Scattering of antiplane shear wave by a propagating crack at the interface of two dissimilar elastic media

An analysis of the scattering of horizontally polarized shear wave by a semi-infinite crack running with uniform velocity along the interface of two dissimilar semi-infinite elastic media has been carried out. The mixed boundary value problem has been solved completely by the Wiener-Hopf technique. The effect of different values of the material parameter, the angle of incidence of incident wave and the crack propagation velocity on the stress intensity factor have been illustrated graphically.     

Four coplanar Griffith cracks moving in an infinitely long elastic strip under antiplane shear stress

This paper concerns with the problem of determining the anti-plane dynamic stress distributions around four coplanar finite length Griffith cracks moving steadily with constant velocity in an infinitely long finite width strip. The two-dimensional Fourier transforms have been used to reduce the mixed boundary value problem to the solution of five integral equations. These integral equations have been solved using the finite Hilbert transform technique to obtain the analytic form of crack opening displacement and stress intensity factors. Numerical results have also been depicted graphically.     

Scattering of a SH-wave by an elastic fiber of nonclassical cross section with an interface crack

The problem of interaction of a plane time-harmonic SH-wave with an elastic fiber of quasi-square or quasi-triangular cross section, when an interface crack is present between an infinite elastic matrix and the fiber, is considered. The modified null-field method taking into account the asymptotic behavior of the solution at crack tips is exploited for obtaining numerical results. The effects of fiber shape, fiber/matrix material combination, debonding (crack size), and direction of wave incidence on the scattering amplitude in the far zone are analyzed. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 2, pp. 245–254, March–April, 2008.     

Application of the boundary element method for analysis of the antiplane shear of anisotropic bodies containing thin-walled structures

We have ascertained the limits of reasonable application of the classical boundary element method for the solution of the antiplane problem of the theory of elasticity in the study of bodies with thin-walled elements of structure and geometry. We have proposed an approach for the regularization of singular and quasisingular integrals, which appear inevitably in analyzing thin structures. We give also numerical examples demonstrating the reliability and efficiency of the proposed approach.     

基于贝叶斯分析的不完全维修条件下可修系统的参数估计

可靠性和维修性的参数估计在可修系统建模及维修决策中具有非常重要的地位.不完全维修条件下可修系统的故障时间既不相等也不服从独立分布,这使得可修系统维修模型的参数估计变得十分困难.针对此问题,对第一次故障服从威布尔分布,故障之后进行Kijima类型I的修复性维修和Kijima类型I的预防性维修的可修系统进行了研究,应用贝叶斯分析对威布尔分布的形状参数β、尺度参数η、修复性维修的不完全维修因子ar以及预防性维修的不完全维修因子ap进行估计.仿真算例表明,该方法可以较为准确的对可靠性和维修性参数进行估计.     

Boundary integral equations for an interface linear crack under harmonic loading

The present study is devoted to application of boundary integral equations to the problem of a linear crack located on the bimaterial interface under time-harmonic loading. Using the Somigliana dynamic identity the system of boundary integral equations for displacements and tractions at the interface is derived. For the numerical solution the collocation method with piecewise constant approximation on each linear continuous boundary elements is used. The distributions of the displacements are computed for different values of the frequency of the incident tension-compression wave. Results are compared with static ones.     

An analytical formula for an elastic thin rod shape under composite loading

The Euler problem on the stability of a thin elastic rod under compressing forces is widely known. In a number of papers this problem is generalized to finding the shape of such a rod under the simultaneous action of a compressing force and a torsional moment. The shape is determined by solving a complex nonlinear boundary value problem by numerical methods. In this paper, an approach providing a full analytical solution of the problem for a broad range of external conditions is discussed. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 7, pp. 35–42, 2005.     

Analysis of the effect of transverse shear strains on the stability of multilayer cylindrical shells under external pressure

The effect of transverse shear strains on the critical pressure is investigated using the results of the solution obtained for the problem of the stability "in the small" of elastic multilayer cylindrical shells of regular structure with alternating light and stiff layers. Attention is drawn to the need to estimate the state of stress of the shells in the critical-load zone with the object of studying the desirability of taking the shear effect into account in the stability calculations. The results obtained can be used in calculating the stability of shells made from resin-based composites (glass-reinforced plastics, graphite-reinforced plastics, etc.). The numerical calculations were carried out using a computer.Translated from Mekhanika Polimerov, No. 6, pp. 1066–1070, November–December, 1973.     

Closed-form solutions for a rectangular layer with central crack under anti-plane shear stress

We consider the problem of determining the stress distributionin a finite rectangular elastic layer containing a Griffithcrack which is opened by internal shear stress acting alongthe length of the crack. The mode III crack is assumed to belocated in the middle plane of the rectangular layer. The followingtwo problems are considered: (A) the central crack is perpendicularto the two fixed lateral surfaces and parallel to the othertwo stress-free surfaces; (B) all the lateral surfaces of therectangular layer are clamped and the central crack is parallelto the two lateral surfaces. By using Fourier transformations,we reduce the solution of each problem to the solution of dualintegral equations with sine kernels and a weight function whichare solved exactly. Finally, we derive closed-form expressionsfor the stress intensity factor at the tip of the crack andthe numerical values for the stress intensity factor at theedges of the cracks are presented in the form of tables.     

