层合结构压电器件的机电耦合响应

压电传感嚣和致动器都可以看成是由压电材料层和非压电(弹性)材料层交替铺设而成。对于这类任意铺设的层合板悬臂梁结构,推导出了表示力学变形与外加电场之间耦合效应的解析表达式。进而,又推导出了两类(一类为单层压电-弹性层。另一类为双层压电-弹性层)层合型悬臂梁结构机电耦合性能的解析公式。在该机电耦合模型中,包括了两个压电常数d211和d222。最后。通过比较解析解、实验值以及有限元计算结果,发现它们吻合得很好。     

层合结构压电器件的机电耦合效应

压电传感器和致动器都可以看成是一种复合材料层合板结构，由压电材料层和非压电(弹性)材料层交替铺设而成。对于这类任意铺设的层合板悬臂梁结构，我们推导出了表示力学变形与外加电场之间耦合效应的解析表达式。进而，又推导出了两类(一类为单层压电-弹性层，另一类为双层压电-弹性层)层合型悬臂梁结构机电耦合性能的解析公式。在该机电耦合模型中，包括了两个压电常数d211和d222。此外，还建立了含压电材料的有限元算式，进行了实验测量。最后，通过比较解析解(包括考虑了d222参数的理论值和没有考虑d222参数的理论值)，实验值以及有限元计算结果，发现它们吻合得很好，而且考虑d222是十分必要的。     

Component-wise analysis of laminated anisotropic composites

This paper proposes a one-dimensional (1D) refined formulation for the analysis of laminated composites which can model single fibers and related matrices, layers and multilayers. Models built by means of an arbitrary combination of these four components lead to a component-wise analysis. Different scales can be used in different portions of the structure and this leads to a global–local approach. In this work, computational models were developed in the framework of finite element approximations. The 1D FE formulation used has hierarchical features, that is, 3D stress/strain fields can be detected by increasing the order of the 1D model used. The Carrera Unified Formulation (CUF) was exploited to obtain advanced displacement-based theories where the order of the unknown variables over the cross-section is a free parameter of the formulation. Taylor- and Lagrange-type polynomials were used to interpolate the displacement field over the element cross-section. Lagrange polynomials permitted the use of only pure displacements as unknown variables. The related finite element led straightforwardly to the assembly of the stiffness matrices at the structural element interfaces (matrix-to-fiber, matrix-to-layer, layer-to-layer etc). Preliminary assessments with solid model results are proposed in this paper; various numerical examples were carried out on cross-ply symmetrical fiber-reinforced laminates [0/90/0] and a more complex composite C-shaped model. The examples show that the proposed models can analyze laminated structures by combining fibers, matrices, layers and multilayers and by referring to a unique structural finite element formulation.     

压电层合梁静动力学分析的高精度梁单元

给出了一个对复合材料压电层合梁进行数值分析的高精度压电层合梁单元。基于Shi三阶剪切变形板理论的位移场和Layer-wise理论的电势场,用力-电耦合的变分原理及Hamilton原理推导了压电层合梁单元列式。采用拟协调元方法推导了一个可显式给出单元刚度矩阵的两节点压电层合梁单元,并应用于压电层合梁的力-电耦合弯曲和自由振动分析。计算结果表明,该梁单元给出的梁挠度和固有频率与解析解吻合良好,并优于其它梁单元的计算结果,说明了本文所给压电层合梁单元的可靠性和准确性。研究结果可为力-电耦合作用下压电层合梁的力学分析提供一个简单、精确且高效的压电层合梁单元。     

A new two-dimensional model for electro-mechanical response of thick laminated piezoelectric actuator

This paper investigates the electro-mechanical behaviour of a thick, laminated actuator with piezoelectric and isotropic lamina under externally applied electric loading using a new two-dimensional computational model. The elastic core is relatively thick and thus it is modelled by Timoshenko thick-beam theory. Although the piezoelectric lamina is a beam-like layer, it is formulated via a two-dimensional model because of not only the strong electro-mechanical coupling, but also of the presence of a two-dimensional electric field. It is shown in this paper that a one-dimensional model for the piezoelectric beam-like layer is inadequate. The piezoelectric model is constructed within the scope of linear piezoelectricity. The actuation response is induced through the application of external electric voltage. Under the strong coupling of elasticity and electricity, the strain energy and work of electric potential are presented. The electro-mechanical response of the laminated Timoshenko beam is formulated and determined via a variational energy principle. Numerical examples presented illustrate convincing comparison with finite element solutions and existing published data. New numerical solutions are also presented to investigate the geometric effect on the electro-mechanical bending behaviour.     

