Vibration characteristics of composite/sandwich laminates with piezoelectric layers using a refined hybrid plate model

The free vibration characteristics of laminated composite and sandwich plates with embedded and/or surface-bonded piezoelectric layers is studied, where a hybrid plate theory is proposed for modelling the structural system. It involves a problem of coupled electro-mechanical field. The variation of mechanical/structural displacements across the thickness are modelled by an efficient plate theory, which ensures inter-laminar shear stress continuity as well as stress free condition at the plate top and bottom surfaces. At the same time, this plate model has the distinct advantage of involving unknowns at the reference plane (plate mid-plane) only. For the electrical potential, the through thickness variation is modelled by the layer-wise theory, where the unknowns are taken at all the interfaces including top and bottom surfaces of the plate. However, the degrees of freedom for the electric potential are finally eliminated from the element matrices through condensation. In order to have generality in analysis, the finite element technique is used to approximate the in-plane variation of displacement parameters at the reference plane and electric potential at the different interfaces. For this purpose, an attempt has been made to develop a simple and efficient rectangular element, which satisfies C¹ continuity of transverse displacement at the inter-element boundaries. To validate the proposed model, some numerical examples are solved and the results obtained are compared to the published results. As the number of such published results is not sufficient, new examples covering various features are solved to study different aspects of the proposed model.     

Stochastic perturbation-based finite element for deflection statistics of soft core sandwich plate with random material properties

The effect of random variations in material properties of laminated sandwich plates on the transverse deflections is investigated. An improved higher-order plate model is proposed earlier by the authors, which satisfies the transverse shear stress continuity conditions at the layer interfaces including the zero transverse shear stress conditions at the plate top and bottom surfaces. The theory assumes the variation of in-plane displacements to be cubic with discontinuities in the transverse shear strains at the layer interfaces, while the transverse displacements varies quadratically across the core thickness, thereby including transverse normal deformation of the soft core. The core is considered to behave as a 3-D elastic medium. To obtain the second-order statistics of deflections of sandwich plate, a stochastic C⁰ finite element (FE) based on the first-order perturbation technique is developed, where the lamina properties are considered as basic random variables while the other system properties are assumed to be deterministic. The performance of the improved stochastic laminated sandwich model is demonstrated through comparison of mean and standard deviations (SDs) of deflections obtained through independent Monte Carlo simulations and by comparison with results available in literature.     

Analyses of piezoelectric plates with elliptical notches by special finite element

A novel special finite element with an elliptical notch, based on the complex potential theory and hybrid variational principle, is proposed for mechanical–electrical coupling analyses of piezoelectric plates with notches. The formulations are given and a variety of examples are analyzed. Comparisons are made with existing analytical or numerical data. It is shown that the proposed element is very efficient and accurate. Some new numerical results are given and discussed. It is found, perhaps for the first time according to the authors’ knowledge, that the relationships between the logarithm concentration factor of tangential (θ=0) stress, electrical displacement, and electrical field at the notch tip and logarithm b/a are linear. Some conclusions are drawn based on the results reported herein.     

巨型水压机主工作缸的有限元分析

应用有限元分析软件MSC.MARC对巨型水压机的主工作缸进行静力分析.以三万吨水压机的主工作缸为研究对象,模拟其在最大工作压力(45MPa)下的应力分布,并与实际测量值对比,验证了有限元模型及分析的准确性.同时分析了在仅改变螺钉位置的情况下,主工作缸各主要应力集中处的应力变化规律.     

Vibration analysis of delaminated composite beams and plates using a higher-order finite element

In order to analyze the vibration response of delaminated composite plates of moderate thickness, a FEM model based on a simple higher-order plate theory, which can satisfy the zero transverse shear strain condition on the top and bottom surfaces of plates, has been proposed in this paper. To set up a C⁰-type FEM model, two artificial variables have been introduced in the displacement field to avoid the higher-order derivatives in the higher-order plate theory. The corresponding constraint conditions from the two artificial variables have been enforced effectively through the penalty function method using the reduced integration scheme within the element area. Furthermore, the implementation of displacement continuity conditions at the delamination front has been described using the present FEM theory. Various examples studied in many previous researches have been employed to verify the justification, accuracy and efficiency of the present FEM model. The influences of delamination on the vibration characteristic of composite laminates have been investigated. Especially the variation of ‘curvature of vibration mode’ (i.e., the second-order differential of deflections in vibration mode) caused by delamination has been studied in detail to provide valuable information for the possible identification of delamination. Furthermore, two approaches have been investigated to detect a delamination in laminates by employing this information.     

