Effects of fluid layer at micropolar orthotropic boundary surface

Effects of a fluid layer at a micropolar orthotropic elastic solid interface to a moving point load have been studied. After using the Fourier transform an eigen value approach has been employed to solve the problem. The displacement, microrotation and stress components for a micropolar orthotropic elastic solid so obtained in the physical domain are computed numerically by applying the numerical inversion technique. Micropolarity and anisotropy effects along with that of the depth of the fluid layer on various expressions have been depicted graphically for a particular model. Some special cases of interest have been presented     

Response of orthotropic micropolar elastic medium due to time harmonic source

The present paper is concerned with the plane strain problem in homogeneous micropolar orthotropic elastic solids. The disturbance due to time harmonic concentrated source is investigated by employing eigen-value approach. The integral transforms have been inverted by using a numerical technique to obtain the component of displacement, force stress and couple stress in the physical domain. The results of these quantities are given and illustrated graphically.     

Axi-symmetric problem in micropolar elastic half-space with stretch

The present investigation is concerned with axisymmetric problem in micropolar elastic half-space with stretch. The displacement, force stress, couple stress and vector first moment are obtained for a half-space subjected to an arbitrary normal load and a particular case of impulsive force is studied in detail. The graphs for various quantities have been drawn to illustrate the effect of stretch in each particular case.     

正交各向异性材料结构热变形和热应力分析的无网格法计算模型及应用正交各向异性材料结构热变形和热应力分析的无网格法计算模型及应用

利用无网格伽辽金法（Element-free Galerkin,EFG）建立了正交各向异性材料结构热变形和热应力分析的计算模型,并推导了正交各向异性材料结构热弹性问题的EFG法离散控制方程。选择复合材料冷却栅管算例验证了计算模型和程序的正确性,利用该计算模型分析了具有不同材料方向角及热导率因子、热膨胀系数因子和主次泊松比因子的汽轮机叶轮,得到了其热变形总位移和Mises应力,讨论了材料方向角和上述正交各向异性材料因子对其热变形总位移和Mises应力的影响规律,给出了这些参数的合理取值范围,并选取一组参数与各向同性材料结构进行了热变形和热应力对比分析。结果表明,基于EFG法的热变形总位移和Mises应力的计算精度比有限元法高,材料方向角同时影响热变形总位移和Mises应力的大小和方向,而正交各向异性材料因子只影响热变形总位移和Mises应力的大小,不影响其方向。在复合材料结构设计过程中,合理选取材料方向角和正交各向异性材料因子可有效减小结构热变形和热应力。      

Asymptotic fields near an interface corner in orthotropic bi-materials

Based on the existing asymptotic solutions of the displacement and singular stress fields in the vicinity of a singular point in 2D orthotropic elastic materials, the two simple eigenequations are explicitly given for the symmetric and anti-symmetric deformation modes to determine the orders of the stress singularity at the interface corner in orthotropic bi-materials, respectively. The related displacement and singular stress fields near the interface corner are also explicitly established. The relevant stress intensity factors are defined as in the case of crack problems. The theoretical results have been confirmed by numerical, finite-element-based results in a special bi-material case. The solution obtained in this paper may be applied to the interface corner in the orthotropic/orthotropic, orthotropic/isotropic, and isotropic/isotropic bi-materials, and it will be very useful to evaluate the strength of the bonded orthotropic bi-materials with interface corners.     

Contact stresses for a footing on an orthotropic elastic medium

This paper deals with the contact stress analysis for a strip footing interacting with (i) a homogeneous orthotropic halfplane and (ii) multilayered orthotropic halfplane. The contact stresses have been obtained using a combined approach(finite element method-analytical)in which the stiffness matrix for the footing has been obtained using the finite element method(F.E.M) while for the different cases of orthotropic medium(halfplane) considered here, suitable analytical solutions have been used. The halfplane needs to be discretised only along the contact length. Hence the solution can be obtained with a minimum input data and also the solution scheme is computationally efficient. Results have been presented for the contact stress distribution, displacement profile and bending stress distribution in the footing.     

Finite element method for orthotropic micropolar elasticity

The total potential energy for a body composed of an anisotropic micropolar linear elastic material is developed and used to formulate a displacement type finite element method of analysis. As an example of this formulation triangular plane stress (and plane couple stress) elements are used to analyze several problems. The program is verified by computing the stress concentration around a hole in an isotropic micropolar material for which an exact analytical solution exists. Several anisotropic material cases are presented which demonstrate the dependence of the stress concentration factor on the micropolar material parameters.     

