Laminated Plate Model Research Articles

A higher order finite element including transverse normal strain for linear elastic composite plates with general lamination configurations

This paper describes a higher-order global–local theory for thermal/mechanical response of moderately thick laminated composites with general lamination configurations. In-plane displacement fields are constructed by superimposing the third-order local displacement field to the global cubic displacement field. To eliminate layer-dependent variables, interlaminar shear stress compatibility conditions have been employed, so that the number of variables involved in the proposed model is independent of the number of layers of laminates. Imposing shear stress free condition at the top and the bottom surfaces, derivatives of transverse displacement are eliminated from the displacement field, so that C 0 interpolation functions are only required for the finite element implementation. To assess the proposed model, the quadratic six-node C 0 triangular element is employed for the interpolation of all the displacement parameters defined at each nodal point on the composite plate. Comparing to various existing laminated plate models, it is found that simple C 0 finite elements with non-zero normal strain could produce more accurate displacement and stresses for thick multilayer composite plates subjected to thermal and mechanical loads. Finally, it is remarked that the proposed model is quite robust, such that the finite element results are not sensitive to the mesh configuration and can rapidly converge to 3-D elasticity solutions using regular or irregular meshes.

Simulating Effective Engineering Elastic Constants of the Stator Core Lamination

In this paper, we study the problem of effective engineering elastic constants of stator core lamination of water turbogenerator. The three-dimensional transformations of elastic constants of composite lamina between the principal material coordinate system and the reference coordinate system are given, then the stator core lamination is modeled as the composite laminate and by utilizing the thick laminated plate model, we determine effective engineering elastic constants of the stator core lamination. Finally, a simple example is included to demonstrate the validity of the model and the programme codes.

Recursive formulae for wave propagation analysis of FGM elastic plates via reverberation-ray matrix method

Through a laminated plate model, a recursive formulation for the method of reverberation-ray matrix (MRRM) is proposed for the analysis of free wave propagation in an elastic plate with material properties varying along the thickness direction. In contrast to the traditional MRRM, the present new formulation behaves well for high frequency computation, while the heavy computational cost of storage and memory can also be cut down. Numerical examples are given to analyze dispersion characteristics of waves in FGM plates, and the comparison among traditional MRRM and the recursive formulation demonstrates the significant efficiency of the proposed recursive formula.

Parameter estimation in active plate structures

In this paper two non-destructive methods for elastic and piezoelectric parameter estimation in active plate structures with surface bonded piezoelectric patches are presented. These methods rely on experimental undamped natural frequencies of free vibration. The first solves the inverse problem through gradient based optimization techniques, while the second is based on a metamodel of the inverse problem, using artificial neural networks. A numerical higher order finite element laminated plate model is used in both methods and results are compared and discussed through a simulated and an experimental test case.

On the ‘ply discount method’ for determining effective thermo-elastic constants of laminates containing transverse cracks

Abstract Elastic constants and thermal expansion coefficients of a laminate containing transverse ply cracks are often calculated by reducing selected elastic moduli of the damaged plies. This approach is often referred to as the ‘ply discount method’. In the present paper, specific ply moduli required for reduction are identified by enforcing compatibility with inter-relationships that exist between the thermo-elastic properties of cracked and uncracked laminates. The effect of laminate geometry is investigated by comparing ply reduction factors as a function of crack density for a number of different stacking sequences. Reduction factors are obtained from higher order laminated plate models of composites containing transverse cracks. A simplified approach for determining inplane modulus reduction factors is also investigated.

Determination of the growth strain of LPCVD polysilicon

This work presents a semi-empirical procedure for determining the through-the-thickness variation of the eigenstrain (eigenstrain is a generic term for any inelastic strain, including plastic strain, free thermal expansion, phase transformation, etc.) that develops during the growth of thin polysilicon films formed using low-pressure chemical vapor deposition (LPCVD). This variation is assumed to depend on the polysilicon microstructure and deposition conditions, but not on the characteristics of the (single crystal silicon) substrate. The procedure involves the use of an elastic laminated plate model to determine the eigenstrain distribution that predicts the experimentally measured substrate curvatures. In comparison to the method presented by A.Ni et al., which relies on incremental etching of a single specimen, an alternative experimental procedure is followed to measure the substrate curvatures of a series of different thickness films. While being significantly more time-consuming, the alternative procedure was expected to lead to improved predictions of the eigenstrain distribution, as it avoids the nonuniform film thicknesses produced by the etching procedure. However, a comparison of the curvature histories measured using the two approaches demonstrates that, as long as sufficiently small increments are used in the shaving method, then the improvement is insignificant. This suggests that the plasma etching does not alter the polysilicon's intrinsic growth strain, and that the etch rate nonuniformities across the substrate are small. The eigenstrain distributions could be used, in conjunction with structural mechanics models, to design multilayered polysilicon devices with prescribed curvatures.

