Analysis of sandwich plates with unbalanced cross-ply faces

The analysis of rectangular sandwich plates constructed of an orthotropic core and unbalanced cross-ply face plates is presented. A double Fourier series approach is used for simply supported sandwich plates under lateral loads. Results are compared to the corresponding sandwich plate results with orthotropic faces. The results indicate that the effect of bending-membrane coupling depends mainly upon the relative thicknesses of the core and faces; other factors include the shear stiffnesses of the core, the degree of anisotropy of the individual plies, the total number and lay-up of plies in the faces and the aspect ratio of the plate.     

Modified membrane finite element formulation for sheet metal forming analysis of planar anisotropic materials

A finite element formulation is derived for sheet metal forming analysis of planar anisotropic materials. The formulation incorporates membrane elements whereas it takes the bending effect into account explicitly. The strain energy term in the formulation is decomposed into the membrane energy term for mean stretching and the bending energy term for pure bending. This procedure needs careful evaluation for the orientation of the anisotropic axes. The formulation is then combined with an effective algorithm to calculate distribution of the blank holding force in each step according to the thickness in the flange region. The calculation employs a special relation between the thickness and the blank holding force. The simulation examples demonstrate the validity and versatility of the developed computer code by showing that the thickness variation in the flange region redistributes the blank holding force during the deformation. The present algorithm can predict accurate deformed shapes and thickness strain distribution with the anisotropy of materials and the variable blank holding force.     

Nonlinear flexural vibration of rectangular moderately thick plates and sandwich plates

Nonlinear flexural vibration is investigated for rectangular Reissner moderately thick plates and sandwich plates. The fundamental equations and boundary conditions are expressed in unified dimensionless form for rectangular moderately thick plates and sandwich plates. Highly accurate solutions of series form with many different movable and immovable boundary conditions, especially with unsymmetrical boundary conditions, are obtained by means of the method of harmonic balance and by developing a new technique of mixed Fourier series in nonlinear analysis. The nonlinear partial differential equations are reduced to an infinite set of simultaneous nonlinear algebraic equations, which are truncated in numerical computations. Solutions of the nonlinear fundamental frequency of rectangular plates are obtained by iteration. The multimode approach includes not only the influences of transverse shearing deformation and rotatory inertia, but also the coupling effect of vibrating modes on the nonlinear fundamental frequency. The present solutions are satisfactory in comparison with other available results.     

Metal sandwich plates optimized for pressure impulses

Survival of a plate against an intense, short duration impulsive loading requires the circumvention of failure modes, including those associated with excessive overall deflection and shear-off at supports and webs. All-metal sandwich plates have distinct advantages over comparable weight monolithic plates, especially for intense water loadings. A recently developed mechanics of dynamically loaded sandwich plates by N. A. Fleck and V. S. Deshpande is extended and modified to address the problem of the minimum weight design of plates of given span that must sustain a uniformly distributed impulsive wave in air or water environments. Requirements for core crushing strength and energy absorption are discussed, as are conditions governing shear-off of the face sheet. Dimensionless parameters governing optimal designs are identified. Specific results are presented for plates with square honeycomb cores outlining trends for the best performance that can be achieved and the optimal distribution of mass between faces and core. Optimally designed sandwich plates can sustain water shocks that are two to three times as large monolithic plates of the same mass and material. The model is used to discuss a number of issues relevant to the design of effective metal sandwich plates, including differing requirements for air and water environments, face sheet shear-off resistance, the role of core strength, and the relation between small-scale tests and full-scale behavior.     

Analytical models of sandwich plates with piezoelectric strip-stiffeners

A theory of sandwich plates with composite-material facings and piezoelectric strip-stiffeners bonded to the surface or embedded in the facings is developed. The stiffeners bonded to the surfaces are modeled using either the plane stress assumption or a first-order shear deformable theory. The former approach is appropriate if the stiffeners represent thin strips, while the latter method can be used in the case where the stiffeners are relatively deep. The stiffeners embedded in the facings in the form of piezoelectric strips are considered using the plane stress assumption.     

