Stress concentration in a transversely isotropic spherical shell with two circular rigid inclusions

The refined Timoshenko-type theory that takes into account the transverse shear strains is used to find an analytic solution for the stress state of transversely isotropic shallow spherical shell with two circular rigid inclusions. The case of a shell with closely spaced rigid inclusions of unequal radii under internal pressure is analyzed numerically. The stresses in the shell increase considerably with decrease in the distance between the inclusions and increase in the transverse shear parameter     

Stress state of a transversely isotropic spherical shell with a rigid circular inclusion

Analytical expressions are derived for the stresses near a rigid circular inclusion in a transversely isotropic shallow spherical shell under uniform pressure. The form of solution depends on the range of the transverse shear compliance parameter. The influence of the relative radius of a rigid inclusion and transverse shear compliance on stress concentration is analyzed __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 12, pp. 67–73, December 2005.     

Acoustic wave interaction with a laminated transversely isotropic spherical shell with imperfect bonding

An exact analysis is carried out to study interaction of a time-harmonic plane-progressive sound field with a multi-layered elastic hollow sphere made of spherically isotropic materials with interlaminar bonding imperfections. A modal state equation with variable coefficients is set up in terms of appropriate displacement and stress functions and their spherical harmonics, ultimately leading to calculation of a global transfer matrix. A linear spring model is adopted to describe the interlaminar adhesive bonding whose effects are incorporated into the global transfer matrix by introduction of proper interfacial transfer matrices. The solution is first used to correlate the perturbation in the material elastic constants of an evacuated and water submerged steel (isotropic) spherical shell to the sensitivity of resonances appearing in the backscattered amplitude spectrum. The backscattering form function, in addition to the acoustic radiation force acting on selected transversely isotropic spherical shells with distinct degrees of material anisotropy, is subsequently calculated and discussed. An illustrative numerical example is given for a multi-layered hollow sphere with two distinct interlaminar interface conditions (i.e., perfectly and imperfectly bonded layers). Limiting cases are considered and fair agreements with solutions available in the literature are established.     

Complex representation of the equations of a transversely isotropic spherical shell with prestresses

The system of equilibrium equations for a transversely isotropic spherical shell with prestresses is represented in a complex form. A method for constructing the general solution of this system is outlined __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 2, pp. 122–132, February 2007. For the centenary of birth of G. N. Savin.     

Stress concentration around a circular hole in a transversely isotropic spherical shell

Analytical expressions for the stresses near a circular hole in a transversely isotropic shallow spherical shell under uniform pressure are derived. The form of the solution depends on the range of change in the compliance to transverse shear. The influence of the relative radius of the hole and the compliance to transverse shear on the stress concentration is analyzed.__________Translated from Prikladnaya Mekhanika, Vol. 40, No. 12, pp. 99–106, December 2004.     

Stress state around a circular hole in a prestressed transversely isotropic spherical shell

The stress state around a circular hole in a prestressed hollow spherical shell is found by expanding the unknown functions into Fourier-Legendre series __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 2, pp. 61–68, February 2008.     

半无限横观各向同性体中共面双裂纹边界元分析

基于双横观各向同性材料基本解的对偶边界元方法,分析了半无限横观各向同性材料中两条共面裂纹的相互作用问题。裂纹面上分别作用着法向和切向两种均布荷载,材料的各向同性面及裂纹面平行于半无限域自由面。数值计算得到了该类裂纹的应力强度因子(SIF)值和两条共面裂纹相互作用的SIF值影响系数。根据数值结果分析了自由面对该类裂纹SIF值的影响,以及裂纹间距与形状、自由面对SIF值影响系数的影响。结果表明,自由面对作用法向力时的该类裂纹SIF值有明显的影响,裂纹间距与形状对SIF值影响系数影响较大,但自由面对SIF值影响系数基本无影响。     

Extreme equilibrium of a shallow spherical shell under isotropic compression (tension)

International Applied Mechanics -     

A periodic array of cracks in a transversely isotropic magnetoelectroelastic material

Magnetoelectroelastic materials are inherently brittle and prone to fracture. Therefore, it is important to evaluate the fracture behavior of these advanced materials. In this paper, a periodic array of cracks in a transversely isotropic magnetoelectroelastic material is investigated. Hankel transform is applied to solve elastic displacements, electric potential and magnetic potential. The problem is reduced into a system of integral equations. Both impermeable and permeable crack-face electromagnetic boundary conditions assumptions are investigated. Quantities of the stress, electric displacement and magnetic induction and their intensity factor are obtained. Effect of the crack spacing on these quantities is investigated in details.     

Solving the equilibrium equations for a transversely isotropic piezoceramic plate

The system of equilibrium equations for nonthin transversely isotropic piezoceramic plates subject to antisymmetric (about the mid-plane) deformation is set up by expanding the unknown functions into Fourier-Legendre series in the thickness coordinate. To find the general solution of the system of equations, a method is proposed, which is then used to solve the stress problem for a plate with a circular hole under mechanical loading __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 10, pp. 96–106, October 2006.     

横观各向同性材料三维裂纹问题的数值分析

严格从三维横观各向同性材料弹性空间问题的Green函数出发,采用Hadamard有限部积分概念,导出了三维状态下单位位移间断(位错)集度的基本解.在此基础上,将三维任意形状的片状裂纹问题归结为求解-组以未知位移间断表示的超奇异积分方程;并给出了边界元离散形式.对方程中出现的超奇异积分,采用了Had-alnard定义的有限部积分来处理.论文最后给出了若干典型片状裂纹问题的数值算例,数值结果表明了本文方法是非常有效的.     

The effective properties of piezoelectric composite materials with transversely isotropic spherical inclusions

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Spatial elastic equilibrium of a variable thickness isotropic cylindrical shell

Institute of Mechanics, Ukrainian Academy of Sciences, Kiev. Ivano-Franko Oil and Gas Institute. Translated from Prikladnaya Mekhanika, Vol. 26, No. 12, pp. 7–15, December, 1990.     

Penny-shaped and half-plane cracks in a transversely isotropic piezoelectric solid under arbitrary loading

Summary The problem of a penny-shaped crack in a transversely isotropic piezoelectric material loaded by both normal and tangential tractions and by electric charges is analyzed. Closed-form solutions are obtained for the full electroelastic fields as well as for the stress and electric displacement intensity factors. Solutions are also obtained for the (non-trivial) limiting case of a half-plane crack. The results are illustrated on the example of piezoceramics PZT-6B. Received 12 July 1999; accepted for publication 20 July 1999     

Dynamic stress intensity factors of two 3D rectangular cracks in a transversely isotropic elastic material under a time-harmonic elastic P-wave

The dynamic stress intensity factors (DSIFs) of two 3D rectangular cracks in a transversely isotropic elastic material under an incident harmonic stress wave are investigated by generalized Almansi’s theorem and the Schmidt method in the present paper. Using 2D Fourier transform and defining the jumps of displacement components across the crack surface as the unknown functions, three pairs of dual integral equations are derived. To solve the dual integral equations, the jumps of the displacement components across the crack surfaces are expanded in a series of Jacobi polynomials. Numerical examples are provided to show the effects of the geometric shape of the rectangular crack, the characteristics of the harmonic wave and the distance between two rectangular cracks on the DSIFs of the transversely isotropic elastic material.