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1.
Summary The paper presents an efficient two-dimensional approach to piezoelectric plates in the framework of linear theory of piezoelectricity.
The approximation of the through-the-thickness variations accounts for the shear effects and a refinement of the electric
potential. Using a variational formalism, electromechanically coupled plate equations are obtained for the generalized stress
resultants as well as for the generalized electric inductions. The latter are deduced from the conservative electric charge
equation, which plays a crucial role in the present model. Emphasis is placed on the boundary conditions at the plate faces.
The model is used to examine some problems for cylindrical bending of a single simply supported plate. Number of situations
are examined for a piezoelectric plate subject to (i) an applied electric potential, (ii) a surface density of force, and
(iii) a surface density of electric charge. The through-thickness distributions of electromechanical quantities (displacements,
stresses, electric potential and displacement) are obtained, and compared with results provided by finite element simulations
and by a simplified plate model without shear effects. A good agreement is observed between the results coming from the present
plate model and finite element computations, which ascertains the effectiveness of the proposed approach to piezoelectric
plates.
Received 17 July 2000; accepted for publication 26 September 2000 相似文献
2.
Recently Nappa obtains a Gurtin-type variational principle for micromorphic thermoelasticity. However, the use of convolutions is of course restricted to the linear case, which sets a limit to the rang of applicability. This paper establishes a classic variational principles for the discussed problem by the semi-inverse method. 相似文献
3.
E. Karapetian M. Kachanov I. Sevostianov 《Archive of Applied Mechanics (Ingenieur Archiv)》2002,72(8):564-587
Summary A correspondence principle is established between elastic and piezoelectric problems for transversely isotropic materials,
in such a way that the knowledge of an elastic solution yields fully coupled electro–elastic fields for the corresponding
piezoelectric problem, provided the elastic solution is written in a certain form. The implementation of this principle is
illustrated by constructing, in a routine way, several piezoelectric solutions involving crack and punch problems (one of
them has not been solved previously).
Received 12 Feburary 2002; accepted for publication 29 April 2002 相似文献
4.
Qing-Hua Qin 《Mechanics Research Communications》2004,31(3):321-330
A dual variational principle is presented for Trefftz finite element analysis. The proof of the stationary conditions of the variational functional and the theorem on the existence of extremum are provided in this paper. They are boundary displacement condition, surface traction condition and interelement continuity condition. Based on the assumed intraelement and frame fields, element stiffness matrix equation is obtained which can easily be implemented into computer programs for numerical analysis with Trefftz finite element method. Two numerical examples are considered to illustrate the effectiveness and applicability of the proposed element model. 相似文献
5.
Summary The dynamic response of a cracked piezoelectric half-space under anti-plane mechanical and in-plane electric impacting loads
is investigated in the present paper. In the study, the crack is assumed parallel to the free surface of the half-space. Laplace
and Fourier transforms are used to reduce the mixed boundary value problems to Cauchy-type singular integral equations in
the Laplace transform domain, which are solved numerically. Then, a numerical Laplace inversion is performed and the dynamic
stress and electric displacement factors are obtained as functions of time and geometry parameters. The dynamic energy release
rate is derived for piezoelectric materials in terms of the electroelastic intensities and is displayed graphically.
Received 5 January 2000; accepted for publication 28 June 2000 相似文献
6.
Dynamic response of a crack in a functionally graded interface of two dissimilar piezoelectric half-planes 总被引:3,自引:0,他引:3
Summary In this paper, the dynamic anti-plane crack problem of two dissimilar homogeneous piezoelectric materials bonded through
a functionally graded interfacial region is considered. Integral transforms are employed to reduce the problem to Cauchy singular
integral equations. Numerical results illustrate the effect of the loading combination parameter λ, material property distribution
and crack configuration on the dynamic stress and electric displacement intensity factors. It is found that the presence of
the dynamic electric field could impede of enhance the crack propagation depending on the time elapsed and the direction of
applied electric impact.
Received 4 December 2001; accepted for publication 9 July 2002
This work is supported by the National Natural Science Foundation of China through Grant No. 10132010. 相似文献
7.
Summary The smooth contact of a rubber half-space dented by a rigid cone apex is analyzed based on the large deformation theory.
The problem is treated as an axially symmetric case, and the material is assumed to be incompressible. The asymptotic equations
for the domain near the apex are derived. They are solved analytically for the shrinking domain, while a numerical solution
is found for the expanding domain in the vicinity of the stress singularity. The purpose of this paper is not only to solve
a typical problem but also to provide an analytical method to solve a large-strain problem with a singular point.
Received 10 July 2001; accepted for publication 24 January 2002 相似文献
8.