A finite element formulation based on an enhanced first order shear deformation theory for composite and sandwich structures

A finite element formulation based on an enhanced first order shear deformation theory is developed to accurately and efficiently predict the behavior of laminated composite and sandwich structures. An enhanced first order shear deformation theory is systematically derived by minimizing the least-squared energy error between the first order shear deformable plate theory and a higher order shear deformable plate theory. In this way, the strain energy of a higher order theory is transformed to that of the Reissner-Mindlin plate theory. This minimization procedure yields a relationship between them that is also used to improve the accuracy of predicted stresses and displacements. The key feature of the proposed theory is in that it can be implemented to commercial FEM packages by simply changing the input, and the results obtained can be also enhanced by post-processing them via a differential quadrature method. Thus, a proposed finite element formulation can be widely used in various application problems. Through numerical examples, the accuracy and robustness of the present formulation are demonstrated.     

Stability and free vibration analysis of thick piezoelectric composite plates using spline finite strip method

In the present study, a spline finite strip with higher-order shear deformation is formulated for stability and free vibration analysis of piezoelectric composite plates. At each knot, the electric potentials on the surfaces and middle plane of each piezoelectric layer are taken as nodal degrees of freedom. However, if a continuous electrode is installed on the surface of the layer, the electric potential on the electrode is changed to structural degree of freedom, so that the equipotential condition on the electrode is automatically satisfied. The analysis can be conducted based on Reddy's third-order shear deformation theory, Touratier's “Sine” model, Afaq's exponential model or Cho's higher-order zigzag laminate theory. Consequently, the shear correction coefficients are not required in the analysis, and an improved accuracy for thick plates over the first-order shear deformation theory is achieved at only little extra computational cost.The numerical results obtained based on different shear deformation theories are presented in comparison with the three-dimensional solutions. The effects of length-to-thickness ratio, fiber orientation, boundary conditions and electrical conditions on the natural frequency and critical buckling load of piezoelectric composite plates are investigated through numerical examples.     

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.     

Dynamic analysis of laminated composite plates with piezoelectric sensor/actuator patches using the FSDT mesh-free method

This paper investigates the active control of laminated composite plates with piezoelectric sensor/actuator patches using an efficient mesh-free method, i.e. the element-free Galerkin (EFG) method. The formulation of the problem is based on the first-order shear deformation plate theory (FSDT) and the principle of virtual displacements. A simple control algorithm coupling the direct and converse piezoelectric effect is used to control the dynamic response of the laminate plate with distributed sensor/actuator patches through a closed control loop. Several example problems are studied to show the influence of stacking sequence and position of sensor/actuator patches on the dynamic responses of the laminate plate. These simulations provide us with the best location of the sensor/actuator patches for active control of the laminate plate.     

基于有限单元法的热风阀阀体模态和谐响应分析

采用有限元分析软件ANSYS对热风阀阀体进行了模态分析和谐响应分析。给出了阀体前4阶的固有频率和振型，并得出了前四阶固有频率下激振力和动应力问的关系。该分析方法和结论为阀体的消除焊接残余应力振动时效工艺提供了理论依据。     

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.     

Strengths and weaknesses of finite element modeling deep hole drilling as compared with beam and column equations

Deep hole drilling has been studied mainly experimentally in the past. Recently, some theories using beam or column equations have been proposed, which involved complicated mathematical efforts. This work analyzed deep hole drilling by a finite element model (FEM). Results of modal analysis on the established FEM were compared with results from Euler beam equations. Further analysis showed that the FEM could also predict straightness deviation as did the column equation. In addition, FEM could analyze the effects of variable support distance which neither beam nor column equation could. Other analysis results are also presented. The results in this study showed the strength and weakness of the FEM.     

Implementation of Hertz theory and validation of a finite element model for stress analysis of gear drives with localized bearing contact

An analytical approach for stress analysis of gear drives with localized bearing contact based on the Hertz theory is proposed. The proposed approach provides a complete and effective solution of the contact problem but satisfaction of the hypotheses for application of the Hertz theory is its main drawback. On the other hand, a finite element model has been developed and validated in terms of the contact area, maximum contact pressure, pressure distribution, maximum Tresca stress, and Tresca stress distribution underneath the contacting surfaces. Validation of the finite element model is provided for those cases wherein the Hertz theory can be applied. The obtained results confirm the applicability of the proposed approach for gear drives with localized bearing contact wherein edge contact is avoided by surface modifications and whole crowning of tooth surfaces is provided.     

Axisymmetric response of circular plates with piezoelectric layers: an exact solution

Electromechanical responses of symmetric circular laminates consisting of piezoelectric layers are studied, and the influence of surface and interlayer electrodes are involved. The laminates are traction-free on the top and bottom surfaces, but may be subjected to external forces at the lateral edge and to voltages applied across certain layers. Under axisymmetric deformation conditions, an approximate model which employs Kirchhoff hypothesis and incorporates the charge equation of electrostatic is established. Then, a closed-form three-dimensional solution of the laminates is generated in a very straightforward manner by the solution of the approximate model. The three-dimensional solution fulfills all field equations and interface or surface conditions as well as the specified electric edge boundary conditions; the only restriction is that the mechanical edge boundary conditions are satisfied in an average manner, rather than point by point. Thus, according to Saint-Venant's principle the proposed solution is exact in the interior region of the laminates.