Preliminary assessment of sandwich plates subject to blast loads

The question motivating the present study is whether metal sandwich plates with sufficiently strong cores are able to sustain substantially larger blast loads than monolithic solid plates of the same material and total mass. Circular plates clamped at their edges are considered under blast loads large enough to produce substantial deflections. The material is elastic–perfectly plastic. Material strain-rate dependence and fracture are neglected. A dynamic finite element formulation for elastic–plastic solids is employed to analyze the plate response. Uniformly distributed blast impulses are considered. As a basis for comparison, complete results are obtained for solid plates for both zero-period and finite-period impulses. Similar computations are carried out for a set of sandwich plates having tetragonal truss cores. The potential for superior strength and energy absorbing capacity of the sandwich plates is demonstrated compared with solid plates having the same mass. The importance of both the strength and energy absorbing capacity of the core are highlighted for superior blast resistance. Proposals for further research are made.     

Buckling of laminated sandwich plates subjected to partial edge compression

The buckling characteristics of sandwich plates having laminated stiff layers are studied for different types of partial edge loadings using a refined plate theory. With this plate theory, the through thickness variation of transverse shear stresses is represented by piecewise parabolic functions where the continuity of these stresses is satisfied at the layer interfaces by taking jumps in the transverse shear strains at the interfaces. The transverse shear stresses free condition at the plate top and bottom surfaces is also satisfied. It is quite interesting to note that this plate model having all these refined features requires unknown parameters only at the reference plane. To have a generality in the present analysis, finite element technique is adopted and it is carried out with newly developed triangular element, as existing finite elements cannot accommodate this plate model. So far, no solution exists in the literature for the problem of sandwich plate subjected to partial edge loading. The present analysis is first validated for the case of an isotropic plate subjected to partial edge compression and then it is extended to analyze sandwich plates. Few results are presented.     

Buckling of multi-layer sandwich plates by the finite strip method

This paper presents a finite strip method for the stability analysis of rectangular multi-layer sandwich plates. The method permits freedom of in-plane displacements for all the stiff layers, thus excludes the assumption of common shear angle for all cores as adopted in some previous works. Numerical examples of various multi-layer sandwich plates with different boundary conditions and under different edge loadings are included.     

移动荷载作用下夹层板的动力学响应仿真分析

应用层合板理论将夹层板等效为一个正交各向异性板,分别计算出了实体金属夹芯、金属泡沫夹芯、正六边形蜂窝夹芯、金属波纹板夹芯四种夹层板的等效刚度,再应用正交各向异性板理论和模态叠加原理分析了这四种夹层板在移动荷载作用下的动力学响应,并对此做了比较分析,得出移动荷载作用下正六边形蜂窝夹层板相对于其它三种夹层板更具有优越性,而实体金属夹层板是这四种夹层板中承载能力最差的.所得结果对桥梁,公路的建设具有一定的指导意义.     

Thermoelastic analysis of functionally graded sandwich plates with a homogeneous core

This paper is concerned with the thermoelastic analysis of functionally graded (FG) sandwich plates with a homogeneous core by a numerical method. The core layer is homogeneous ceramic while two facesheets are inhomogeneous metal-ceramic FGMs having the power-law volume fractions. The metal-ceramic FG sandwich plates are characterized by the relative thicknesses of three layers, the width-thickness and aspect ratios of plate, and the volume fractions of metal and ceramic. Meanwhile, the problem is formulated using the hierarchical models exhibiting the spectral model accuracy and implemented by 2-D natural element method (NEM). The hierarchical models are based upon the 3-D elasticity and NEM is applied to the mid-surface of plate to approximate the triple-vectored in-plane displacement field. The accuracy of hierarchical models are examined with respect to the model order, from which the (3, 3, 4) hierarchical model is chosen for the thermoelastic analysis. The thermoelastic responses obtained by the present method are compared with the existing analytic solutions, and those are parametrically investigated with respect to the above-mentioned design parameters. It is found that the present method shows a reasonable accuracy and the thermoelastic responses of FG sandwich plates are remarkably influenced by the design parameters.