A coupled finite element model for the consolidation of nonisothermal elastoplastic porous media

A coupled finite element model for the analysis of the deformation of elastoplastic porous media due to fluid and heat flow is presented. A displacement-pressure temperature formulation is used for this purpose. This formulation results in an unsymmetric coefficient matrix, even in the case of associated plasticity. A partitioned solution procedure is applied to restore the symmetry of the coefficient matrix. The partitioning procedure is an algebraic one which is carried out after integration in the time domain. For this integration, a two-point recurrence scheme is used. The finite element model is applied to the investigation of nonisothermal consolidation in various situations.     

Dynamic analysis of composite plate with multiple delaminations based on higher-order zigzag theory

In a recent paper, Cho and Kim [Journal of Applied Mechanics] proposed a higher-order cubic zigzag theory of laminated composites with multiple delaminations. The proposed theory is not only accurate but also efficient because it work with a minimal number of degrees of freedom with the application of interface continuity conditions as well as bounding surface conditions of transverse shear stresses including delaminated interfaces. In this work, we investigate the dynamic behavior of laminated composite plates with multiple delaminations. A four-node finite element based on the efficient higher-order zigzag plate theory of laminated composite plates with multiple delaminations is developed to refine the prediction of frequencies, mode shape, and time response. Through the dynamic version of the variational approach, the dynamic equilibrium equations and variationally consistent boundary conditions are obtained. Natural frequency prediction and time response analysis of a composite plate with multiple delaminations demonstrate the accuracy and efficiency of the present finite element method. To prevent penetration violation at the delamination interfaces, unilateral contact constraints by Lagrange multiplier method are applied in the time response analysis. The present finite element is suitable for the prediction of dynamic response of thick composite plates with multiple and arbitrary shaped delaminations.     

A time-domain high-order spectral finite element for the simulation of symmetric and anti-symmetric guided waves in laminated composite strips

A time domain spectral finite element is developed for improving the efficiency of numerical simulations of guided waves in laminated composite strips. The finite element relies on a new generalized laminate mechanics model formulated to represent symmetric and anti-symmetric Lamb waves. The laminate mechanics incorporate third-order polynomial terms for the approximation of axial and transverse displacement fields through the thickness and consider the displacements of the upper and lower surfaces as degrees of freedom. The laminate theory formulation is easily expanded to a high-order layerwise model. Based on the resultant governing equations of the laminate section, a new finite element with 8 nodal degrees of freedom is formulated; its nodes are collocated with Gauss–Lobatto–Legendre integration points in order to improve computational efficiency. Stiffness and mass matrices are assembled and the transient response is predicted using the explicit central differences time integration scheme. The transient response of Aluminum, Carbon Fiber Reinforced Polymer laminated and sandwich strips is investigated. Numerical results are validated against a semi-analytical solution. The accuracy and computational efficiency of the introduced element regarding the prediction of symmetric and anti-symmetric wave propagation is also quantified.     

Micromechanics-based constitutive modeling for unidirectional laminated composites

A micromechanics-based constitutive model is developed to predict the effective mechanical behavior of unidirectional laminated composites. A newly developed Eshelby’s tensor for an infinite circular cylindrical inclusion [Cheng, Z.Q., Batra, R.C., 1999. Exact Eshelby tensor for a dynamic circular cylindrical inclusion. J. Appl. Mech. 66, 563–565] is adopted to model the unidirectional fibers and is incorporated into the micromechanical framework. The progressive loss of strength resulting from the partial fiber debonding and the nucleation of microcracks is incorporated into the constitutive model. To validate the proposed model, the predicted effective stiffness of transversely isotropic composites under far field loading conditions is compared with analytical solutions. The constitutive model incorporating the damage models is then implemented into a finite element code to numerically characterize the elastic behavior of laminated composites. Finally, the present predictions on the stress–strain behavior of laminated composite plate containing an open hole is compared with experimental data to verify the predictive capability of the model.     

Analytical solution to a mixed boundary value elastic problem of a roller-guided panel of laminated composite

This study presents an analytical solution to elastic field in a roller-guided panel of symmetric cross-ply laminated composite material. The mixed boundary value two-dimensional plane stress elasticity problem is formulated in terms of a single displacement potential function. This reduces the problem to the solution of a single fourth order partial differential equation of equilibrium as the other equilibrium equation is satisfied automatically. The solution is obtained in terms of an infinite Fourier series. To present some numerical results, a panel of glass/epoxy laminated composite is considered and different components of stress and displacement at different sections of the panel are presented graphically. To justify the present analytical solution, it is compared with the finite element solution obtained by using the commercial software ANSYS. It is found that the two solutions agree well with each other. This ensures that the formulation developed in this study based on the displacement potential approach can be used to obtain analytical solution of an elastic field in structural elements of laminated composite under any mode of boundary conditions prescribed in terms of either stress, displacement or any combination of these.     