Rotational Effect on the Propagation of Waves in a Magneto-Micropolar Thermoelastic Medium

The present paper aims to explore how the magnetic field, ramp parameter, and rotation affect a generalized micropolar thermoelastic medium that is standardized isotropic within the half-space. By employing normal mode analysis and Lame’s potential theory, the authors could express analytically the components of displacement, stress, couple stress, and temperature field in the physical domain. They calculated such manners of expression numerically and plotted the matching graphs to highlight and make comparisons with theoretical findings. The highlights of the paper cover the impacts of various parameters on the rotating micropolar thermoelastic half-space. Nevertheless, the non-dimensional temperature is not affected by the rotation and the magnetic field. Specific attention is paid to studying the impact of the magnetic field, rotation, and ramp parameter of the distribution of temperature, displacement, stress, and couple stress. The study highlighted the significant impact of the rotation, magnetic field, and ramp parameter on the micropolar thermoelastic medium. In conclusion, graphical presentations were provided to evaluate the impacts of different parameters on the propagation of plane waves in thermoelastic media of different nature. The study may help the designers and engineers develop a structural control system in several applied fields.     

Transverse Stress Decay in a Specially Orthotropic Strip under Localized Normal Edge Loading

Solutions are presented for the stresses in a specially orthotropic infinite strip which is subjected to localized uniform normal loading on one edge while the other edge is either restrained against normal displacement only, or completely fixed. The solutions are used to investigate the diffusion of load into the strip and in particular the decay of normal stress across the width of the strip. For orthotropic strips representative of a broad range of balanced and symmetric angle-ply composite laminates, minimum strip widths are found that ensure at least 90% decay of the normal stress across the strip. In addition, in a few cases where, on the fixed edge the peak shear stress exceeds the normal stress in magnitude, minimum strip widths that ensure 90% decay of both stresses are found. To help in putting these results into perspective, and to illustrate the influence of material properties on load diffusion in orthotropic materials, closed-form solutions for the stresses in similarly loaded orthotropic half-planes are obtained. These solutions are used to generate illustrative stress contour plots for several representative laminates. Among the laminates, those composed of intermediate-angle plies, i.e., from about 30 degrees to 60 degrees, exhibit marked changes in normal stress contour shape with stress level. The stress contours are also used to find 90% decay distances in the half-planes. In all cases, the minimum strip widths for 90% decay of the normal stress exceed the 90% decay distances in the corresponding half-planes, in amounts ranging from only a few percent to about 50% of the half-plane decay distances. The 90% decay distances depend on both material properties and the boundary conditions on the supported edge.     

Analytical solution for the singular stress distribution due to V-notch in an orthotropic plate material

On the basis of general solutions of two-dimensional linear elasticity, displacement and singular stress fields near the singular point in orthotropic materials are derived in closed form expressions. According to the presented expressions, analysis formulas of displacement and singular stress fields near the tip of a V-notch under the symmetric and the anti-symmetric modes are obtained subsequently. The open literatures devoted to developing stress singularity near the tip of the V-notch in anisotropic or orthotropic materials. In this study, however, not only direct eigenequations were derived, but also the explicit solutions of displacement and singular stress fields were obtained. At the end, the correctness of the formulas of the singular stress field near the tip of the V-notch has been verified by FEM analysis.     

Plane Elastic Problem of a Crack Normal to and Terminating at Bimaterial Interface of Isotropic and Orthotropic Half Plates

In this paper, the displacement and stress fields for a crack normal to and terminating at a bimaterial interface of isotropic and orthotropic half planes are studied as a plane problem. The eigenequation, by which the order of stress singularity is determined, is given in an explicit form. A discriminant function is presented to judge whether the stress singularity at the crack tip is greater than -1/2 or not. An explicit closed form expression is derived for the displacement and stress distribution near the crack tip.     

