基于精确Cosserat模型的螺旋杆稳定性分析

弹性杆的螺旋线平衡问题在DNA、纤维、海底电缆和输油管线等方面具有应用背景.Kirchhoff动力学比拟是分析弹性细杆平衡稳定性的有效方法.Kirchhoff模型中包括中心线无拉伸变形和截面无剪切变形的基本假定与生物大分子等软物质的实际状况有较大差异.基于精确Cosserat模型,考虑中心线的拉伸压缩变形和截面剪切变形,以及剪切变形引起杆中心线转动导致切线轴相对截面法线轴的偏离,以Euler角表达截面姿态,建立圆截面弹性杆的动力学普遍方程.在静力学范畴内讨论螺旋线平衡状态的Liapunov稳定性和Euler稳定性问题,导出稳定性条件及轴向力和扭矩的Euler临界值.证明螺旋杆平衡的静态Liapunov稳定性和Euler稳定性条件是动态Liapunov稳定性的必要条件.     

Mathematical models and solution algorithms for computational design of RC piles under structural effects

The paper presents mathematical models and solution algorithms for RC pile design, through scanning soil stratums from top to downwards with an interactive scanner band. The equilibrium of transferred loads from the superstructure, friction forces and tip bearing forces are considered for the design, which leads to optimum pile length. The most important contribution of this research for designers is supplying an efficient tool to obtain optimum pile length and reinforced concrete design of pile foundation systems. A program package has been developed in MATLAB depending on the proposed algorithm. Soil behaviors depending on external effects, active and passive zone distributions are considered. All possible effects in all freedom degrees are taken into account in design process. Stress and strain distributions due to axial loads, bending moments, shear forces and torsional moments may be monitored. The optimum pile length, cross section dimension and reinforcement details may be found by using developed algorithm.     

Nonlinear models of suspension bridges

Nonlinear variational equations describing one type of suspension bridges are proposed and studied. The variational equations describe the behaviour of road bed, main cables and cable stays. The road bed is described by two functions connected with vertical and horizontal deformation of any cross section. The main cable is considered to be perfectly flexible and inextensible. The cable stays only resist tensile forces. The variational equations are derived from the principle of minimum potential energy. The existence of solution is based on the Brouwer Fixed Point Theorem. The local uniqueness and continuous dependence on the data represented by gravitational forces acting on the road bed are studied. The local results are based on the Implicit Function Theorem for Banach spaces. A certain stability criterion for suspension bridges is formulated and this criterion indicates how to influence the stability of suspension bridges.     

散射裂变截面的最优设计

在[1]中讨论了反应堆散射裂变截面的最优设计,基于下列单能静态各向同性迁移方程     

Minimization of the weight of ribbed cylindrical shells made of a viscoelastic composite

The minimization of the weight of ribbed viscoelastic composite cylindrical shells under a long-term external pressure is considered. The shells are strengthened with six inner stiffening rings with identical geometric parameters and a square cross section. It is assumed that the shell material obeys the linear law of hereditary creep and the displacements across the shell wall are distributed according to the Timoshenko hypothesis. The shell must withstand an external pressure of –0.5 MPa without the loss of stability for an unlimited time. The parameters of optimization are the intensity of reinforcement and thickness of its covering and the height and width of the stiffening rings. It is found that the weight of an optimum ribbed shell is 24% lower than that of an optimum cylindrical shell without ribs.     

Nonlinear Analysis and Optimum Design of Guyed Masts

In this paper the nonlinear analysis and design optimization of guyed masts is addressed. The mast is modeled as a 3D truss and is supported by catenary cable elements that have nonlinear elastic behavior. For nonlinear static analysis, an innovative procedure is proposed that divides the structure into linear and nonlinear parts and analyzes them separately. The proposed method satisfies the equilibrium and compatibility by establishing and solution of a set of nonlinear equations. The optimization problem employs the sizes of members, initial cable tensions and the positions of anchor on the ground and tie level of cables on the mast as design variables. To facilitate the optimization solution, a compatible sensitivity analysis procedure is proposed. Sensitivities of objective function, displacement and strength constraints in the mast and cables, subjected to a variety of load combinations including dead, wind and ice loads are calculated. Numerical examples are provided to show the nonlinear analysis procedure and the applicability of the algorithm to optimum design of practical guyed masts.     

