Elastic Rods with Moderate Roration

Based on the theory of a directed or Cosserat curve of Green, Naghdi and several of their co-workers, several properly invariant approximate theories of an elastic rod are developed. The approximate theories are applicable when a rotation tensor associated with the motion of the rod is moderate. In one of these theories, some of the strains are moderate while others are small. A second theory where all of the strains are small is also developed. This revised version was published online in August 2006 with corrections to the Cover Date.     

On the Material Symmetry of Elastic Rods

This paper presents a treatment of material symmetry for hyperelastic rods. The rod theory of interest is based on a Cosserat (or directed) curve with two director fields, and was developed in a series of works by Green, Naghdi and several of their co-workers. The treatment is based on Murdoch and Cohen's work on material symmetry of Cosserat surfaces. Two material symmetry groups are discussed: one pertains to the strain-energy function, while the other pertains to the response functions. The paper closes by showing how the treatment relates to the form-invariant approach used in Green and Naghdi's papers and a treatment proposed recently by Cohen. This revised version was published online in July 2006 with corrections to the Cover Date.     

Elastic dynamics variational principle for nonlinear elastic body

Based on paper, the variational principle and generalized variational principle of elastic dynamics for elastic body with nonlinear stress-strain relations are introduced in this paper. The generalized instantaneous variational principle is also raised for the mixed harmonious displacement element and the mixed harmonious stress element.     

Saint-Venant's Principle in the Asymptotic Analysis of Elastic Rods with One End Fixed

The authors take advantage of an already stated Saint-Venant's principle for a linear elastic free rod to obtain a generalization in the case of the rod fixed on one end. The result is established for star-shaped cross sections and assumes some regularity on the axial forces. Also, an exposition of the technique and its conjecture for the case of the rod fixed on both of its ends is given.     

Deduction of Saint-Venant"s Principle for the Asymptotic Residue of Elastic Rods

Let u(ε) be a rescaled 3-dimensional displacement field solution of the linear elastic model for a free prismatic rod Ω^ε having cross section with diameter of order ε, and let u ⁽⁰⁾ –Bernoulli–Navier displacement – and u ⁽²⁾ be the two first terms derived from the asymptotic method. We analyze the residue r(ε) = u(ε) − (u ⁽⁰⁾ + ε² u ⁽²⁾) and if the cross section is star-shaped, we prove such residue presents a Saint-Venant"s phenomenon near the ends of the rod. This revised version was published online in August 2006 with corrections to the Cover Date.     

Theory of Supercoiled Elastic Rings with Self-Contact and Its Application to DNA Plasmids

Methods are presented for obtaining exact analytical representations of supercoiled equilibrium configurations of impenetrable elastic rods of circular cross-section that have been pretwisted and closed to form rings, and a discussion is given of applications in the theory of the elastic rod model for DNA. When, as here, self-contact is taken into account, and the rod is assumed to be inextensible, intrinsically straight, transversely isotropic, and homogeneous, the important parameters in the theory are the excess link Δℒ (a measure of the amount the rod was twisted before its ends were joined), the ratio ω of the coefficients of torsional and flexural rigidity, and the ratio d of cross-sectional diameter to the length of the axial curve C. Solutions of the equations of equilibrium are given for cases in which self-contact occurs at isolated points and along intervals. Bifurcation diagrams are presented as graphs of Δℒ versus the writhe of C and are employed for analysis of the stability of equilibrium configurations. It is shown that, in addition to primary, secondary, and tertiary branches that arise by successive bifurcations from the trivial branch made up of configurations for which the axial curve is a circle, there are families of equilibrium configurations that are isolas in the sense that they are not connected to bifurcation branches by paths of equilibrium configurations compatible with the assumed impenetrability of the rod. Each of the isolas found to date is connected to a bifurcation branch by a path which, although made up of solutions of the governing equations, contains regions on which the condition of impenetrability does not hold. This revised version was published online in July 2006 with corrections to the Cover Date.     

Bounds for the Effective Elastic Properties of Completely Random Planar Polycrystals

Bounds have been developed for the elastic moduli of completely random planar polycrystals, the shape and crystalline orientations of the constituent grains of which are supposed to be uncorrelated. Explicit results for the aggregates of orthotropic crystals are demonstrated. This revised version was published online in August 2006 with corrections to the Cover Date.     

带孔隙损伤的弹性固体的广义变分原理

应用弹性微结构理论,建立了具广义力场带孔隙损伤线弹性固体的基本模型．应用变积方法,同时分别建立了带孔隙损伤弹性固体四类和两类变量的广义变分原理,这些变分原理对应着带孔隙损伤弹性固体微分方程和初值边值条件．应用弹性微结构理论,建立了带孔隙损伤的弹性Timoshenko 梁的基本方程,得到带孔隙损伤的弹性Timoshenko 梁两类变量的广义变分原理．这些广义变分原理为近似求解带孔隙损伤的弹性问题提供了有效途径．     

非圆截面弹性细杆的螺旋线平衡及稳定性

本文研究端部受力和力矩作用，且存在初曲率和初扭率的非圆截面弹性细杆的螺旋线平衡及其稳定性。描述弹性细杆平衡状态的Kirchhoff方程存在与杆的螺旋线平衡状态相对应的特解。直杆和圆环杆为螺旋线状态的两种特例。文中分析了螺旋线的几何特性与作用力和力矩之间的相互关系，并导出螺旋线平衡的一次近似解析形式稳定性判据。分析表明，松弛状态下弹性杆可处于螺旋线状态，直杆只有在轴向压力的作用下才能保持螺旋线平衡。无初曲率和初扭率弹性杆的螺旋线平衡稳定性必要条件是杆截面绕副法线轴的抗弯刚度大于或等于绕法线轴的抗弯刚度。此条件也适用于带初扭率的圆环杆及更普遍情形。无初曲率和初扭率的圆截面杆的螺旋线平衡恒稳定。     

多阶变截面杆的弹性稳定计算

本文研究单阶和多阶截面杆在集中和分布轴向荷载作用下的弹性稳定计算方法,首次给出了其整体稳定和局部稳定的解析解.     

