Interactions due to mechanical/thermal sources in a micropolar thermoelastic medium possessing cubic symmetry

The present problem is the deformation of micropolar thermoelastic solids with cubic symmetry under the influence of various sources acting on the plane surface. Analytic expressions for displacement components, microrotation, force stress, couple stress, and temperature distribution are obtained in the physical domain for Lord–Shulman (L–S) and Green–Lindsay (G–L) theories of thermoelasticity by applying integral transforms. A numerical inversion technique has been applied to obtain the solution in the physical domain. The numerical results are presented graphically for a particular model.     

Saint-Venant's problem for linear piezoelectric bodies

We seek a solution for a piezoelectric cylinder acted on the end faces by applied tractions and charges, under the hypothesis that both the stress and electric displacement fields depend linearly on the axial coordinate. The analysis, restricted to monoclinic materials of crystallographic class 2, leads to an explicit solution in terms of the strain and electric fields, which depend on the stress and charge resultants and on two scalar functions determined by the solution of a plane piezoelectric problem.     

Solution of a viscoelastic boundary-value problem on the action of a concentrated force in an infinite plane

We formulate a theorem containing the solution of a boundary-value problem of isotropic linear viscoelasticity on the action of a concentrated force in an infinite plane. The two creep functions that are used in the constitutive relations and correspond to the shear and bulk expansion states and assumed to be independent; the general forms of these functions are not specified. Formulas are presented for the stress, strain, and displacement components.     

ELECTRO-MAGNETO-THERMOELASTIC PLANE WAVES IN MICROPOLAR SOLID INVOLVING TWO TEMPERATURES

<正>The model of equations of micropolar generalized magneto-thermoelasticity is introduced within the context of the theory of two temperatures generalized thermoelasticity and we consider a problem of an isotropic homogeneous micropolar medium taking into account the heat effects and allowing the magnetic field effects.A plane wave analysis is employed to obtain the exact formulas of the two temperatures(conductive and mechanical),displacement components, micro-rotation components,stresses,couple stresses,induced electric current,electric field and magnetic field.Arbitrary application is chosen to enable us to get the complete solution.The considered variables are presented graphically and discussions are made for the results.     

Influence of couple-stresses on stress concentrations around the cavity

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Non-linear micropolar and classical continua for anisotropic discontinuous materials

Non-linear Cosserat and Cauchy anisotropic continua equivalent to masonry-like materials, like brick/block masonry, jointed rocks, granular materials or matrix/particle composites, are presented.An integral procedure of equivalence in terms of mechanical power has been adopted to identify the effective elastic moduli of the two continuous models starting from a Lagrangian system of interacting rigid elements. Non-linear constitutive functions for the interactions in the Lagrangian system are defined in order to take into account both the low capability to carry tension and the friction at the interfaces between elements. The non-linear problem is solved through a finite element procedure based on the iterative adjustment of the continuum constitutive tensor due to the occurrence of some limit situation involving the contact actions of the discrete model.Differences between the classical and the micropolar model are investigated with the aid of numerical analyses carried out on masonry walls made of blocks of different size. The capability of the micropolar continuum to discern, unlike the classical continuum, the behaviour of systems made of elements of different size is pointed out. It is also shown that for anisotropic materials, even in the elastic case, the micropolar solution in general does not tend to the classical solution when the size of the elements vanishes.     

均布荷载作用下悬臂磁电弹性梁的解析解

对磁电弹性平面问题进行了研究，给出了用拟调和位移函数表达的通解，进而以试凑法按平面应力问题推导出了均布荷载作用下悬臂磁电弹性粱的解析解，所得解有易于理解、便于校对、形式统一简洁的特点。本文还将计算结果与压电材料和弹性材料相应结果进行了分析、比较，为验证各种数值计算方法提供了参考依据。     

Solution of the plane stress problems of strain-hardening materials described by power-law using the complex pseudo-stress function

In the present paper,the compatibility equation for the plane stress problems of power-law materials is transformed into a biharmonic equation by introducing the so-calledcomplex pseudo-stress function,which makes it possible to solve the elastic-plastic planestress problems of strain hardening materials described by power-law using the complexvariable function method like that in the linear elasticity theory.By using this generalmethod,the close-formed analytical solutions for the stress,strain and displacementcomponents of the plane stress problems’of power-law materials is deduced in the paper,which can also be used to solve the elasto-plastic plane stress problems of strain-hardeningmaterials other than that described by power-law.As an example,the problem of a power-law material infinite plate containing a circular hole under uniaxial tension is solved byusing this method,the results of which are compared with those of a known asymptoticanalytical solution obtained by the perturbation method.     