Numerical simulation of hypervelocity impacts of a projectile on laminated composite plate targets by means of improved SPH method

Abstract This paper is concerned with the numerical simulation of hypervelocity impacts (HVIs) of a projectile on laminated composite plate targets. When the numerical simulation of HVIs is performed by means of a conventional smoothed particle hydrodynamics (SPH) method, loss of interactions among particles causes numerical fractures. To prevent the numerical fractures, the improved SPH method with new particle generation and particle merger techniques is used. For the laminated composite plate targets of weak delamination strength, a numerical laminated plate model for the SPH method is proposed to realize the discontinuity of stresses between neighboring layers of the laminated composite plate targets. The numerical simulation was carried out for an aluminum projectile striking to laminated graphite/epoxy (Gr/Ep) composite plate targets with several different layup configurations. Through the numerical simulation, the HVI responses of the projectile on the laminated composite plate targets are discussed.

Strengthening of unidirectionally reinforced concrete slabs with composite material Theoretical and experimental study

This paper deals with the flexural strengthening of unidirectionally reinforced concrete slabs by means of thin carbon fibre reinforced plastic (CFRP) plates. A simplified laminated plate model has been used to describe the behaviour of a three layered plate in simple (cylindrical) bending in response to three point line loads. The static and kinematic methods of limit analysis were used to approximate the ultimate load capacity for multilayered plates and identify different collapse mechanisms. A unidirectionally reinforced concrete slab strengthened with CFRP was designed as a three layered plate. Experimental results were obtained and compared with theoretical predictions.

RC two-way slabs strengthened with CFRP strips: experimental study and a limit analysis approach

This paper deals with strengthening of reinforced concrete (RC) two-way slabs with carbon fibre reinforced plastic (CFRP) strips bonded to the tensile face. The first part deals with an experimental study. The fibre reinforced plastics (FRP) strengthened slab test presents a failure mode with debonding of the external FRP strips from the slab. The second part deals with a limit analysis modelling. The strengthened slab is designed as a three-layered plate. A simplified laminated plate model is used to describe the behaviour of three-layered plate supported in four sides, which is subjected to a load in the centre. The upper bound theorem of limit analysis is used to approximate the ultimate load capacity and identify the different collapse mechanisms. Experimental results are compared with theoretical predictions.

RC beams strengthened with composite material: a limit analysis approach and experimental study

This paper deals with the flexural strengthening of reinforced concrete beams by means of thin carbon fibre reinforced plastic (CFRP) plates. A simplified laminated plate model is used to describe the behaviour of three-layered plate in cylindrical bending which were subjected to third-point line loads. The upper bound theorem of limit analysis is used to approximate the ultimate load capacity for multi-layered plates and identify different collapse mechanisms. A reinforced concrete beam strengthened by CFRP is designed as a three-layered plate. Experimental results are obtained and a comparison with theoretical predictions made.

Mixed mode delamination in plates: a refined approach

Abstract Energy release rate and its mode partition in layered plates are analysed by using an improved laminated plate model. The adhesion between layers is modelled by means of a linear interface acting in the opening and sliding failure mode directions. Stress singularities at the crack tip are recovered when the stiffness of the interface approaches infinity. Kirchhoff or Reissner–Mindlin plate models are employed to describe the layers. Analytical solutions of the relevant governing equations are obtained through a variational formulation of an augmented total potential energy, in which the stiffness of the interface introduces kinematics constraints in the form of a penalty functional. Closed form solutions for energy release rates are given evidencing the effectiveness and the simplicity of the proposed model. Comparisons with fracture mechanics results––when available––are shown discussing the validity of the proposed mechanical model to predict mode partition. Interesting features emerging with the introduction of the layer-wise Reissner–Mindlin model are also highlighted, particularly with reference to coupling terms arising from shear effects.