     

Analysis of laminated anisotropic plates and shells using symbolic computation

The extension of classical isotropic plate and shell solutions and finite element formulations to cope with orthotropic/monoclinic laminated and shear deformable structures often involves very complex intermediate stages and final results within the derivations. This paper examines four case studies covering the use of symbolic computation to manage this complexity. These case studies comprise the derivation of a catalogue of solutions to orthotropic circular plate problems, the formulation of two axisymmetric shell finite elements (respectively using Flügge’s shear-rigid shell assumptions and the shear-flexible assumptions of Soldatos) and the derivation of the eighth-order governing differential equation for a laminated monoclinic or orthotropic shell. The emphasis is placed upon the techniques required to achieve these derivations using symbolic computation, and the considerable effort involved in putting the results into publishable form is noted.     

Finite element aided design of laminated and sandwich plates using reanalysis methods

Classical finite element programs are not well suited to the design of composite structures, because they are primarily analysis tools and need much time for the data input and as well as for the interpretation of the results. The aim of this paper is to develop a program which allows very fast analyses and reanalyses for design process, thanks to a fast reanalysis method with changes of data and conditions. Speed in the analysis is obtained by simplification of the analysed structure and limitations in its geometrical generality and improvements in numerical methods. The use of the program is made easy with interactive user-friendly facilities.     

Nonlinear vibration analysis of composite laminated and sandwich plates with random material properties

Nonlinear vibration analysis is performed using a C⁰ assumed strain interpolated finite element plate model based on Reddy's third order theory. An earlier model is modified to include the effect of transverse shear variation along the plate thickness and Von-Karman nonlinear strain terms. Monte Carlo Simulation with Latin Hypercube Sampling technique is used to obtain the variance of linear and nonlinear natural frequencies of the plate due to randomness in its material properties. Numerical results are obtained for composite plates with different aspect ratio, stacking sequence and oscillation amplitude ratio. The numerical results are validated with the available literature. It is found that the nonlinear frequencies show increasing non-Gaussian probability density function with increasing amplitude of vibration and show dual peaks at high amplitude ratios. This chaotic nature of the dispersion of nonlinear eigenvalues is also revealed in eigenvalue sensitivity analysis.     

Development of a novel boring tool with anisotropic dynamic stiffness to avoid chatter vibration in cutting: Part 1: Design of anisotropic structure to attain infinite dynamic stiffness

This paper presents a novel design method of the anisotropic structure to attain infinite dynamic stiffness to avoid chatter vibration in boring operations. Because a long and slender tool is used for boring operations, the stiffness of the tool holder is likely to decrease, resulting in low chatter stability. Although it is difficult to improve the stiffness of the boring holder itself, the nominal dynamic stiffness for the cutting process can be improved by designing an appropriate anisotropy in the dynamic stiffness of the boring tool. In this study, we formulate a theoretical relationship between the mechanical structural dynamics and chatter stability in boring operation and present the basic concept of tool design with anisotropic structure. In the actual tool design, ideal anisotropy may not be realized because of the influence of design error. Therefore, an analytical study was conducted to clarify the influence of the design error on the vibration suppression effect. Analytical investigations verified that the similarity of the frequency response functions in the modal coordinate system and the design of the compliance ratio according to the machining conditions are important. Furthermore, we designed a boring tool with an anisotropic structure which can achieve the proposed anisotropic dynamics. The frequency response function was evaluated utilizing FEM analysis. The estimated anisotropic dynamics of the proposed structure could significantly improve the nominal dynamics for boring operations.     

Modified Quadratic Compression Method for mass and stiffness updating

The paper presents the modified Quadratic Compression Method (QCM) for both mass and stiffness model updating. The modeling error is defined in a parametric setup, i.e. with pre-specified principal submatrices multiplied by unknown scalar parameters. The optimal parameters are obtained by minimizing the error in a squared down version of the eigenvalue equation, and of the mass orthogonality condition, thus with reduced computation yet with no loss of information. The method has closed ties with Minimization of the Error in the Constitutive Equation (MECE), and in some cases is shown to belong to that class with a particular choice of the weighting matrix. Theoretical analysis of the propagation of the noise into the identified parameters, as well as extensive simulations, reveal that QCM has in some cases desirable noise filtering properties.     