A. Yavari S. Sarkani J. N. Reddy 《Archive of Applied Mechanics (Ingenieur Archiv)》2001,71(9):625-639
Summary The bending solutions of the Euler–Bernoulli and the Timoshenko beams with material and geometric discontinuities are developed
in the space of generalized functions. Unlike the classical solutions of discontinuous beams, which are expressed in terms
of multiple expressions that are valid in different regions of the beam, the generalized solutions are expressed in terms
of a single expression on the entire domain. It is shown that the boundary-value problems describing the bending of beams
with jump discontinuities on discontinuous elastic foundations have more compact forms in the space of generalized functions
than they do in the space of classical functions. Also, fewer continuity conditions need to be satisfied if the problem is
formulated in the space of generalized functions. It is demonstrated that using the theory of distributions (i.e. generalized
functions) makes finding analytical solutions for this class of problems more efficient compared to the traditional methods,
and, in some cases, the theory of distributions can lead to interesting qualitative results. Examples are presented to show
the efficiency of using the theory of generalized functions.
Received 6 June 2000; accepted for publication 24 October 2000 相似文献
9.
An expression of the generalized principle of virtual work for the boundary value problem of the linear and anisotropic electromagnetic field is given. Using Chien's method, a pair of generalized variational principles (GVPs) are established, which directly leads to all four Maxwell's equations, two intensity-potential equations, two constitutive equations, and eight boundary conditions. A family of constrained variational principles is derived sequentially. As additional verifications, two degenerated forms are obtained, equivalent to two known variational principles. Two modified GVPs are given to provide the hybrid finite element models for the present problem. 相似文献
10.
Li-Hua Jin 《Acta Mechanica Solida Sinica》1988,1(3):291-300
In this paper, the idea of variational principles of linear elastic theory is used to establish generalized variational principles for linear elastic materials with voids. The fundamental equations of linear elastic materials with voids used have already been established in Ref. [5]. 相似文献
11.
Summary In this paper, the eigen-equations governing antiplane stress singularities in a bonded piezoelectric wedge are derived analytically.
Boundary conditions are set as various combinations of traction-free, clamped, electrically open and electrically closed ones.
Application of the Mellin transform to the stress/electric displacement function or displacement/electric potential function
and particular boundary and continuity conditions yields identical eigen-equations. All of the analytical results are tabulated.
It is found that the singularity orders of a bonded bimaterial piezoelectric wedge may be complex, as opposed to those of
the antiplane elastic bonded wedge, which are always real. For a single piezoelectric wedge, the eigen-equations are independent
of material constants, and the eigenvalues are all real, except in the case of the combination C–D. In this special case,
C–D, the real part of the complex eigenvalues is not dependent on material constants, while the imaginary part is.
Received 26 March 2002; accepted for publication 2 July 2002 相似文献
12.
Noël Lahellec 《Journal of the mechanics and physics of solids》2007,55(9):1932-1963
A new method for determining the overall behavior of composite materials comprised of nonlinear inelastic constituents is presented. Upon use of an implicit time-discretization scheme, the evolution equations describing the constitutive behavior of the phases can be reduced to the minimization of an incremental energy function. This minimization problem is rigorously equivalent to a nonlinear thermoelastic problem with a transformation strain which is a nonuniform field (not even uniform within the phases). In this first part of the study the variational technique of Ponte Castañeda is used to approximate the nonuniform eigenstrains by piecewise uniform eigenstrains and to linearize the nonlinear thermoelastic problem. The resulting problem is amenable to simpler calculations and analytical results for appropriate microstructures can be obtained. The accuracy of the proposed scheme is assessed by comparison of the method with exact results. 相似文献
13.
Summary This paper deals with interaction problems of elliptical and ellipsoidal inclusions under bending, using singular integral
equations of the body force method. The problems are formulated as a system of singular integral equations with Cauchy-type
or logarithmic-type singularities, where unknown functions are densities of body forces distributed in the x,y and r,θ,z directions in infinite bodies having the same elastic constants as those of the matrix and inclusions. In order to satisfy
the boundary conditions along the elliptical and the ellipsoidal boundaries, the unknown functions are approximated by a linear
combination of fundamental density functions and polynomials. The present method is found to yield the exact solutions for
a single elliptical or spherical inclusion under a bending stress field. It yields rapidly converging numerical results for
interface stresses in the interaction of inclusions.
Received 9 September 1999; accepted for publication 15 January 2000 相似文献
14.
X. F. Ding T. Furukawa H. Nakanishi 《Archive of Applied Mechanics (Ingenieur Archiv)》2002,72(2-3):107-118
Summary This paper investigates the stress-focusing effect in an infinitely long cylinder under rotationally asymmetrical instantaneous
thermal loading on the basis of the generalized thermoelastic Lord–Shulman (L-S) and Green–Lindsay (G-L) theories. Combined
forms of the governing equations of both theories are given in a cylindrical coordinate system. The two-dimensional generalized
thermoelastic problems are solved by numerical inversion of Laplace transform. Calculations have been performed to find distributions
of thermal stresses on the basis of the L-S theory. Stress-focusing phenomena under different heating conditions are presented.
