自主泳动弹性绳的轨迹模拟

研究柔性结构与流体间耦合作用,可以促进软体机器人的发展.通过速度快、精度高的数值模拟方法模拟水下机器人的实时运动轨迹,可以为真实实验提供测试方向与理论牵引,增大实验成功的可能性.本文研究有自主运动趋势的弹性绳在二维流场中的运动轨迹.首先,对弹性绳离散化建模并同时考虑拉压与扭转弹性力,从能量角度建立动力学方程,此模型可以较为真实地反映弹性绳内力对其运动产生的作用.然后基于半拉格朗日法建立流体求解器. 最后,提出简化的基于动量方程的浸入边界法作为耦合算法,通过直接修正网格速度代替浸入边界力法中力源项的作用.使用这种算法求解耦合作用兼具简便性与快速性.对弹性绳模型、流体模型与简化耦合模型依次解算,模拟了正弦形式波动弹性绳在水中的运动轨迹.结果显示,弹性绳在弹性内力与流固相互作用力共同影响下,该种新的浸入边界法可以实现对水下弹性绳运动轨迹的模拟.数值实验显示弹性绳的自主运动参考模型的初相位改变时,其前进方向会发生改变.该仿真模拟算法与平台可以为细长形软体水生机器人的研发提供参考.      

GENERALIZATION OF KIRCHHOFF KINETIC ANALOGY TO THIN ELASTIC SHELLS 1)

将弹性细杆的"Kirchhoff动力学比拟"方法推广到弹性薄壳,使弹性薄壳的变形在物理概念上和刚体的运动对应, 在数学表述上等同,从而可以用刚体动力学的理论和方法研究弹性薄壳的变形,为连续的弹性薄壳提供新的离散化方法. 在直法线假设下,在弹性中面上构筑空间正交轴系, 此轴系沿坐标线"运动"的角速度构成两自变量的弯扭度. 沿两个坐标线的弯扭度表达了弹性薄壳的变形和位形,证明了弯扭度之间以及弯扭度与中面切矢间的相容关系. 用Euler角和Lam$\acute{e}$系数表达了非完整约束和中面位形的微分方程,用弯扭度和Lam$\acute{e}$系数表达了应变和应力以及内力及其本构方程.导出了用分布内力集度表达的弹性薄壳在变形后位形上的平衡偏微分方程组,方程的形式与刚体动力学的Euler方程和弹性细杆的Kirchhoff方程具有相似性,实现了Kirchhoff动力学比拟对弹性薄壳的推广.总结了弹性薄壳静力学和刚体动力学以及弹性细杆静力学在概念上的比拟关系.最后给出了一个算例. 为研究弹性薄壳的变形和运动提供新的建模方法和研究思路.也可进一步推广到弹性薄壳动力学.     

Propagation of elastic waves in circular rods homogeneous over the cross section

Propagation of elastic waves in circular rods and in rods with a cylindrical cavity is numerically studied. The influence of the rod size on the wave propagation velocity is analyzed. A phenomenon of repeated rebound in short homogeneous rods is described.     

Kirchhoff动力学比拟对弹性薄壳的推广

将弹性细杆的"Kirchhoff动力学比拟"方法推广到弹性薄壳,使弹性薄壳的变形在物理概念上和刚体的运动对应, 在数学表述上等同,从而可以用刚体动力学的理论和方法研究弹性薄壳的变形,为连续的弹性薄壳提供新的离散化方法. 在直法线假设下,在弹性中面上构筑空间正交轴系, 此轴系沿坐标线"运动"的角速度构成两自变量的弯扭度. 沿两个坐标线的弯扭度表达了弹性薄壳的变形和位形,证明了弯扭度之间以及弯扭度与中面切矢间的相容关系. 用Euler角和Lam$\acute{e}$系数表达了非完整约束和中面位形的微分方程,用弯扭度和Lam$\acute{e}$系数表达了应变和应力以及内力及其本构方程.导出了用分布内力集度表达的弹性薄壳在变形后位形上的平衡偏微分方程组,方程的形式与刚体动力学的Euler方程和弹性细杆的Kirchhoff方程具有相似性,实现了Kirchhoff动力学比拟对弹性薄壳的推广.总结了弹性薄壳静力学和刚体动力学以及弹性细杆静力学在概念上的比拟关系.最后给出了一个算例. 为研究弹性薄壳的变形和运动提供新的建模方法和研究思路.也可进一步推广到弹性薄壳动力学.      