Buckling and post-buckling behavior of laminated plates using the generalized nonlinear formulation

In this paper the buckling and post-buckling analysis of symmetrically laminated cross-ply plates has been considered using the generalized formulation of which the von Karman type formulation is a special case. Unlike the von Karman type formulation, the governing equations of the present formulation are nonlinear in all the displacement parameters of the plate. This obviates the use of hitherto known solution techniques for nonlinear plate analysis. To overcome this difficulty the perturbation technique has been followed in this paper. Numerical results indicate that the two formulations differ by about 2.5% for thicker perfect plates and the difference ceases to exist as the imperfection value of the plate increases.     

Impact resistance performance and optimal design of a sandwich beam with a negative stiffness core

Numerical analyses were carried out to investigate the response of a sandwich beam with a negative stiffness (NS) core under quasistatic compression and low-velocity impact at the center. By varying the thicknesses of face sheets and interlayers and the lengths of segments, a parametric study on the impact resistance of the sandwich beam is conducted. The maximal deflection of the top face sheet and the strain energy stored in the NS beam were recorded at the moment when the impactor’s velocity decreased to zero. Based on the impact simulation, a multi-objective optimization problem on the beam configuration was set up to find out the most efficient anti-deformation design at the impact velocity of 2500 mm/s. To solve the problem with the surrogate model method, an optimal Latin hypercube sampling (OLHS) technique and a two-phase differential evolution (ToPDE) algorithm were utilized to generate calculation points in the design space, respectively. Then different surrogate models including the RSM model, the Kriging model and the RBF model, were compared to give the best approximation of the original problem. In the end, the genetic algorithm (GA) dealing with discrete optimization problems was employed to obtain the optimum solutions. Results indicate that different parts of the NS beam dominate the resistance to deformation under different levels of impact intensity. The largest portion of the strain energy is stored in the four curved plates. In the obtained optimization solution, the longest segment is near the two ends and the flat plates near the top are thicker, which is instructive to the beam design on improving impact resistance.

     

Impact of lubricant formulation on the friction properties of carbon fiber clutch plates

Since their introduction over ten years ago, carbon fiber based friction materials have been employed by transmission builders in a wide variety of applications, including torque converter clutches, synchronizers, limited slip devices and shifting clutches. This new generation of materials gives improved durability relative to cellulose; carbon fiber materials offer inherently greater wear resistance and improved resistance to thermal degradation. However, carbon fiber based materials also bring inherently different friction characteristics than their cellulose based counterparts. As a result, a different approach to lubricant formulation is required to provide optimized friction control in applications where they are used. It is well known that in order to achieve and maintain the required friction in a clutch, the correct combination of surface properties and additive chemistry is required. In this paper the impact of different additive chemistries on the friction of carbon fiber clutch plates has been investigated. It will be shown that with the appropriate choice of additive system, carbon fiber based friction plates can offer a number of performance improvements over more conventional materials. Copyright © 2006 John Wiley & Sons, Ltd.     

Thermomechanical buckling of laminated composite and sandwich plates using global–local higher order theory

In this paper, a global–local higher order theory has been used to study buckling response of the laminated composite and sandwich plates subjected to thermal/mechanical compressive loads. The present global–local theory satisfies the free surface conditions and the geometric and stress continuity conditions at interfaces, and the number of unknowns is independent of the layer numbers of the laminate. Based on this higher-order theory, a refined three-noded triangular element satisfying C¹ weak-continuity conditions has been also proposed. The present theory not only predicts accurately the buckling response of general laminated composite plates but also calculates the critical buckling loads of the soft-core sandwich plates. However, numerical results show that the global higher-order theories as well as first order theories encounter some difficulties and overestimate the critical buckling loads for the sandwich plates with a soft core.     

一边弹性支承三边自由矩形板对接处角刚度的识别

通过试验模态分析,寻找一边弹性支承三边自由对接长方形板的最低阶弯曲振型及对应的固有频率,将对接板的动力学问题转化为一边弹性支承的对接梁来求解,借助计算机代数语言,编写对接梁的传递矩阵法程序,推导出对接处含角刚度作为符号的方程,输入板的最低阶弯曲振型所对应的固有频率就可识别出该处的角刚度,并通过实例验证此法的有效性.