An analytical solution for long-wave scattering by a submerged circular truncated shoal

An analytical solution of the long-wave (or shallow-water) equation in closed-form is obtained for simple harmonic waves scattered by a submerged circular truncated shoal. This analytical solution is firstly validated against Longuet-Higgins’s classical analytical solution for a submerged cylinder, and then validated against numerical solutions obtained by using the DRBEM (dual reciprocity boundary-element method) model for a submerged circular truncated cone. Finally, the analytical solution is used to investigate the changing trend of maximum wave amplification, the trace pattern of focal position of wave-energy versus the wave period and the influence of shoal submergence on wave-energy trapping.     

An exact analytical solution of the inverse problem for a plasma cylinder expanding in a compressible medium

A strict analytical solution of the wave equation with cylindrical symmetry in a region with mobile boundaries was obtained by the method of inverse problems with allowance for the interaction of nonlinear arguments. The proposed method is universal and applicable to solving both inverse and direct problems for arbitrary values of the initial radius and displacements. The solution describes the near wave field of an expanding plasma piston, including the field formed in the initial moments of a pulsed expansion process. The solution gives exact values of a given pressure and velocity wave profile at a fixed point of the wave zone in the initial moment, as well as particular finite values of the pressure and velocity at a mobile boundary of the expanding plasma piston at the moments of time approaching zero. The solution is obtained with allowance for additional nonlinear conditions.     

On the dynamical thermoelasticity problem for a hollow funtionally graded cylinder

A thermoelasticity problem of a pressurized infinite cylinder made of functionally graded material is solved analytically where material properties vary with radial position. Time dependent thermal and mechanical boundary conditions are assumed to act on the inner and outer surfaces of the cylinder. For thermal boundary conditions, temperature is prescribed on both surfaces, whereas for mechanical boundary conditions, tractions are prescribed on the boundaries. Obtaining distribution of temperature throughout the cylinder, the dynamical structural problem is solved and closed form relations are extracted for distributions of stress components.     

Evaluation of the T-stress and stress intensity factor for a cracked plate in general case using eigenfunction expansion variational method

This paper investigates the T-stress and stress intensity factor for a cracked plate in general case. In the general case, the shape of boundary and the applied loading are arbitrary. The eigenfunction expansion variational method (EEVM) is developed to evaluate the T-stress and stress intensity factor. For the traction boundary value problem, the EEVM is equivalent to the theorem of least potential energy in elasticity. Therefore, the EEVM possesses a clear physical meaning and it does not depend on any boundary collocation scheme. Several numerical examples are presented, which include: (1) a line crack in circular plate and (2) a line crack in rectangular plate. Numerical examination for convergence in an example is carried out.     

The biharmonic problem and progress in the development of analytical methods for the solution of boundary-value problems

A comparative analysis of harmonic and biharmonic boundary-value problems for 2D problems on a rectangle is given. Some common features of two types of problems are emphasized and special attention is given to the basic distinction between them. This distinction was thoroughly studied for the first time by L. N. G. Filon with respect to some plane problems in the theory of elasticity. The analysis permits to introduce an important aspect of the general solution of boundary-value problems. The procedure for solving the biharmonic problem involves both the method of homogenous solutions and the method of superposition. For some cases involving self-equilibrated loadings on one pair of sides of the rectangle, the complete solution, including calculation of the quantitative characteristics of the displacements and stresses, is given. The efficiency of the numerical implementation of the general solutions is shown. The analysis of the quantitative data allows to elucidate some main points of the Saint-Venant principle.     

Analytical solution for the axisymmetric plane strain electroelastic dynamics of a special non-homogeneous piezoelectric hollow cylinder

By virtue of the introduction of a dependent variable and the separation of variables technique, the axisymmetric plane strain electroelastic dynamic problem of a special non-homogeneous piezoelectric hollow cylinder is transformed to a Volterra integral equation of the second kind about a function with respect to time, which can be solved successfully by means of the interpolation method. Then the solutions of displacements, stresses, electric displacements and electric potential are obtained. The present method is suitable for a piezoelectric hollow cylinder with an arbitrary thickness subjected to arbitrary mechanical and electrical loads. Numerical results are finally presented.     