Analytical solutions for vibrations of laminated and sandwich plates using mixed theory

A semi-analytical method has been presented in this paper to evaluate the natural frequencies as well as displacement and stress eigenvectors for simply supported, cross-ply laminated and sandwich plates by using higher order mixed theory. Models based on equivalent single layer as well as layerwise (LW) theories have been formulated. By assuming a non-linear variation of axial displacements through the plate thickness, the warping of the transverse cross-section has been considered. Hamilton’s principle has been employed to derive the equilibrium equations. The proposed LW model fulfills a priori the continuity of displacements as well as the transverse and the normal stress components at each interface between two adjacent layers. Results obtained by present higher order mixed theory have been found in good agreement with those obtained by three-dimensional elasticity solutions. After establishing the accuracy of present results for orthotropic plates, new results for thin and thick sandwich plates have been presented which can serve as benchmark solutions for future investigations.     

Impact response of a cracked orthotropic medium-revisited

Elastodynamics response of an infinite orthotropic medium containing a central crack under impact loading has been investigated. Laplace and Fourier transforms have been employed to reduce the transient problem to the solution of a pair of dual integral equations in the Laplace transform domain which has finally been solved by the method of iteration in the low frequency case. Analytic expressions for the stress intensity factors and crack opening displacement are also obtained for low frequency.     

An elasticity analysis for the generally and specially orthotropic beams subjected to concentrated loads

A classical elasticity solution for the stress and displacement fields in loaded orthotropic beams is presented. The corresponding stress equations, derived from a stress function which satisfies the orthotropic analogue of the biharmonic equation, are written as Fourier series. From these expressions, the stress distributions in a series of centrally loaded generally and specially orthotropic beams are calculated. A detailed discussion of these stress distributions at selected beam sections and their symmetry about the loading axis is also presented. The stress fields are found to be unique relative to what is calculable from beam theory; for example, the stress distribution about the loading axis of a generally orthotropic beam is not symmetric. Finally, regions where beam theory coincides with the classical theory are identified.     

Identification of material parameters of micropolar theory for composites by homogenization method

The objective of the present work is to develop an analytical homogenization method to derive higher-order material parameters of micropolar theory. With help of Airy’s stress function, the constitutive equations for a homogenized micropolar medium are analytically established by considering a cylindrical representative volume element (RVE) subjected to quadratic and cubic boundary displacement conditions. Both porous and composite materials are considered, an analytical relation between the intrinsic length and the microstructural parameters is given.     

Thermomechanical Deformation in an Orthotropic Micropolar Thermoelastic Solid

The thermomechanical deformation in an orthotropic micropolar generalized thermoelastic half-space is investigated. Descarte’s method, along with the irreducible case of Cardon’s method, is used to obtain the roots of an eight-degree equation. Laplace and Fourier transform techniques are used to obtain the general solution for the set of boundary value problems. Particular types of boundary conditions have been taken to illustrate the utility of the approach. The transformed components of the stresses and temperature distribution have been obtained. A numerical inversion technique is employed to invert the integral transform, and the resulting quantities are presented graphically.     

Analytical solution for orthotropic composite plate containing a mode I crack along principle axis

Analytical stress analyses are presented for orthotropic composite materials containing a through crack under uniaxial normal loads (mode I). A harmonic differential equation has been established for the orthotropic plates with axes normal to the three orthogonal planes of material symmetry by introducing new complex variables. The complex theory was employed to find stress functions to satisfy the equilibrium equation, compatibility equation and boundary condition at infinite and crack surfaces. An analytical solution was examined in the case of isotropic materials. It is demonstrated that the analytical solution obtained is correct for the orthotropic composite plates.     

A note on energy flux in micropolar elastic waves

The expressions for the time average power per unit area, the kinetic energy per unit volume, strain energy per unit volume and velocity of energy flux are derived for the case of a plane time harmonic micropolar elastic waves and it has been shown that the time-average energy density is equally divided between the time-averages of the kinetic and strain energy densities. The energy ratios of reflected micropolar elastic waves with the angle of emergence of incident longitudinal displacement wave have been shown graphically.     

Behavior of Rayleigh surface waves in an anisotropic media lying over a prestressed orthotropic half-space

The present paper discusses the propagation of Rayleigh waves in an anisotropic layer with finite thickness lying over a prestressed orthotropic half-space. An anisotropic media and orthotropic media are supposed for the upper layer and lower half-space, respectively. Dispersion equation and displacement components are computed in a compact form considering the case that the displacement and stress are continuous at the interface and stress vanishes on a free surface. Graphs are sketched to represent the effect of density, initial stress and height of the layer on wave velocity. The graphs are also configured to exhibit the mode of propagation of Rayleigh waves. This paper is an attempt to explain the nature of Rayleigh waves mathematically.