Delamination in composite plates: influence of shear deformability on interfacial debonding

An elastic interface model is introduced to investigate the effects of in-plane and out-plane shear stresses on interfacial debonding in laminated composite plates by means of the energy release rate concept. This is done by utilising an improved laminated plate model in which the Reissner–Mindlin kinematics type for each layers is coupled with an adhesion mechanism modelled by means of a linear interface model, acting in the opening and sliding failure mode directions. The problem is faced through an analytical solution procedure. Increasing the stiffnesses of the interface leads to restoring displacement continuity at the interface between layers and to recovering energy release rate components through the work performed by the singular stress field at the crack tip. In view of the great importance of shear deformation in laminated composite plates the effect of shear stresses on the mechanism of delamination are investigated pointing out new features which emerge from the interaction of normal and shear stresses acting on the transverse section near the crack tip. Several examples of mixed mode delamination schemes used in experimental applications are examined, showing the influence of transverse shear stresses in coupling with normal stresses on energy release rates determination.

403 軸対称加熱を受ける傾斜機能平板の材料組成最適化問題 : ニューラルネットワークによるアプローチ(GS-1 アルゴリズム)

In this study, a neural network is applied to an optimization problem of material compositions for an infinite functionally graded plate due to axisymmetric heat supply. Using analytical procedure of a laminated plate model, the analytical solution for FGM plate is derived approximately. As the optimization problem of minimizing the thermal stress distribution, the numerical calculations are carried out making use of neural network, and the optimum material composition is determined at arbitrary heat area and transfer coefficient. Furthermore, the results obtained by neural network and ordinary non-linear programming method are compared.

FLEXURAL–TORSIONAL COUPLING EFFECT ON VIBRATIONAL CHARACTERISTICS OF ANGLE-PLY LAMINATES

A mainly experimental investigation is presented on the vibrational characteristics of angle-ply laminate made of carbon/epoxy composite material, considering the effect of flexural–torsional coupling stiffness. This consists of a resonance test on a cantilevered laminated plate model by using laser holographic interferometry. An exact comparison of the coupling effect was achieved by employing two special types of angle-ply laminates, each consisting of eight plies in which one type had the least possible, and the other type, no coupling stiffness at all. The observed results show that the effect of flexural–torsional coupling stiffness on the resonance frequencies is only marginal. By contrast, the vibrational mode shapes are found to be affected considerably by the coupling stiffness. Moreover, the amount of this coupling effect is also observed to depend both on the fiber orientation and the aspect ratio of the plate model. An analytical study was also conducted by using the Ritz energy method and a good agreement between the experimental and the theoretical values is observed upon comparison.

A Laminated Plate Model of an Adhesive-Bonded Taper-Taper Joint Under Tension

An analytical model of the strain and stress distributions in a taper-taper adhesive-bonded joint between two composite flat plates has been developed using first-order laminated plate theory. A correction for transverse shear deformation effects was included. The model was derived under the assumption of plane strain in the adherends and consists of eighteen first-order, linear, coupled ordinary differential equations with variable coefficients. The model was solved numerically using the Linear Shooting Method. Finite element models were also developed to verify the results of the analytical model using the COSMOS/M commercial software package.

Material Damping Analysis of Smart Hybrid Composite Laminated Plate Structures

Material damping analysis of a generally laminated smart hybrid composite plate has been presented in this paper. The present analytical formulation is an integrated micro-macromechanical method. Analytical equations derived at the lamina level together with a classical laminated thin plate theory predict the equivalent material specific damping capacity (SDC) of a general smart hybrid composite laminated plate structure. The micro-niechanical equations based on the mechanics of material have been used for the calculation of the elastic stiffness and SDC ot an intraply hybrid composite lamina. Present objective is mainly to get a first hand information on the basic material damping behavior of hybrid composite laminate. Therefore, numerical studies have been carried out for a typical shape memory alloy (SMA) smart composite laminated plate model. The effects of the laminate fiber orientaton and the SMA volume fraction on the SDC and natural frequencies of the laminate were evaluated.

