基于物理的变形曲线在结构形状优化中的应用

用各向异性模型定义NURBS曲线的变形能,基于所提出的变形能模型,用有限元法对NURBS曲线表达的设计边界进行模态计算,然后,将设计边界用模态向量的线性组合参数化表示。将这种基于边界特征向量的几何形状表示方法应用于优化参数定义．提出了一种适用于结构形状优化的自适应几何精化方法,它有效地将户型有限元分析、优化方法和设计边界的形状表达集成在一起。     

Rays and modes for plane wave coupling into a large open-ended circular waveguide

Generalizing an earlier study of high-frequency plane wave coupling into a wide semi-infinite parallel-plane waveguide, this investigation is concerned with coupling into a large semi-infinite circular waveguide. Emphasis is placed on the interplay between ray fields and mode fields, on the excitation mechanism of each, and on their properties when the field incidence angle is strongly oblique, thereby introducing marked azimuthal asymmetries. The tools of analysis are the geometrical theory of diffraction (GTD), physical optics (PO) and hybrid ray-mode theory. The results reveal that coupling from edge-diffracted rays into a waveguide mode occurs when such rays emanating from the flash points on the edge line up with rays in the modal congruence. However, the diffracted ray caustics between initial reflections do not coincide with the cylindrical caustic of the mode, and only after many reflections is there synchronism between the edge-diffracted and modal rays. Complete synchronism throughout obtains for each angular harmonic constituent of the field, for which the incident wave is conical. Under these conditions, one may also distinguish a multiple reflected truncated conical geometric optical beam, the analog of the geometric optical sheet beam in plane parallel geometry. A variety of other ray and modal characteristics are elucidated as well from different perspectives, thereby granting insight into the ray-mode phenomenology in the circular wave-guide environment. Such insight is expected to be useful when one attempts to deal with nonideal but strongly guiding configurations.     

Theoretical analysis of transient waves in a simply-supported Timoshenko beam by ray and normal mode methods

The dynamic transient responses of a simply-supported Timoshenko beam subjected to an impact force are investigated by two theoretical approaches – ray and normal mode methods. The mathematical methodology proposed in this study for the ray method enable us to construct the solution for the interior source problem and to extend to solve the complicated problem for the multi span of the Timoshenko beam. Numerical results based on these two approaches are compared. The comparison in this study indicates that the normal mode method is more computationally efficient than the ray method except for very short time after the impact. The long-time transient responses are easily calculated using the normal mode method. It is shown that the average long-time transient response converges to the corresponding static value. The Timoshenko beam theory is more accurate than the Bernoulli–Euler beam theory because it includes shear and rotary inertia. This study also provides the slender ratio for which the Bernoulli–Euler beam can be used for the transient-response analysis of the displacement. Moreover, the resonant frequencies obtained from finite element calculation based on the three-dimensional model are compared with the results calculated using the Timoshenko beam and Bernoulli–Euler beam theories. It is noted in this study that the resonant frequency can be accurately determined by the Timoshenko beam theory if the slender ratio is larger than 100, and by the Bernoulli–Euler beam theory if the slender ratio is larger than 400.     

Interferometry and reconstruction of strongly refracting fields in two-dimensional boundary layer flow

 Optical methods like interferometry as non-intrusive experimental techniques are used for fine analysis of flowfields. The accuracy of the measuring method is very important for the applicability of its results to CFD validation. A common evaluation method to reconstruct interferograms is based on the assumption, that the object ray propagates along a straight line. But the strong bending of rays that occurs, e.g. in supersonic boundary layer flow, cannot be neglected without losses in reconstruction quality. Since the reconstruction of a two-dimensional boundary layer flow can be considered as an one-dimensional problem, the phase difference of the object and reference ray at the interferogram can be related analytically to the refractive-index distribution using a Taylor series expansion. The resulting interferometric equation is an ordinary non-linear second-order differential equation, which can be integrated by numerical methods. By application of this interferometric equation on the one hand, the error in the “classical” interferometry resulting from the ray bending neglection can be estimated. On the other hand, the accuracy in evaluation of interferograms of two-dimensional boundary layer flow can be improved by solving this equation. Received: 23 May 1996 / Accepted: 21 September 1996     

On caustics associated with horizontal rays and vertical modes

Wave propagation in a medium with slowly varying inhomogeneities can sometimes be modelled by a combination of normal mode theory in one direction and ray theoretical methods in the other directions. Caustics can occur in the ray theory ansatz. Here we consider those caustics using a Lagrange manifold approach.     