不同压电介质界面上的反平面运动裂纹

利用积分变换技术,得到不同压电介质界面上的平面运动裂纹问题的分析解。结果表明应力及电位移强度因子均与界面裂纹扩展速度及材料参数相关,这不同于均匀压电介质中运动裂纹的结论,当两种压电介质完全相同时,本文结果将退化为均匀压电介质中反平面运动裂纹问题的解。     

Fundamental solution for bonded materials with a free surface parallel to the interface. Part II: Solutions of concentrated force acting at the interior of the substrate and the case when the force acting at the interface

In this work, the exact analyses are presented for the plane problem of a coating material subjected to a concentrated force acting at the interior of the substrate and the case when the force at the interface. The stress functions are constructed as an infinite series form by utilizing the method of image. According to the orders of the image points from lower to higher, the terms in the stress functions series have the recursive relationships. For the case when the force acting at the substrate, the first two terms are the original stress functions for a homogenous infinite plane subjected to a concentrated force, which are known and simple. For the case when the force acting at the interface, the fundamental solution is obtained for two bonded dissimilar semi-infinite plane. The stress functions in this solution can be used as the first two terms for the problem considered in this paper. Therefore, all other terms can be derived by the recurrence equations explicitly. Also, through comparisons between the theoretical results and the numerical results by FEM, it is verified that the convergence rate of the solutions is very rapid. In most practical cases only the first several image points can ensure the solutions with satisfactory accuracy.     

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.     

An asymmetrical dynamic model for bridging fiber pull-out of unidirectional composite materials

An elastic analysis of an internal crack with bridging fibers parallel to the free surface in an infinite orthotropic elastic plane is studied. An asymmetrical dynamic model for bridging fiber pull-out of unidirectional composite materials is presented for analyzing the distributions of stress and displacement with the internal asymmetrical crack under the loading conditions of an applied non-homogenous stress and the traction forces on crack faces yielded by the bridging fiber pull-out model. Thus the fiber failure is determined by maximum tensile stress, resulting in fiber rupture and hence the crack propagation would occur in a self-similarity manner. The formulation involves the development of a Riemann-Hilbert problem. Analytical solution of an asymmetrical propagation crack of unidirectional composite materials under the conditions of two moving loads given is obtained, respectively. After those analytical solutions were utilized by superposition theorem, the solutions of arbitrary complex problems could be obtained.     

Deformation in micropolar cubic crystal due to various sources

The response of a micropolar cubic crystal due to various sources has been studied. The eigenvalue approach using Laplace and Fourier transforms has been employed to solve the problem. The integral transforms have been inverted by using a numerical technique to obtain the displacement, microrotation and stress components in the physical domain. The results of normal displacement, normal force stress and tangential couple stress have been compared for micropolar cubic crystal and micropolar isotropic solid and illustrated graphically.     

Some problems in plane thermopiezoelectric materials with holes

Piezoelectric materials have recently attracted considerable attention due to their potential use in intelligent structural systems. In this paper, we treat the plane problem of thermopiezoelasticity with various holes and subject to coupled mechanical, electric and thermal loads. An analytical solution is obtained by applying the technique of conformal mapping and some identities in the Stroh formalism. The solution has a simple unified form for various holes such as ellipse, circle, triangle and square. By way of the solution, the expressions for the energy release rate and stress intensity factors of cracks are presented. Numerical results for concentration coefficients of stress and electric displacement along the hole boundary are given to assess the acceptability of the proposed method.     

Axisymmetric free vibrations of infinite thermoelastic plate

The propagation of axisymmetric free vibrations in an infinite homogeneous isotropic micropolar thermoelastic plate without energy dissipation subjected to stress free and rigidly fixed boundary conditions is investigated. The secular equations for homogeneous isotropic micropolar thermoelastic plate without energy dissipation in closed form for symmetric and skew symmetric wave modes of propagation are derived. The different regions of secular equations are obtained. At short wavelength limits, the secular equations for symmetric and skew symmetric modes of wave propagation in a stress free insulated and isothermal plate reduce to Rayleigh surface wave frequency equation. The results for thermoelastic, micropolar elastic and elastic materials are obtained as particular cases from the derived secular equations. The amplitudes of displacement components, microrotation and temperature distribution are also computed during the symmetric and skew symmetric motion of the plate. The dispersion curves for symmetric and skew symmetric modes and amplitudes of displacement components, microrotation and temperature distribution in case of fundamental symmetric and skew symmetric modes are presented graphically. The analytical and numerical results are found to be in close agreement.     