Transient Thermal Stress Analysis of a Nonhomogeneous Plate Taking into Account the Relative Heat Transfer at Boundary Surfaces.

Nonhomogeneous materials such as FGM (Functionally Gradient Materials) have arbitrarily distributed and continuously varying material properties. For such nonhomogeneous materials, the heat conduction equation takes a nonlinear form, which makes theoretical treatment of the temperature change difficult, and it is almost impossible to obtain the exact solution. In this paper, taking into account the effect of the heat transfer at the heated surface and cooled end, a one-dimensional transient heat conduction problem of a plate made of such nonhomogeneous materials is treated theoretically. Introducing the analytical technique for a laminated plate model, and considering the number of lamina to be sufficiently large, the temperature solution for such a nonhomogeneous plate is approximately derived. The associated thermal stress distribution for an infinitely large nonhomogeneous plate is formulated under the traction free-condition. Numerical calculations are carried out for a nonhomogeneous plate, made of zirconium oxide and titanium alloy. Numerical results such as temperature change and the thermal stress distribution are shown graphically, and the influences of a change of relative heat transfer coefficient at the heated and cooled surfaces and of a change of nonhomogeneity are briefly examined.

Numerical analysis of thickness shear thin film piezoelectric resonators using a laminated plate theory

Finite element matrix equations are derived from a two-dimensional, piezoelectric high frequency laminated plate theory. Two-layer ZnO/Si and three-layer ZnO/SiO/sub 2//Si thin film resonators vibrating at the fundamental thickness shear mode are investigated using the finite element models. Straight crested waves propagating in a resonator are studied. Resonant frequency, mode shapes and electromechanical coupling coefficient of the fundamental thickness shear mode are calculated and presented with respect to the C-axis orientation of the ZnO layer, and thickness ratios of the layers in a resonator. The results from the laminated plate model are checked against the three dimensional finite element solution and found to be accurate for the fundamental thickness shear and its anharmonic overtones. The plate model does not yield as accurate a frequency spectrum for flexure, face shear and extensional modes. >

All-moving active aerodynamic surface research

The structural and aerodynamic characteristics of a new class of active flight control surface are presented. This new type of surface uses a symmetric, subsonic aerodynamic shell which is supported at the quarter-chord by a main spar and actively pitched by an adaptive torque-plate. The structural mechanics of the torque-plate and several actuator elements are detailed, including newly invented interdigitated electrode (IDE) and constrained directionally attached piezoelectric (CDAP) elements. Laminated plate models demonstrate that both generate similar deflections with comparable torsional stiffness. An experimental torque-plate specimen constructed from PSI-5A-S2 piezoceramic shows high torsional deflections and stiffness as well as excellent correlation with theory. The constrained torque-plate was integrated into a 12.5 cm span *5 cm chord adaptive missile fin which was designed for Mach 0.6 flight under standard conditions. The specimen showed static pitch deflections up to +or-8.1 degrees and dynamic deflections of +or-19 degrees at resonance. The active surface was also wind tunnel tested up to 40 m s-1 and demonstrated invariant pitch deflections as a function of airspeed, a steady break frequency of 50 Hz, no flutter, buffet or divergence tendencies and steady lift coefficient changes up to +or-0.51.

One-Dimensional Transient Heat Conduction and Associated Thermal Stress Problems of a Plate with Nonhomogeneous Material Properties.

The one-dimensional transient heat conduction problem of a nonhomogeneous plate with arbitrarily distributed and continuously varied material properties, such as FGM (functionally gradient materials), is treated theoretically in this paper. For such a nonhomogeneous plate, the heat conduction equation becomes nonlinear, therefore the theoretical treatment is very difficult and the exact solution is almost impossible to obtain. Introducing the analytical procedure of the laminated plate model, and thereafter, taking into account the constraint that the number of lamine becomes sufficiently large, the analytical temperature solution for such a completely nonhomogeneous plate is derived. Furthermore, the associated thermal stress components for an infinitely long non-homogeneous plate are formulated under the mechanical condition of being traction free. As a numerical example, the plate composed of alumina and aluminum alloy is considered. The numerical results for temperature change and the associated thermal stress distributions are shown in the figures, and the effects of nonhomogeneity (change of the volume fraction of two different materials)on thermoelastic behaviors are briefly examined.