An exact solution for an anisotropic plate with an elliptic hole under arbitrary remote uniform moments

The problem of an anisotropic plate containing an elliptic hole subjected to remote bending or twisting moments is considered. In contrast with the previous works on the problem, the requirement that the deflection be a single-valued function is satisfied by introducing a correction constant. An exact solution for general anisotropic materials under arbitrary uniform loading conditions is derived. Explicit expressions for the deflection and moments on the edge of an elliptic hole in an orthotropic plate subjected to bending or twisting moments are obtained. The moment intensity factors as the elliptic hole degenerates into a crack are given.     

Contact stresses in an infinite plate containing a smooth circular insert under thermal load

Summary. A solution is presented for the contact problem with a smooth circular elastic insert in an infinite, linearly elastic plate under thermal load. The thermal load considered here includes the temperature gradient applied at infinity and a uniform temperature change. One of the major difficult parts in solving the present problem is that separation may occur between an insert or inclusion and the surrounding matrix under a nonuniform expansion of the matrix and the insert due to a temperature change. Based on the complex potential theory and the method of analytical continuation, the problem is reduced to a singular integro-differential equation which is solved numerically. Results are presented for the contact angle and for the normal and circumferential stresses at the plate-insert interface. Exact solutions are found for the current problem for a special case when the material properties of the plate and the insert are identical.     

Nonlinear stability analysis of a perforated FGM plate under thermal load

The nonlinear thermal stability analysis of a perforated Ni/Al₂O₃ FGM plate with temperature-dependent thermoelastic material properties is carried out through a finite element approach based on the first-order shear deformation theory and the von-Karman's nonlinear kinematics. The thermoelastic material properties of the FGM plate are varied in the thickness direction, and the Mori-Tanaka homogenization scheme is applied to evaluate these properties. After validating the results of the current formulation, parametric studies are conducted to examine the effects of temperature-dependent material properties, material in-homogeneity, cutout shape and size, edge boundary conditions, aspect and slenderness ratios on the thermal buckling and postbuckling response of perforated FGM plate.     

Spalling in a two-layer plate under an impact load

A two-dimensional model of a damaged medium is examined. The model is implemented numerically on the basis of Wilkin's method with modifications that take into account the introduction of damages. The impact loading of a two-layer iron and aluminum target is modeled numerically using the developed model of a damaged medium. The results of analysis of target damage are presented.Translated from Problemy Prochnosti, No. 9, pp. 55–57, September, 1991.     

Reflection of plate acoustic waves produced by a periodic array of mechanical load strips or grooves

The reflection of fundamental acoustic waves propagating in a thin piezoelectric plate by a periodic array of conducting strips of finite thickness or grooves has been theoretically and experimentally investigated. The analysis has shown that electrical shorting and mass loading affect the relationship of neighboring region impedances in a contrary manner. In some cases, these effects are comparable, and there exists a certain strip thickness for each piezoactive fundamental plate mode at which the reflection coefficient can become zero. A high efficiency of grooved reflector for plate acoustic waves was theoretically revealed. Experimental results for mass loading and grooved reflections, which have been obtained for an SH/sub 0/ wave propagating in the Y-X lithium niobate plate, are in a good agreement with the theory. They show a high efficiency of such reflectors and confirm the validity of using a model based on an equivalent circuit for the analysis of their operation. Investigations indicate that nearly 100% reflection of the SH/sub 0/ wave in the lithium niobate plate can be obtained with the use of a mass loading reflector containing 10 silver strips of thickness d/h=0.08 or a grooved reflector containing eight grooves of depth d/h=0.25. Here h is the plate thickness and d is the reflector thickness or depth.     

Failure of a plate with a circular hole resulting from an array of surface cracks

The problem of brittle failure of an isotropic homogeneous plate perforated by a circular hole as a result of the development of an array of small equal surface cracks was investigated. The plate was loaded by a uniform uniaxial stress at an arbitrary inclination with respect to the system of the cracks. From the study the critical value of the applied stress for failure of the plate by propagation of the most vulnerable crack was determined. Useful results governing the dependence of the critical stress on the number of cracks, the inclination of the applied stress, the length of the cracks and the Poisson's ratio of the plate were derived.     