一种考虑界面相物性影响的界面单元法

界面是由复杂的界面相简化而成的,界面破坏实际是界面相材料的破坏。数值计算为了方便,如经典模型和内聚力模型等,都把很薄的界面相作无厚度化处理。导致只能考虑界面的面力,而无法考虑界面相内的应力(平行于界面方向的应力)。使界面失效准则先天性地排除了界面相内部应力的影响,从界面相材料失效机理的角度来看这是不够严谨的。本文将界面相材料等效为一种弹性连续体,由界面本构关系推导得到了一种新的界面单元。该单元具有界面参数易确定、对界面相物性可以进行等效描述等优点。通过商用有限元软件ABAQUS和用户子程序UEL实现了数值分析,并与直接物理模型的数值模拟结果进行对比,证明了本方法的简便及准确性。通过对不同界面相厚度结构的进一步分析,探讨了本文方法的可行范围。     

Ray method for surface waves on a ferromagnetic fluid

The ray method, or geometrical optics method, is used to study surface waves on a ferromagnetic fluid of variable depth. Both time-dependent and time-reduced cases are considered on the basis of the shallow-water approximation. An application of the time-reduced ray method leads to the discovery of edge waves on a ferromagnetic fluid over a uniformly sloping bottom.     

An evolutionary search technique to determine natural frequencies and mode shapes of composite Timoshenko beams

Natural frequencies and mode shapes of composite Timoshenko beams are determined by a diversity guided evolutionary algorithm (DGEA) with different boundary conditions. After applying boundary conditions, frequency equation is obtained in determinant form. Then, natural frequencies and consequently mode shapes are obtained using DGEA where the absolute value of determinant is the subject of optimization. Advantages of employing DGEA are: first, all natural frequencies are produced in a simple run, second, its simplicity for implementation and third, the procedure is not computationally prohibitive. Results clearly show the applicability of the proposed method for obtaining natural frequencies and mode shapes.     

Low-energy impact response of composite and sandwich composite plates with piezoelectric sensory layers

An efficient model reduction based methodology is presented for predicting the global (impact force, plate deflection and electric potential) and through-thickness local (interfacial strains and stresses) dynamic response of pristine simply-supported cross-ply composite and sandwich composite plates with piezoelectric sensory layers subjected to low-energy impact. The through-thickness response of the laminate is modelled using coupled higher-order layerwise displacement-based piezoelectric laminate theories. Linearized contact laws are implemented for simulating the impactor–target interaction during impact. The stiffness, mass, piezoelectric and permittivity matrices of the plate are formulated from ply to structural level and reduced by applying a Guyan reduction technique to yield the structural system in state space. This reduction technique enables the formulation of a plate–impactor structural system of minimum size (1 term per vibration mode for composite plates – 2 terms for sandwich plates) and reduces computational cost, thus facilitating applicability for real-time impact and vibration control.     

一弹性层覆盖于半无限弹性介质对表面点冲击载荷的瞬态响应

利用广义射线理论,研究了一弹性层覆盖于半无限弹性介质表面受法向动集中荷载作用情形表面处的位移响应.给出了一种计算瞬态响应的有效方法,首先根据反射次数的不同将射线自动分组,然后将同一组中具有相同积分路径的积分式自动合并并一次性完成积分.运用该技术,计算量大大减少,使得广义射线法应用于较长时间响应计算的工作得到推进.数值结果中给出了两种情形位移响应的特点,一种情形是弹性层比半空间层硬,另一种情形是弹性层比半空间层软.