An analytical solution for hydraulic conductivity of concrete considering properties of the Interfacial Transition Zone (ITZ)

As a composite material, hydraulic conductivity of concrete depends on conductivity of its components that are the mortar, aggregates and the Interfacial Transition Zone (ITZ). Since hydraulic conduction is analogous to heat and electrical conduction, analytical models from these analogous areas relating effective conductivity of composite to conductivity of its components can be used to find the effective hydraulic conductivity of concrete as a function of properties of its components, i.e., aggregate, mortar and the ITZ. However, effect of the conduction in the ITZ has not been considered in these models. This paper presents an analytical solution for the hydraulic conductivity of concrete as a three-phase composite material. The solution is an extension to the model originally proposed for conduction of composite media with randomly suspended spheres. Results of the proposed model compare well against the experimental results and those obtained from rigorous numerical analysis using the Finite Element (FE) method. The principal significance of this study lies in the development of a versatile analytical model that can be employed as a quick tool for assessment of hydraulic conductivity of concrete without the need for sophisticated FE models at the meso-scale level. It offers more insight into effect of different components of concrete on its overall conductivity.     

考虑载荷作用次数的机械零部件可靠性灵敏度分析方法

 为了研究载荷多次作用时,机械零部件的可靠度及可靠性灵敏度变化规律,从灵敏度角度修改零件的设计参数,降低制造成本,建立一种可靠性模型结合了随机摄动法、Edgeworth级数技术,并考虑了载荷的作用次数．摄动法和Edgeworth级数可以在基本随机参数的前4阶矩已知的情况下,研究具有任意分布参数的机械零件的可靠性灵敏度设计问题,顺序统计量理论考虑了载荷作用次数在可靠度和灵敏度计算中的影响．使用这种模型计算出的可靠度会随着载荷作用次数而变化,这与静态的可靠度计算方法存在差别．以某一型号的螺栓为算例,应用此模型计算了其可靠度、随机变量均值和方差的可靠性灵敏度．由提出的方法得到了可靠度和可靠性灵敏度值及其随载荷作用次数变化的曲线．可靠度及可靠性灵敏度随载荷作用次数变化的规律是：载荷作用次数增加,可靠度值降低,变化趋势单调;载荷作用次数达到最大时,可靠度达到最小;随机变量均值和方差的灵敏度随载荷作用次数变化出现不同的变化趋势,其中螺栓截面直径的均值和方差灵敏度随载荷作用次数的变化最大,随作用次数的增加,螺栓截面直径的参数将对螺栓的可靠性起主要的决定作用．     

An analytical solution of the rebound indentation problem for an isotropic linear viscoelastic layer loaded with a spherical punch

A unilateral frictionless axisymmetric contact problem for an isotropic viscoelastic layer attached to a rigid substrate and loaded with a spherical indenter is considered. It is assumed that the indentation protocol is composed of two stages. In the indentation phase, the layer is subjected to displacement loading, while at the end of the first stage, the load is immediately removed and the second stage, called the recovery phase, lasts for a theoretically indefinite time. Under the assumption of time-independent Poisson’s ratio, we derive closed-form analytical expressions for the contact force (in the indentation phase) and for the indentation displacement (in the the recovery phase). The obtained closed-form analytical solution is valid for the indentation phase with an arbitrary monotonic loading displacement and can be used for evaluation of the rebound indentation test for soft biological tissues and originally suggested for assessment of articular cartilage viability.     

An exact solution of the first-exit time problem for a class of structural systems

The mean time to escape from a region of desired operations is one the basic reliability measures in stochastic dynamics. In general, a precise solution of the first-exit time problem is unavailable. This paper demonstrates an exact solution of the mean exit time problem for a multidimensional non-dissipative Lagrangian system excited by additive Gaussian white noise. We identify the Fokker–Planck equation whose solution characterizes the mean time needed to reach a critical energy and explicitly construct the solution. For illustration, we apply the developed theory to engineering examples. We calculate the mean time of the standard operation for a flexural nanotube with likely noise-induced buckling and analyze the mean time of the stable functioning for a gyroscope subjected to random and dissipation torques. It is demonstrated that the solution of the first-exit time problem for a non-dissipative system gives a quite good approximation to a numerical solution of a similar problem for a system with small dissipation.     

An analytical solution for the effect of initial stress,rotation, magnetic field and a periodic loading in a thermo-viscoelastic medium with a spherical cavity

In this article, an analytical solution for the effect of initial stress, the rotation, and the relaxation times in a magneto-thermo-viscoelastic homogeneous medium with a spherical cavity subjected to periodic loading is presented. The distribution of displacements, temperature, and stresses in a homogeneous medium, in the context of generalized thermo-elasticity using the Green-Lindsay (GL) theory is discussed and obtained in analytical form. The results are displayed graphically to illustrate the effect of initial stress, the rotation, relaxation times, magnetic field, and viscoelasticity. Comparisons are made with the previous work in the absence of rotation and initial stress.     