由基模态构造任意支撑杆的多项式型轴向刚度

给出了当杆的横截面积均匀而材料线密度为已知多项式时，由基模态构造任意支撑方式下杆的多项式型的轴向刚度系致的方法，证明了所得轴向刚度的正值性．     

A properly invariant theory of small deformations superposed on large deformations of an elastic rod

In the context of the direct or Cosserat theory of rods developed by Green, Naghdi and several of their co-workers, this paper is concerned with the development of a theory of small deformations which are superposed on large deformations. The resulting theory is properly invariant under all superposed rigid body motions. Furthermore, it is also valid for elastic rods which are subject to kinematical constraints, and it specializes to a linear theory of an elastic rod which is invariant under superposed rigid body motions. The construction of these theories is based on the method developed by Casey & Naghdi [1] who established similar theories for unconstrained nonpolar elastic bodies.     

A Variational Rod Model with a Singular Nonlocal Potential

The classical theory of elastic rods does not account for the possibility that large deformations may involve distinct points along the rod occupying the same physical space. We develop an elastic rod model with a pairwise repulsive potential such that, if two non-adjacent points along the rod are close in physical space, there is an energy barrier which prevents contact while for points nearby along the rod the potential is describable classically. This framework is developed to prove the existence of minimizers within each homotopy class, where the idea of topological homotopy of a curve is generalized to elastic rods as framed curves. Finally, the relevant first-order optimality conditions are derived and used to investigate the regularity of minimizers.     

Time- and frequency-domain analysis using lumped mass global collocation

Quite recently, a novel global collocation method for the eigenvalue analysis of freely vibrated elastic structures was proposed (Archive of Applied Mechanics: DOI: ). This paper extends the latter methodology on several levels, in both the time and frequency domain. Firstly the formulation is updated so that it can also deal with rods of variable cross section. Then, the fully populated mass matrices of the previous formulation are properly replaced by lumped masses, thus saving still more computer effort. Subsequently, a new general formulation for the transient response analysis is proposed. Finally, a novel procedure for the coupling of two neighboring collinear rods is presented. The theory is supported by six test cases concerning elastic rods of constant and variable cross sections. Among these, transient analysis refers to the response of a single rod due to a Heaviside-type loading as well as to the impact between two collinear rods of different cross sections.     

轴向冲击载荷作用下直杆弹性动态屈曲的研究

本文利用分叉的概念,从应力波理论出发,把轴向冲击载荷作用下直杆的弹性动态屈曲问题化为特征值问题,从而导出直杆动态屈曲的临界分叉准则。同时,本文对一端固支直杆受轴向冲击时的弹性屈曲问题进行了实验研究,测到的临界屈曲时间和理论预计值基本符合,证实了理论模型的合理性.理论和实验两方面的结果都表明,直杆受轴向冲击载荷作用时的屈曲现象发生在波动过程的前期,因此在处理这类问题时考虑波动效应是必要的。     

Postbuckling Behavior of Compressed Rods in an Elastic Medium

The postbuckling of rods loaded by a compressive force P in an elastic medium is considered. The resolving nonlinear equation is obtained, and a method for solving this equation is given. It is shown that, for large lengths, in contrast to the case without elastic medium, the deflection increases as the force P decreases after the loss of stability. Several simple finite-element models, namely, the problems of compression of multilink rods with links connected by springs, are considered to confirm this effect.     

Multivalued solutions of the spatial problems of nonlinear deformation of thin curvilinear rods

We have developed a finite-element model to study the spatial deformation of elastic rods at large displacements. A numerical algorithm for constructing multivalued nonlinear solutions in the presence of many bifurcation and limit points is formulated. Results of a study of the stability supercritical equilibrium forms of elastic rods, which were supported experimentally, are reported. Chaplygin Siberian Aviation Institute, Novosibirsk 630051. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 2, pp. 141–149, March–April, 1998.     

Nonlinear spatial bending of shear-deformable curvilinear rods

A finite element is proposed for analyzing nonlinear deformation and stability of three-dimensional rods at arbitrarily large elastic displacements. Timoshenko’s model is used for taking transverse shear strains into account. The accuracy and convergence of numerical solutions are studied by an example of problems of nonlinear bending of curvilinear rods.     