The effects of thermomechanical coupling and relaxation time on the stress-focusing phenomena as well as the singularity of
stresses are discussed.
Received 15 November 2000; accepted for publication 15 November 2001 相似文献
15.
Variation of the stress intensity factor along the front of a 3-D rectangular crack subjected to mixed-mode load 总被引:3,自引:0,他引:3
Summary The singular integral equation method is applied to the calculation of the stress intensity factor at the front of a rectangular
crack subjected to mixed-mode load. The stress field induced by a body force doublet is used as a fundamental solution. The
problem is formulated as a system of integral equations with r
−3-singularities. In solving the integral equations, unknown functions of body-force densities are approximated by the product
of polynomial and fundamental densities. The fundamental densities are chosen to express two-dimensional cracks in an infinite
body for the limiting cases of the aspect ratio of the rectangle. The present method yields rapidly converging numerical results
and satisfies boundary conditions all over the crack boundary. A smooth distribution of the stress intensity factor along
the crack front is presented for various crack shapes and different Poisson's ratio.
Received 5 March 2002; accepted for publication 2 July 2002 相似文献
16.
Ya-Pu Zhao 《Archive of Applied Mechanics (Ingenieur Archiv)》2002,72(1):77-84
Summary The morphological stability of epitaxial thin elastic films on a substrate by van der Waals force is discussed. It is found
that only van der Waals force with negative Hamaker constant tends to stabilize the film, and the lower bound for the Hamaker constant is also obtained for the stability of thin film.
The critical value of the undulation wavelength is found to be a function of both film thickness and external stress. The
charateristic time-scale for surface mass diffusion scales to the fourth power to the wavelength of the perturbation.
Received 4 December 2000; accepted for publication 31 July 2001 相似文献
17.
From the Boltzmann‘ s constitutive law of viscoelastic materials and the linear theory of elastic materials with voids, a constitutive model of generalized force fields for viscoelastic solids with voids was given. By using the variational integral method, the convolution-type functional was given and the corresponding generalized variational principles and potential energy principle of viscoelastic solids with voids were presented. It can be shown that the variational principles correspond to the differential equations and theinitial and boundary conditions of viscoelastic body with voids. As an application, a generalized variational principle of viscoelastic Timoshenko beams with damage was obtained which corresponds to the differential equations of generalized motion and the initial and boundary conditions of beams. The variational principles provide a way for solving problems of viscoelastic solids with voids. 相似文献
18.
X. X. Hu T. Sakiyama K. Itakura 《Archive of Applied Mechanics (Ingenieur Archiv)》2002,72(4-5):330-341
Summary A numerical procedure is proposed for the analysis of free vibrations of pretwisted thin plates. An accurate strain–displacement
relationship based on the thin-shell theory combined with the finite element method using triangular plate elements with three
nodes and nine degrees of freedom for each node is utilized. The vibration characteristics of pretwisted thin plates with
different twist rates and aspect ratios are studied. The numerical results are compared with the previous results obtained
by various types of finite elements and by the Rayleigh–Ritz method. The effect of the twist rate on the vibration characteristics
is studied briefly.
Received 28 February 2001; accepted for publication 18 December 2001 相似文献
19.
On consistent plate theories 总被引:1,自引:0,他引:1
R. Kienzler 《Archive of Applied Mechanics (Ingenieur Archiv)》2002,72(4-5):229-247
Summary Applying the uniform-approximation technique, consistent plate theories of different orders are derived from the basic equations
of the three-dimensional linear theory of elasticity. The zeroth-order approximation allows only for rigid-body motions of
the plate. The first-order approximation is identical to the classical Poisson-Kirchhoff plate theory, whereas the second-order
approximation leads to a Reissner-type theory. The proposed analysis does not require any a priori assumptions regarding the
distribution of either displacements or stresses in thickness direction.
Received 10 January 2002; accepted for publication 16 April 2002 相似文献
20.
M. Kamiński 《Archive of Applied Mechanics (Ingenieur Archiv)》2001,71(10):679-694
Summary The main goal of the paper is to present theoretical aspects and the finite element method (FEM) implementation of the sensitivity
analysis in homogenization of composite materials with linear elastic components, using effective modules approach. The deterministic
sensitivity analysis of effective material properties is presented in a general form for an n-components periodic composite, and is illustrated by the examples of 1D as well as of 2D heterogeneous structures. The results
of the sensitivity analysis presented in the paper confirm the usefulness of the homogenization method in computational analysis
of composite materials the method may be applied to computational optimization of engineering composites, to the shape-sensitivity
studies and, after some probabilistic extensions, to stochastic sensitivity analysis of random composites.
Received 10 November 2000; accepted for publication 24 April 2001 相似文献