隔声性能随着面板厚度和夹层厚度的增加而提高,随着入射角和方位角的增大而减小;在计算频段内(0~5000Hz),逆流入射时传声损失随着马赫数的增大而减小,顺流入射时却随着马赫数的增大而增大。