On the free shapes of elastic rods

The problem of free shape consists in finding the form that an elastic body must have in a natural state in order that it shall assume a given form in an equilibrium configuration under the action of assigned loads. The problem, that is of interest in itself, arises in some practical applications and can constitute a preliminary step in the study of some mechanical properties of classes of equilibrium configurations that are not natural states. This paper examines the problem of free shape for inextensible elastic rods which in equilibrium are subject only to the action of forces and couples applied to the ends, and whose deformations can be described by the theory of finite displacements of thin rods due to Kirchhoff. After the general equations governing the problem have been deduced, they are employed to give a classification of the free shapes of rods that in equilibrium are circular rings.     

On the theory of porous elastic rods

We consider the direct approach to the theory of rods, in which the thin body is modelled as a deformable curve with a triad of rigidly rotating orthonormal vectors attached to every material point. In this context, we employ the theory of elastic materials with voids to describe the mechanical behavior of porous rods. First, we derive the dynamical nonlinear field equations of the model. Then, in the framework of linear theory, we prove the uniqueness of the solution to the associated boundary-initial-value problem. We identify the relevant field quantities from the theory of directed curves by comparison with the three-dimensional equations of straight porous rods. Finally, for orthotropic and homogeneous rods, we determine the constitutive coefficients in terms of the three-dimensional elasticity constants by solving several problems in the two different approaches.     

Experimental investigation of longitudinal wave propagation in an elastic rod with coulomb friction

This paper presents the experimental results obtained from the propagation of a compression stress wave generated by the longitudinal impact of two cylindrical elastic rods. One of these rods is subjected to a uniformly distributed coulomb-friction force. In order to determine the stress-wave shape and the decay rate, the rod is subjected to longitudinal impact for different values of coulomb friction. As the stress wave propagates along the rod, it is measured at strain-gage stations located on the stationary rod.In order to correlate the experimental results, the solution of the modified wave equation with coulomb friction is obtained for the longitudinal impact of two semi-infinite rods.     

Large elastic deformations in thin cantilever rods due to concentrated loadings

In this paper the problem of large elastic deformations in cantilever thin rods subjected to concentrated loads is considered. Taking into account the incompressibility assumption of the center line and the equations relating the internal moments with the curvatures and torsion of the rod before and after the deformation, the non-linear equilibrium system, composed of six coupled differential equations of first order, is transformed to a new system of higher order. The cases of geometries of initially curved rods and their cross-sections were investigated, for which the higher order system of equations may be decoupled and solved in a closed form. Several applications of thin curved cantilever rods were made and the potentialities of the method were shown with these examples.     

Efficiency of a corrugated shell as a radial spring

This paper deals with the problem of radial support of prismatical rods. The radial expansion of the rods and the limits of radial pressure acting on them are prescribed, so that an upper limit of the spring rate is imposed. The weight of the radial support must be kept as low as possible; hence, its efficiency of material utilization should be high. Specifically, the efficiency of a corrugated cylindrical shell employed as a radial-spring system is investigated. As a preliminary convenience, general formulas are set up to describe the efficiency of material utilization in springs. Then, the elastic properties and the stresses of corrugated shells with various shapes of convolutes are established. Finally, from the formulas for the spring efficiency, the elastic properties, and the stress of the corrugated shells, their efficiency of material utilization as springs is established.     

Isogeometric collocation for nonlinear dynamic analysis of Cosserat rods with frictional contact

Nonlinear Dynamics - We present a novel isogeometric collocation method for nonlinear dynamic analysis of three-dimensional, slender, elastic rods. The approach is based on the geometrically exact...     

Wave-based defect detection and interwire friction modeling for overhead transmission lines

In this study, the feasibility of continuous, online monitoring of power lines using ultrasonic waves is considered. Local and global wave-based approaches for wire break detection in overhead transmission lines are presented. Both methods use a sending/receiving transducer to generate an ultrasonic, longitudinal, elastic wave in the cable. Defects in the cable cause a portion of the incident ultrasonic wave to be reflected back to the transducer, which when received, can be used to identify the presence of the defect. Although the transducers can only be attached to the surface of the cable, subsurface wires can also be interrogated since elastic energy spreads to these wires through friction contact. This study also explores how the elastic energy of a propagating wave becomes distributed among contacting rods via friction contact. This work focuses specifically on a two-rod system in which the wave energy from an excited “active” rod is transmitted to a neighboring “passive” rod through friction contact. An energy-based model is used to approximate the time average elastic wave power in the two rods as a function of propagation distance. Power predictions from the energy-based model compare well with experimental measurements and finite element simulations.