非圆截面弹性细杆的平衡稳定性与分岔

本文研究存在初始曲率或挠率的非圆截面弹性细杆的平衡及稳定性问题,在两端受力矩单儿作用的条件下,杆的平衡微分方程可转换为用欧拉角表述的一阶自治系统,并有可能利用相平面的奇点理论分析弹性细杆平衡状态的稳定性,文中对杆截面的对称性,以及杆的初始曲率和挠率对平衡状态性的影响进行了定性分析,导出了解析形式的稳定性判据,揭示了杆平衡状态的列态分岔现象。     

Structural function theory of generalized variational principles for linear elastic materials with voids

In this paper,we have obtained generalized variational principles for linear elasticmaterials with voids from structural function theory.Correspondent relations betweenstructural functions and generalized variational principles are given.     

带圆开孔的弹性约束适度椭圆板的自由振动分析

采用弹性理论并结合边界摄动技术,对带中心圆孔的适度椭圆薄板的自由振动基频进行了分析．当薄板的内边界受弹性约束,外边界为自由,导出了自由振动基频的解析解．同时,利用ANSYS软件进行了数值模拟,通过经典边界条件下基频结果的对比,验证了基于本文理论解的计算结果的精确性．本方法可以有效用于处理具有曲线边界的薄板结构的自由振动问题．     

无网格方法中本质边界条件的处理

基于新的离散模定义，采用移动最小二乘近似方法，给出了场变量的近似表达形式；从约束变分原理出发，给出了无网格方法中新的本质边界条件的处理方案——罚函数法；对权函数、罚函数的选择对计算精度的影响进行了研究。数值计算结果表明该方法不仅简单合理，而且具有较高的精度和稳定性。     

A planar rod model with flexible cross-section for the folding and the dynamic deployment of tape springs: Improvements and comparisons with experiments

A planar rod model with flexible cross-section has been recently proposed in literature (Guinot et al., 2012). This model is especially suitable for the modeling of tape springs, which develop localized folds due to the flattening of the cross-section. Starting from a complete non-linear elastic shell model, original kinematics assumptions (inspired from the elastica model) have been made to describe the important in-plane changes of the cross-section shape. In the present work, the choice of the position of the rod reference line is discussed. This choice plays an important role in the overall behavior because of the large changes of the cross-section shape. We show that the model published in Guinot et al. (2012) can be improved by considering the centerline as the rod reference line. This enhanced model is then validated through quantitative comparisons with experimental results of dynamic deployments taken from literature.     

Existence and Integral Representations of Weak Solutions for Elastic Plates with Cracks

The existence and continuous dependence on the data are investigated in Sobolev spaces for the problem of bending of a Reissner-Mindlin-type plate weakened by a crack when the displacements or the moments and force are prescribed along the two sides of the crack. The cases of both an infinite and a finite plate are considered, and representations are sought for the solutions in terms of single layer and double layer potentials with distributional densities. This revised version was published online in August 2006 with corrections to the Cover Date.     

THE FIRST ORDER APPROXIMATION OF NON-KIRCHHOFF-LOVE THEORY FOR ELASTIC CIRCULAR PLATE WITH FIXED BOUNDARY UNDER UNIFORM SURFACE LOADING (Ⅰ)

Based on the approximation theory adopting non-kirchhoff-Love assumption for three dimensional elastic plates with arbitrary shapes^[1],[2], the author derives a functional of generalized variation for three dimensional elastic circular plates, thereby obtains a set of differential equations and the relate boundary conditions to establish a first order approximation theory for elastic circular plate with fixed boundary and under uniform loading on one of its surface. The analytical solution of this problem will present in another paper.     

弹性接触问题的常刚度迭代方法及其加速

通过引入接触间隙荷载，在荷载项中反映接触状态变化的影响，避免了重新形成接触刚度矩阵，构造了弹性接触问题的常刚度迭代格式。然后借助于不动点迭代的Steffensen加速技术给出了一种求解弹性接触问题的常刚度迭代加速算法。文中最后给出两个算例表明了本文方法的有效性。     

拉压不同弹性模量薄板上圆孔的应力分析

采用弹性理论研究了拉压不同弹性模量薄板上圆孔的孔边应力集中问题．采用广义虎克定律推导出了拉压不同弹性模量薄板上圆孔边的应力平衡方程,并联合利用应力函数及边界条件得到了拉压不同弹性模量薄板上圆孔边的应力表达式．算例分析表明,当薄板材料的拉压弹性模量相差较大时,采用经典弹性理论研究薄板上圆孔的孔边应力是不合适的,当经典弹性理论与拉压不同弹性模量弹性理论的计算结果间的差别超过工程允许误差5%时,应该采用拉压不同弹性模量弹性理论进行计算．     

Solving Stress Problems for Elastic Systems of Anisotropic Shells of Revolution with Regard for Transverse Shear and Reduction

An approach is proposed for refined solution of stress problems for elastic systems consisting of coaxial shells of revolution. Transverse shear and reduction are taken into account. Multivariant calculations made for orthotropic cylindrical shells with elliptical end-plates allow us to analyze the influence of the semiaxis ratio and intermediate supports on the stress–strain state of the shell systems under consideration