Optimization of open cross sections of thin-walled beams with plate-shell-flanges

The paper is devoted to a monosymetrical cold-formed thin-walled beam with open cross section. Its flange consists of plates and circular shells. The beam is under pure bending. The cross section is characterized by dimensionless parameters. The authors are searching for an optimal cross section shape of considered beam. This optimal shape is determined by means of parametric optimization. The dimensionless objective function is so defined as to comprise both cross section area and a maximal allowable bending moment. The constraints follow from the local buckling conditions and geometric restrictions. Moreover, there are optimized cross sections of beams, for which the shear center is located either in the web or in the centroid of the cross section. Results are compared and analyzed. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Optimum design of vibrating cantilevers

We determine the optimum tapering of a cantilever carrying an end mass, i.e., the shape which, for a given total mass, yields the highest possible value of the first fundamental frequency of harmonic bending vibrations in the vertical plane.Three different cases are considered. In the first case, all cross sections are assumed to be geometrically similar. In the second case, the cross sections are assumed to be rectangular and of given width. Finally, we consider a rectangular cross section of given height. This third case is shown to be degenerate in the absence of end mass.The first author takes the opportunity of thanking the authorities of the Technical University of Denmark for generous financial aid for his work at the University. We also thank our colleague Lic. Techn. Niels Olhoff for many valuable discussions during the course of the numerical computations.     

Mathematical modeling of electromagnetic wave propagation in heterogeneous lossy coaxial cables with variable cross section

In this work, we focus on the time-domain simulation of the propagation of electromagnetic waves in non-homogeneous lossy coaxial cables. The full 3D Maxwell equations, that described the propagation of current and electric potential in such cables, are classically not tackled directly, but instead a 1D scalar model known as the telegraphist's model is used. We aim at justifying, by means of asymptotic analysis, a time-domain “homogenized” telegraphist's model. This model, which includes a nonlocal in time operator, is obtained via asymptotic analysis, for a lossy coaxial cable whose cross section is not homogeneous.     

The optimal compliance problem for thin torsion rods: A 3D-1D analysis leading to Cheeger-type solutions

We consider the variational problem which consists in minimizing the compliance of a prescribed amount of isotropic elastic material placed into a given design region when it is subjected to a given load. We perform the asymptotics of this problem when the design region is a straight cylinder with infinitesimal cross section. The results presented in this Note concern the pure torsion regime and state the existence of optimal shapes for the limit problem. When the filling ratio tends in turn to zero, these optimal shapes concentrate on the boundary of the Cheeger set of the section of the design region.     

Effect of antioxidant distribution in polycaprolactam on the variation of strength and deformability at elevated temperatures

The effect of quinhydrone distribution over the cross section on the strength and deformability at elevated temperatures has been investigated for specimens of polycaprolactam. The optimum concentrations of quinhydrone in the surface layer of polycaprolactam retaining maximum strength over an extended period in a hot-air medium have been determined. The most probable areas of formation and localization of structural defects under thermal action have been established.Mekhanika Polimerov, Vol. 3, No. 2, pp. 296–301, 1967     

带人工雨线的拉索在风激励下的响应

通过在风洞中对一具有可调动力特性、雨线位置和风向角的带人工雨线的拉索模型进行了试验,研究了拉索的风雨激振特性.试验结果和其他研究人员的结果进行了仔细对比,得到了一些新的结论,澄清了过去的一些模糊认识.结果表明,带人工雨线的水平索在风向为零时的响应可以用Den Hartog驰振机制来解释,而风向不为零时,拉索表现为限速振动或限速和驰振的混合型振动.     

Flexural analysis of reinforced concrete T cross sections according to EC2 standard for strains εc2 smaller than 2.0‰

The paper discusses a detailed analysis of a concrete T cross section with the neutral axis within the web using the parabolic stress distribution for the design stress‐strain relationship of the concrete according to the EC2 standard.     

The offshore wind farm array cable layout problem: a planar open vehicle routing problem

In an offshore wind farm (OWF), the turbines are connected to a transformer by cable routes that cannot cross each other. Finding the minimum cost array cable layout thus amounts to a vehicle routing problem with the additional constraints that the routes must be embedded in the plane. For this problem, both exact and heuristic methods are of interest. We optimize cable layouts for real-world OWFs by a hop-indexed integer programming formulation, and develop a heuristic for computing layouts based on the Clarke and Wright savings heuristic for vehicle routing. Our heuristic computes layouts on average only 2% more expensive than the optimal layout. Finally, we present two problem extensions arising from real-world OWF cable layouts, and adapt the integer programming formulation to one of them. The thus obtained optimal layouts are up to 13% cheaper than the actually installed layouts.     

