Interaction of time-harmonic SH waves with a crack-like inclusion: edge region analysis

Elastodynamic stress concentration near the tips of a crack-like inclusion of finite length generated by the diffraction of high-freqency time-harmonic SH waves is analyzed. It is shown that the stress intensity factors at the tips of inclusion are provided by the fields describing the solution of the static boundary value problem for a semi-infinite strip and edge waves travelling between the two inclusion tips. The solution to the problem is expressed in a closed form that is computationally effective and yields accurate results in the resonance region of dimensionless wave numbers. This revised version was published online in July 2006 with corrections to the Cover Date.     

层合板复合材料连杆机构非线性动态分析模型

以层合板复合材料连杆机构为研究实例,考虑层合板构件大变形导致的非线性因素影响,用拉格朗日方法建立此类机构的弹性动力学模型,得到机构的非线性有限元动态方程。所建模型体现了非线性因素对机构动态性能的影响,为提高层合板复合材料机构动力学模型的精度,以改善机构的设计和动态性能,提供了一定理论依据;并为进一步研究该类机构的内共振、主共振,以及各种组合共振、多重共振等非线性振动特性打下了基础。     

On the intersonic crack propagation in an orthotropic medium

Motivaded by recent theoretical studies the elastodynamic response of an orthotropic material with a semi-infinite line crack, which propagates intersonically. is revisited through an approach which differs from those used in previous studies. The near tip stress and displacement fields are obtained for Mode I and Mode II of steady state crack propagation. The strain energy release rate analysis confirms that the Mode I is physically impossible due to the order of stress singularity, which is larger then one half. For Model II the order of stress is less than one half and it is shown that a steady state intersonic propagation is allowed only for a particular crack tip velocity which is a function of the material orthotropy.     

A hybrid finite difference and moving least square method for elasticity problems

In this paper, a novel hybrid finite difference and moving least square (MLS) technique is presented for the two-dimensional elasticity problems. A new approach for an indirect evaluation of second order and higher order derivatives of the MLS shape functions at field points is developed. As derivatives are obtained from a local approximation, the proposed method is computationally economical and efficient. The classical central finite difference formulas are used at domain collocation points with finite difference grids for regular boundaries and boundary conditions are represented using a moving least square approximation. For irregular shape problems, a point collocation method (PCM) is applied at points that are close to irregular boundaries. Neither the connectivity of mesh in the domain/boundary or integrations with fundamental/particular solutions is required in this approach. The application of the hybrid method to two-dimensional elastostatic and elastodynamic problems is presented and comparisons are made with the boundary element method and analytical solutions.     

Determination of the scattered fields of an SH-wave by an eccentric coating-fiber ensemble using DEIM

To date, the existing theories pertinent to the determination of the scattered fields of an inhomogeneity have been limited to certain topological symmetries for which the method of wave-function expansion is widely used. In the literature the wave-function expansion method has also been employed to the case involving concentric coated fiber. An alternative approach is the dynamic equivalent inclusion method (DEIM) proposed by Fu and Mura [L.S. Fu, T. Mura, The determination of elastodynamic fields of an ellipsoidal inhomogeneity. ASME J. Appl. Mech. 50 (1983) 390-396.] who found the scattered field of a single spheroidal inhomogeneity. The pioneering work of Eshelby [J.D. Eshelby, The determination of the elastic field of an ellipsoidal inclusion, and related problems, Proc. R. Soc. London, Ser. A A241 (1957) 376-396.] on elastostatic EIM is based on polynomial form of eigenstrains which holds certain useful properties and subsequently its application is only effective for certain relevant situations and not necessarily efficient for other problems. Nevertheless, Fu and Mura’s analysis is also based on polynomial eigenstrains. It will be shown that taking the dynamic homogenizing eigenstrains in the form of the series expansion whose general term is products of functions of r and trigonometric functions of θ, is more rigorous and attractive for the problem under consideration. This natural form of solution gives very accurate result with just the first few terms of the series. Moreover, this work aims to extend the DEIM to the case of coated fiber obstacle with the rather complex topology where the coating-fiber phases are not concentric. The effect of variableness of the coating thickness on the elastodynamic fields is examined. Comparison with other analytical solutions, whenever available, establishes the remarkable accuracy and robustness of the proposed theory.     

Distributed-elementary-source self-regularized dyadic Green's functions for modeling the massloading effect in acoustic devices

A concept for the simulation of two-dimensional models of massive electrodes in micro-acoustic devices has been presented. The method is based on a mesh-less analysis of the underlying boundary value problem. An efficient procedure for the calculation of the involved dyadic Green's functions has been introduced. Major advantage of the proposed method is in the ability of pre-calculating and storing relevant data for the characterization of individual substructures. The latter property is by construction amenable to parallel computing. Glimpse of the numerical results and figures facilitate the discussion of the underlying ideas.     

Analytical modeling of the elastic structural response of tubes to internal detonation loading

The internal detonation loading of cylindrical shells involves loads that propagate at high speeds. Since the speed of the gaseous detonation can be comparable to the flexural-wave-group speed, the excitations of flexural waves in the tube wall become significant. Flexural waves can result in high strains, which may exceed the equivalent static strains (caused by the same nominal loading pressure) by up to a factor of 4. This paper presents a new analytical model for the transient elastodynamic structural response of cylindrical shells with finite length to internal detonation loading. It is shown that, due to the consideration of the effects of transverse shear and rotary inertia, the predictions of dynamic structural response of tubes provided by this model are in better agreement with the experimental results, than existing analytical models. The model is verified through comparison with experimental results reported in the literature.     

计入内齿板变形的环式减速器弹性动力分析

环式减速器是一类新型的少齿差行星传动装置,具有传动比大、承载能力高、结构紧凑、制造成本低和适应性广等诸多优点。为改善系统的动力学性能,建立了环式减速器的弹性动力学方程,计入了高速轴、内齿板、啮合轮齿及轴承等的弹性变形。利用ANSYS软件创建了内齿板的有限元模型,以具有等效刚度的弹簧约束内齿板的刚体运动,求解了一个机构运动周期内各相内齿板的应力、位移与弹性变形。将基于ANSYS的内齿板有限元分析与环式减速器的弹性动力分析相结合,经迭代计算,揭示了系统中各零部件的真实受力情况。研究表明,内齿板的拉压变形与弯曲变形均对环式减速器的动力学性能具有重要影响,内齿板的弹性变形将导致行星轴承的实际使用寿命低于预期的设计寿命。     

弹性曲柄摇杆机构的基频特性分析

揭示了曲柄摇杆机构的基频（一阶固有频率）与机构位置之间的对应关系，并从理论上进行了探讨，通过一个曲柄摇杆机构实例进行了计算，验证了理论分析的正确性。     

正交异性体弹性动力学的一类反平面问题

应用Ｃмирнов的方法求得了正交异性体反平面问题波动方程的函数不变解。根据这一解，导出了具有任意自相似指数的反平面弹性动力学问题的一般解。这个求解方法是基于解的解析函数的一般表达，这个表达可以迅速地把所论问题化为某些半平面上的Ｒｉｅｍａｎｎ－Ｈｉｌｂｅｔ问题。半平面上的Ｒｉｅｍａｎｎ－Ｈｉｌｂｅｒｔ问题容易用通常的如Ｍусхелцщвцлц的方法去解决，作为实例，文中对若干问题进行了求解。