The periodic problem for a system of coplanar thin ribbons under longitudinal shear

We give the general outline of the construction of systems of singular integral equations for linearly and circularly periodic two-dimensional problems of the theory of cracks and thinwalled inclusions and the solution of these problems using the method of collocations taking account of the limited number of intervals of integration. As an example we study the dependence of the generalized stress intensity factors on identical systems of thin elastic ribbons forming one, two, and three columnsin an infinite isotropic medium using the conditions of longitudinal shear under the influence of a uniform stress field at infinity. In a particular case we obtain results for the corresponding systems of cracks or absolutely rigid inclusions and films. The method makes it possible to study the interaction of rows of closely placed defects. Translated fromMatematichni Metodi ta Fiziko-Mekhanichni Polya, Vol. 40, No. 2, 1997, pp. 91–99.     

Likelihood ratio tests for equality of shape under varying degrees of orientation invariance

We consider a problem from image cytometry where the objective is to describe possible changes in the shape and orientation of cellular nuclei after treatment with a toxin. The shapes of nuclei are represented by individual ellipses. It is argued that the shape comparison problem can be formulated as a generalization of a hypothesis test for the equality of covariance matrices. For many cell types, the test statistic should be invariant with respect to orientations of the cells. For other cell types, the test statistic should be equivariant with respect to orientations of the cells, but invariant with respect to orientations of the images. Likelihood ratio tests (LRTs) are derived under a Wishart model. The likelihood maximization uses a new result about the minimization of the determinant of a sum of matrices under individual rotations. The applicability and limitations of these LRTs are demonstrated by means of simulation experiments. The reference distributions of the test statistics under the null hypothesis are obtained using unrestricted and restricted randomization procedures. Justification for the Wishart model is provided using a residual diagnostic method. The scientific implications of the results are considered.     

Design sensitivity for arch structures with respect to midsurface shape under static loading

We consider in this paper an example of structural optimization in which the structure is a loaded arch and the design variable is the shape of the arch. We concentrate on differentiability of static response with respect to shape changes. After recalling the arch equation with its functional spaces and the optimization problem, we state a differentiability theorem and provide a detailed proof. Numerical use of this result is finally discussed.     

An analysis of turbulent film condensation on a sphere with variable wall temperature under the effect of local shear stress

This paper presents an investigation into turbulent film condensation on a sphere with variable wall temperature. Under the wide range of vapor velocity, the wall temperature and the local film shear stress were considered. The result shows that under the high velocity vapor, the increase of the temperature amplitude will bring out a larger Nusselt number, and the increase is about 2.7–5.6%. Besides, under the effect of the local film shear stress, the mean Nusselt number will decrease about 0.65–0.8%. Furthermore, the paper then discusses the influence of shears and temperature amplitudes on the local dimensionless film thickness and heat transfer characteristics. Finally, the results developed in the current study are compared with those generated by previous theoretical results.     

Finite element dynamic analysis of unsymmetric composite laminated beams with shear effect and rotary inertia under the action of moving loads

The finite element dynamic response of an unsymmetric composite laminated orthotropic beam, subjected to moving loads, has been studied. One-dimensional finite element based on classical lamination theory, first-order shear deformation theory, and higher-order shear deformation theory having 16, 20 and 24 degrees of freedom, respectively, are developed to study the effects of extension, bending, and transverse shear deformation. The theories also account for the Poisson effect, thus, the lateral strains and curvatures can be expressed in terms of the axial and transverse strains and curvatures and the characteristic couplings (bend–stretch, shear–stretch and bend–twist couplings) are not lost. The dynamic response of symmetric cross-ply and unsymmetric angle-ply laminated beams under the action of a moving load have been compared to the results of an isotropic simple beam. The formulation also has been applied to the static and free vibration analysis.     

An improved lower bound for deflections of laminated cantilever beams including the effect of transverse shear deformation

A previous paper (reference [3]) has formulated a version of the well-known plane stress problem of the end-loaded cantilever beam of narrow rectangular cross section in a way which allowed the statement of upper and lower bounds for the deflection of the beam, through use of the principles of minimum potential and complementary energy. In extension of the work in reference [3] we here derive an improved lower bound, with the consequence that now the upper and the lower bound coincide for the limiting case of vanishing depth to span ratio of the beam. This means that we have a rigorous proof of the correctness of the ‘elementary strength of materials’ result for the case of a very slender beam, in addition to quantitatively reliable corrections to the elementary result for the case of beams which are not slender.