Optimal design of beams for prescribed compliance under alternative loads

A global optimality condition is established for minimum-weight design of sandwich beams with elementwise constant cross section for prescribed compliances in alternative states of loading. This condition requires a nonnegative linear combination of the mean-square curvatures of an element in the considered states of loading to have the same value for all elements. The use of the condition in the determination of the minimum-weight design is illustrated by examples.This research was sponsored by the Air Force Flight Dynamics Laboratory, Wright-Patterson Air Force Base, Ohio, under Contract No. F33615-69-C-1826. The authors wish to express their thanks to Professor J. B. Martin, Brown University, for helpful discussions.     

Mixed-integer models for topology optimization in sheet metal design

Topology optimization lies at the heart of many design tasks in mechanical engineering. For those sheet metal products that consist of a bundle of separate channels (such as conduits) we formulate the design task as a linear mixed-integer optimization problem. The design goal is to find a topology where each channel has a given cross section area, using a minimum amount of sheet met al. In addition to a light-weight design, stiffness should also be taken into account. The entire approach is demonstrated in the design of a conduit with five separate channels. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Behavior of waveguide modes in a neighborhood of the critical cross section

A curved waveguide of variable thickness filled with an inhomogeneous medium is considered. Shortwave asymptotic equations are obtained which describe the waveguide modes near the critical cross section. The amplitudes of waves reflected from the critical cross section and also of waves filtering through the postcritical section of the waveguide are obtained.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 42, pp. 181–188, 1974.     

隧洞围岩应力复变函数分析法中的解析函数求解

利用复变函数理论进行地下任意开挖断面隧洞围岩应力分析的前提,是根据围岩应力边界条件方程推导出两个解析函数．从Harnack定理出发,将隧洞围岩应力边界条件方程转化成积分方程;把Laurent级数有限项表示的映射函数引入积分方程中,将以任意开挖断面为边界条件的解析函数求解转化成以单位圆周线为边界条件的求解问题．对积分方程中各被积函数在讨论域内的解析性进行了分析,在此基础上利用留数理论求解了方程中各项积分值,并获得了用来表示任意开挖断面隧道围岩应力的两个解析函数通式．给出了圆形和椭圆形隧道的两个解析函数求解算例,所获得的结果与文献中的结果一致．利用留数理论推导出的两个解析函数通式,适用于任意开挖断面隧洞的围岩应力解析解的计算,且计算过程更为简单,计算结果更为精确．     

Nonisothermal gas flow in a long channel analyzed on the basis of the kinetic <Emphasis Type="Italic">S</Emphasis>-Model

The nonisothermal steady rarefied gas flow driven by a given pressure gradient (Poiseuille flow) or a temperature gradient (thermal creep) in a long channel (pipe) of an arbitrary cross section is studied on the basis of the linearized kinetic S-model. The solution is constructed using a high-order accurate conservative method. The numerical computations are performed for a circular pipe and for a cross section in the form of a regular polygon inscribed in a circle. The basic characteristic of interest is the gas flow rate through the channel. The solutions are compared with previously known results. The flow rates computed for various cross sections are also compared with the corresponding results for a circular pipe.     

Pressure of a plane stamp of nearly circular cross section on an elastic half-space : PMM vol. 40, n 6, 1976, pp. 1143–1145

An approximate method of solving the contact problem of impressing a plane stamp of nearly circular cross section into an elastic half-space is suggested. The friction of the contact surface is neglected. A numerical algorithm for the method is produced. An elliptical and rectangular stamps are considered as examples.There is no general method of solving the problems for stamps of nearly circular cross section. Apart from the classical problem of a plane elliptical stamp, the literature gives solutions for the problems of polygonal stamps, with each problem however requiring a different approach. An approximate solution for the problem of impressing a stamp of nearly circular cross section into an elastic half-space is given in [1]. The method makes it possible to use the same approach to solve the contact problem for an arbitrary region of contact, and to construct an universal numerical algorithm. The program can be adapted to each particular case by making the corresponding changes in the procedure of computing the Fourier coefficients of the equation of the boundary of the area of contact. Below a numerical algorithm for the approximate method in question is given. A more effective formulation of the solution is given for the case of the elliptical stamp.