A mixed problem of plate bending for a regular octagon weakened with a required full-strength hole

The paper addresses a problem of bending of an isotropic elastic plate, bounded by a regular octagon weakened with a required full-strength hole including the origin of coordinates. Coordinate axes pass the middle points of opposite parallel sides of octagon. Rigid bars are attached to each component of the broken line of the outer boundary of the plate. This plate bends under the action of concentrated moments applied to the middle points of the bars. Unknown part of the boundary is free from external forces. Using the methods of complex analysis, the plate deflection and required full-strength contours are determined. Numerical analysis is performed, and the corresponding graphs are constructed.     

Evaluating crack tip stress field in a thin glass plate under thermal load

The stress field around a propagating crack tip in a quenched thin glass plate is discussed through experimental and theoretical analyses. Instantaneous phase-stepping photoelasticity using a CCD camera equipped with a pixelated micro-retarder array is used for measuring the crack tip stress field. From the successive phase maps of principal direction, the position and the velocity of the crack tip are evaluated. On the other hand, the fracture parameters, that is, the stress intensity factors and the T-stress are determined from the phase maps of the retardation. Experimental results obtained for a straight crack show good agreement with those obtained by theory of elasticity. The results also indicate that the direction of the crack propagation arising in the quenching process is not determined by the direction of the maximum principal stress. Furthermore, the results show that the T-stress criterion is inappropriate to evaluate the crack path instability in a quenched thin glass plate.     

Limiting state of an orthotropic plate weakened by a periodic system of collinear cracks

On the basis of a modified δ _c -model of cracks, we study the limiting state of an orthotropic plate made of a material satisfying the general strength condition and weakened by a system of collinear cracks. The relations for the determination of major parameters of the model of cracks (the size of process zones, stresses in these zones, and the crack-tip opening displacements) are deduced. The mechanism of fracture of the plate containing a periodic system of collinear cracks is investigated. The influence of the degree of anisotropy and geometric parameters of the problem on the formation of the process zones and limiting state of the plate is revealed. The region of safe loading of an orthotropic viscoelastic plate with cracks is determined. The influence of the rheological parameters of the material on the region of safe loading is analyzed. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 44, No. 6, pp. 58–66, November–December, 2008.     

Solutions of multiple crack problems of a circular plate or an infinite plate containing a circular hole by using Fredholm integral equation approach

Presented is an elementary solution, which is a particular solution of the circular plate containing one crack. The solution consists of two parts and satisfies the following conditions: (i) the first part corresponds to a pair of normal and tangential concentrated forces acting at a prescribed point on both edges of a single crack; (ii) the second part corresponds to some distributed tractions along both edges of the crack; (iii) the obtained elementary solution, i.e. the sum of the first and second parts, satisfies a traction free condition on the circular boundary. Using this elementary solution and taking some undetermined density of the elementary solution along each crack, a system of Fredholm integral equations of multiple crack problems can always be obtained. The multiple crack problems of an infinite plate containing a circular hole can be solved in a similar way. Several numerical examples are given in this paper.     

Focusing of an elliptic vortex beam by a square Fresnel zone plate

We propose a new (to our knowledge) method for performing beam shaping. Calculations show that beam patterns including diamond, rhombus, and hollow beam with diamond-shaped dark core can be generated in the focal plane of a square Fresnel zone plate by choosing appropriate parameters of an incident elliptic vortex beam. Numerical simulations have demonstrated the validity and effectiveness of this method.     

强动载荷下焊接钢板力学性能及本构模型研究

为研究强动载荷下船用焊接钢板的力学性能.开展了典型船用焊接钢板母材、焊缝和热影响区的准静态拉伸试验、高温拉伸试验及SHPB动态压缩试验,分析了焊接钢板材料在不同应力状态下的力学行为,基于力学性能试验结果拟合了焊接钢板母材、焊缝和热影响区材料的本构模型.结果 表明:准静态条件下,与母材相比,焊缝和热影响区材料的屈服强度与...