Axisymmetric free vibrations of infinite micropolar thermoelastic plate

The propagation of axisymmetric free vibrations in an infinite homogeneous isotropic micropolar thermoelastic plate without energy dissipation subjected to stress free and rigidly fixed boundary conditions is investigated. The secular equations for homogeneous isotropic micropolar thermoelastic plate without energy dissipation in closed form for symmetric and skew symmetric wave modes of propagation are derived. The different regions of secular equations are obtained. At short wavelength limits, the secular equations for symmetric and skew symmetric modes of wave propagation in a stress free insulated and isothermal plate reduce to Rayleigh surface wave frequency equation. The results for thermoelastic, micropolar elastic and elastic materials are obtained as particular cases from the derived secular equations. The amplitudes of displacement components, microrotation and temperature distribution are also computed during the symmetric and skew symmetric motion of the plate. The dispersion curves for symmetric and skew symmetric modes and amplitudes of displacement components, microrotation and temperature distribution in case of fundamental symmetric and skew symmetric modes are presented graphically. The analytical and numerical results are found to be in close agreement.     

Plane micropolar elasticity with surface flexural resistance

We propose a linear surface/interface model for plane deformations of a micropolar elastic solid based on a higher-order surface elasticity theory capable of incorporating bending and twisting effects. The surface/interface is modeled as a bending-resistant Kirchhoff micropolar thin shell perfectly bonded to the boundary of the solid. It is anticipated that by combining micropolar bulk and surface effects in this way, the enhanced model will most accurately capture the essential characteristics (in particular, size dependency) required in the modeling of materials with significant microstructure as well as in the modeling of classes of nanomaterials. The corresponding boundary value problems are particularly interesting in that they involve boundary conditions of order higher than that of the governing field equations. We illustrate our theory by analyzing the simple problem of a circular hole in a micropolar sheet noting, in particular, the extent to which surface effects and micropolar properties each contribute to the deformation of the sheet.     

Asymmetrical dynamic fracture model of bridging fiber pull-out of unidirectional composite materials

An elastic analysis of an internal crack with bridging fibers parallel to the free surface in an infinite orthotropic anisotropic elastic plane is studied, and asymmetrical dynamic fracture model of bridging fiber pull-out of unidirectional composite materials is presented for analyzing the distributions of stress and displacement with the internal asymmetrical crack under the loading conditions of an applied non-homogenous stress and the traction forces on crack faces yielded by the bridging fiber pull-out model. Thus the fiber failure is ascertained by maximum tensile stress, the fiber ruptures and hence the crack propagation should also appear in the modality of self-similarity. The formulation involves the development of a Riemann-Hilbert problem. Analytical solution of an asymmetrical propagation crack of unidirectional composite materials under the conditions of two increasing loads given is obtained, respectively. In terms of correlative material properties, the variable rule of dynamic stress intensity factor was depicted very well. After those analytical solutions were utilized by superposition theorem, the solutions of arbitrary complex problems could be gained.     

刚度微分法计算压电材料平面断裂问题

把计算应变能释放率的刚度微分法推广到压电材料平面断裂问题．在此基础上，利用压电材料平面断裂问题的有限元数值解作为真实场，用Ｓｏｓａ的平面问题裂端渐近解作为辅助场，由推广的交互Ｍ积分法求得了应力强度因子ＫＩ，ＫＩＩ和电位移强度因子ＫＩＶ．算例表明，计算结果与理论解符合得很好     

RESPONSE OF MICROPOLAR THERMOELASTIC SOLID WITH VOIDS DUE TO VARIOUS SOURCES UNDER GREEN NAGHDI THEORY

Green-Naghdi (G-N) theory of thermoelasticity is employed to study the deformation of micropolar thermoelastic solid with voids considering the influence of varions sources acting on the plane surface....