An adaptive strategy for the bivariate solution of finite element problems using multivariate nested Padé approximants

Most engineering applications involving solutions by numerical methods are dependent on several parameters, whose impact on the solution may significantly vary from one to the other. At times an evaluation of these multivariate solutions may be required at the expense of a prohibitively high computational cost. In the present paper, an adaptive approach is proposed as a way to estimate the solution of such multivariate finite element problems. It is based upon the integration of so‐called nested Padé approximants within the finite element procedure. This procedure includes an effective control of the approximation error, which enables adaptive refinements of the converged intervals upon reconstruction of the solution. The main advantages lie in a potential reduction of the computational effort and the fact that the level of a priori knowledge required about the solution in order to have an accurate, efficient, and well‐sampled estimate of the solution is low. The approach is introduced for bivariate problems, for which it is validated on elasto‐poro‐acoustic problems of both academic and more industrial scale. It is argued that the methodology in general holds for more than two variables, and a discussion is opened about the truncation refinements required in order to generalize the results accordingly. Copyright © 2014 John Wiley & Sons, Ltd.     

一种使用矢量网络分析仪的阻抗测量改进方法

基于反射法理论提出了一种使用矢量网络分析仪测量集总参数元件阻抗的方法,引入阻抗匹配电路,拓宽了矢量网络分析仪的阻抗测量范围.通过对匹配电路二端口网络模型中参量A的分析,给出相应的被测元件的阻抗计算式,消除了夹具对测量结果的影响.采用矢量网络分析仪直接测量法和该阻抗测量法分别测量了5种不同阻值的金属膜电阻,结果表明,该阻抗测量方法的测量精度高于矢量网络分析仪直接测量的精度,可在30 kHz～100 MHz频率范围内实现几欧至千欧阻抗的精确测量.     

Numerical solution of an inverse diffusion problem for the moisture transfer coefficient in a porous material

On the basis of the solution of a nonlinear diffusion equation with initial and boundary conditions, a transfer coefficient of moisture in a sample of a porous material is found by minimization of a functional, which expresses error of the calculated profile of moisture concentration in well defined time moments from their experimental values for the defined moisture transfer coefficient. In this case the transfer coefficient as opposed to previous studies is found as a sum of a power function and an exponential function of the moisture concentration. The exponent of the power function depends on time. Thus, a more accurate coincidence of the calculated profiles of the moisture concentration to their experimental profiles is gained in comparison to the investigations performed by other authors. The exponential term provides a good coincidence of the mentioned profiles for big times nearby the boundary of the sample, where the moisture evaporation to the atmosphere takes place.     

An accurate solution for the responses of circular curved beams subjected to a moving load

In this paper, an accurate and effective solution for a circular curved beam subjected to a moving load is proposed, which incorporates the dynamic stiffness matrix into the Laplace transform technique. In the Laplace domain, the dynamic stiffness matrix and equivalent nodal force vector for a moving load are explicitly formulated based on the general closed‐form solution of the differential equations for a circular curved beam subjected to a moving load. A comparison with the modal superposition solution for the case of a simply supported curved beam confirms the high accuracy and applicability of the proposed solution. The internal reactions at any desired location can easily be obtained with high accuracy using the proposed solution, while a large number of elements are usually required for using the finite element method. Furthermore, the jump behaviour of the shear force due to passage of the load is clearly described by the present solution without the Gibb's phenomenon, which cannot be achieved by the modal superposition solution. Finally, the present solution is employed to study the dynamic behaviour of circular curved beams subjected to a moving load considering the effects of the loading characteristics, including the moving speed and excitation frequency, and the effects of the characteristics of curved beams such as the radius of curvature, number of spans, opening angles and damping. The impact factors for displacement and internal reactions are presented. Copyright © 2000 John Wiley & Sons, Ltd.     

An analytical solution for the large deflections of a slender sandwich beam with a metallic foam core under transverse loading by a flat punch

The large deflections of slender ultralight sandwich beams with a metallic foam core are studied under transverse loading by a flat punch, in which interaction of bending and stretching induced by large deflections is considered. Firstly, a unified yield criterion for metallic sandwich structures considering the effect of core strength is proposed, which is valid for metallic sandwich cross-sections with various core strengths and geometries. This can reduce to the yield criterion for a solid monolithic cross-section and the classical yield criterion for sandwich cross-sections with a weak core, respectively. Then, analytical solutions for the large deflections of fully clamped and simply supported metallic foam core sandwich beams are derived under transverse loading by a flat punch, respectively. Comparisons of the present solutions with experimental results are presented and good agreements are found. The effects of the core strength, the size of loading punch and the boundary conditions on the structural response of sandwich beams are discussed in detail. It is shown that the axial stretching induced by large deflections has significant effect on the load-carrying and energy absorption capacities of sandwich structures in the post-yield regime, and the load-carrying and plastic energy absorption capacities of metallic foam core sandwich beams may be underestimated as the core strength is neglected in analysis, especially for the sandwich beams with a strong core.