CONSOLIDATION THEORY OF UNSATURATED SOIL BASED ON THE THEORY OF MIXTURE(Ⅱ)

The present paper uses the mathematics model for consolidation of unsaturatedsoil developed in ref.[1]to solve boundary value problems.The analytical solutionsfor one-dimensional consolidation problem are gained by making use of Laplacetransform and finite Fourier transform.The displacement and the pore water pressureas well as the pore gas pressure are found from governing equations simultaneously.The theoretical formulae of coefficient and degree of consolidation are also given inthe paper.With the help of the method of Galerkin Weighted Residuals,the finiteelement equations for two-dimensional consolidation problem are derived.A FORTRANprogram named CSU8 using8-node isoparameter element is designed.A plane strainconsolidation problem is solved using the program,and some distinguishing features onconsolidation of unsaturated soil and certain peculiarities on numerical analysis arerevealed.These achievements make it convenient to apply the theory proposed by theauthor in engineering practice.     

An exact solution for a multilayered two-dimensional decagonal quasicrystal plate

By extending the pseudo-Stroh formalism to two-dimensional decagonal quasicrystals, an exact closed-form solution for a simply supported and multilayered two-dimensional decagonal quasicrystal plate is derived in this paper. Based on the different relations between the periodic direction and the coordinate system of the plate, three internal structure cases for the two-dimensional quasicrystal layer are considered. The propagator matrix method is also introduced in order to treat efficiently and accurately the multilayered cases. The obtained exact closed-form solution has a concise and elegant expression. Two homogeneous quasicrystal plates and a sandwich plate made of a two-dimensional quasicrystal and a crystal with two stacking sequences are investigated using the derived solution. Numerical results show that the differences of the periodic direction have strong influences on the stress and displacement components in the phonon and phason fields; different coupling constants between the phonon and phason fields will also cause differences in physical quantities; the stacking sequences of the multilayer plates can substantially influence all physical quantities. The exact closed-form solution should be of interest to the design of the two-dimensional quasicrystal homogeneous and laminated plates. The numerical results can also be employed to verify the accuracy of the solution by numerical methods, such as the finite element and difference methods, when analyzing laminated composites made of quasicrystals.     

Analysis of Laminated Rubber Bearings with a Numerical Reduction Model Method

In this paper, we present a reduction method for modeling slender laminated elastomeric structures, which is developed in the context of nearly incompressible hyperelasticity. This method, based on a finite element formulation, consists in projecting the unknown fields onto a polynomial basis in order to reduce the dimension of the problem and the model size. Two types of finite elements are used, one for plane-strain and the other for 3D structures. Comparisons with classical finite element models on single layers show the reliability of the present method. The method proposed successfully predicts the global and local behavior and since it reduces both the model size and the computing time. It can be used to model slender bearing consisting of several layers.     

Investigation of effective material properties in composites with internal defect or reinforcement particles

This paper is concerned with the investigation of the effective material properties of internally defective or particle-reinforced composites. An analysis was carried out with a novel method using the two-dimensional special finite element method mixing the concept of equivalent homogeneous materials. A formulation has been developed for a series of special finite elements containing an internal defect or reinforcement in order to assure the high accuracy especially in the vicinity of defects or reinforcements. The adoption of the special finite element can greatly simplify numerical modeling of particle-composites. The numerical result provides the effective material properties of particle-reinforced composite and explains that the size of particles has great influence on the material properties. Numerical examples also demonstrate the validity and versatility of the proposed method by comparing with existing results from literatures.     

Finite deformation plate theory and large rigid-body motions

A refined non-linear first-order theory of multilayered anisotropic plates undergoing finite deformations is elaborated. The effects of the transverse shear and transverse normal strains, and laminated anisotropic material response are included. On the basis of this theory, a simple and efficient finite element model in conjunction with the total Lagrangian formulation and Newton-Raphson method is developed. The precise representation of large rigid-body motions in the displacement patterns of the proposed plate elements is also considered. This consideration requires the development of the strain-displacement equations of the finite deformation plate theory with regard to their consistency with the arbitrarily large rigid-body motions. The fundamental unknowns consist of six displacements and 11 strains of the face planes of the plate, and 11 stress resultants. The element characteristic arrays are obtained by using the Hu-Washizu mixed variational principle. To demonstrate the accuracy and efficiency of this formulation and compare its performance with other non-linear finite element models reported in the literature, extensive numerical studies are presented.     

Novel shear deformation model for moderately thick and deep laminated composite conoidal shell

This article presents a novel mathematical model for moderately thick and deep laminated composite conoidal shell. The zero transverse shear stress at top and bottom of conoidal shell conditions is applied. Novelty in the present formulation is the inclusion of curvature effect in displacement field and cross curvature effect in strain field. This present model is suitable for deep and moderately thick conoidal shell. The peculiarity in the conoidal shell is that due to its complex geometry, its peak value of transverse deflection is not at its center like other shells. The C¹ continuity requirement associated with the present model has been suitably circumvented. A nine-node curved quadratic isoparametric element with seven nodal unknowns per node is used in finite element formulation of the proposed mathematical model. The present model results are compared with experimental, elasticity, and numerical results available in the literature. This is the first effort to solve the problem of moderately thick and deep laminated composite conoidal shell using parabolic transverse shear strain deformation across the thickness of conoidal shell. Many new numerical problems are solved for the static study of moderately thick and deep laminated composite conoidal shell considering 10 different practical boundary conditions, four types of loadings, six different hl/hh (minimum rise/maximum rise) ratios, and four different laminations.     

Numerical modelling of liquid infusion into fibrous media undergoing compaction

In the present paper, an overall model for the study of a non isothermal fluid flow across a highly compressible porous medium is proposed, in order to be included into a finite element software. This model can be applied to a wide range of activities, and as an application it is used here to model dry route composite manufacturing processes. Indeed, it is to be noted that the spreading of these promising processes fails due to the absence of a numerical model able to capture the resin infusion across the compressed preform thickness. The main difficulty being that this infusion results from a pressure prescribed over the deformable preform/resin stacking involved. From the modelling point of view, problems of this multi-physical analysis are two fold. First the coupling of liquid regions, ruled by Stokes equations, with the fibrous preform regions governed by a Darcy's law, yield badly posed boundary conditions. Second, the interaction phenomena due to the resin flow in the highly compressible preform are not classical. The model developed here includes a modified Beaver–Shaffman–Joseph condition to couple Stokes and Darcy zones, and is based on an ALE formulation of the liquid flow across the deformable porous medium in which finite strains are accounted for with an updated Lagrangian scheme. These mechanical models are also coupled with thermo-chemical models, accounting for resin reticulation under the temperature cycle prescribed by the processing equipment.     

Finite element modelling of quasi-three-dimensional nearly horizontal flow

A quasi-three-dimensional numerical model is presented and applied to some test problems with constant density. The numerical technique is based on a finite element formulation and the three-dimensional problem is factorized into one- and two-dimensional subproblems. The non-linear advection is treated by use of a weak formulation of the characteristics method and the equations are transformed to ‘sigma’ coordinates.     

Four-point combined DE/FE algorithm for brittle fracture analysis of laminated glass

A four-point combined DE/FE algorithm is proposed to constrain the rotation of a discrete element about its linked point and analyze the cracks propagation of laminated glass. In this approach, four linked points on a discrete element are combined with four nodes of the corresponding surface of a finite element. The penalty method is implemented to calculate the interface force between the two subdomains, the finite element (FE) and the discrete element (DE) subdomains. The sequential procedure of brittle fracture is described by an extrinsic cohesive fracture model only in the DE subdomain. An averaged stress tensor for granular media, which is automatically symmetrical and invariant by translations, is used to an accurate calculation of the averaged stress of the DE. Two simple cases in the elastic range are given to certify the effectiveness of the combined algorithm and the averaged stress tensor by comparing with the finite element method and the mesh-size dependency of the combined algorithm and the cohesive model is also investigated. Finally, the impact fracture behavior of a laminated glass beam is simulated, and the cracks propagation is compared with experimental results showing that the theory in this work can be used to predict some fracture characteristics of laminated glass.     

Analysis,modelling, and optimization of laminated glasses as plane beam

A simply supported glass/polyvinyl butyral (PVB)/glass beam is modelled by plane finite elements. The distribution of strain and stress through the beam thickness and along its axis is obtained as a result of linear finite element analysis. It shows that the bending stress in the glass layers is determinant for the load-bearing capability of laminated glasses, but the shear in the PVB-interlayer plays an important role for glass-layer interaction. A mathematical model of triplex glass beam is derived, consisting of a bending curvature differential equation and a differential equation of PVB-interlayer shear interaction. The derived equations are solved analytically with boundary conditions of simply supported beam under uniform transverse load. A parametric study of the derived mathematical model is carried out. The model is utilized for lightweight structure optimization of layer thicknesses. The results of the optimization show that laminated glasses could be superior to monolithic glasses.