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。     

Stretchability and compliance of freestanding serpentine-shaped ribbons

High-performance stretchable electronics have to utilize high-quality inorganic electronic materials such as silicon, oxide or nitride dielectrics, and metals. These inorganic materials usually crack or yield at very small intrinsic strains, for example, 1%, whereas bio-integrated electronics are expected to at least match the stretchability of bio-tissues (20%) and deployable structure health monitoring networks are expected to expand from wafer scale (several centimeters) to cover macroscopic structures (several meters). To minimize strains in inorganic materials under large deformation, metallic and ceramic films can be patterned into serpentine-shaped ribbons. When the ribbon is stretched, some sections of the ribbon can rotate and/or buckle to accommodate the applied displacement, leaving much smaller intrinsic strain in the materials compared to the applied strain. The choice of the shape of the serpentine depends on systematic studies of the geometric variables. This paper investigates the effect of serpentine shapes on their stretchability and compliance through theoretical, numerical, and experimental means. Our closed-form curved beam solutions, FEM results, and experimental measurements have found good agreement with one another. Our results conclude that in general, the narrower ribbon, the larger arc radius and arc angle, and the longer arm length will yield lower intrinsic strain and effective stiffness. When the arm length approaches infinite, the stretchability can be enhanced by several orders. A few unexpected behaviors are found at arc angles that are close to straight bars. With additional practical constraints such as minimum ribbon width and finite overall breadth, the optimal serpentine shape can be accurately determined using our closed-form analytical solution.     

Circulation and mixing times for helical ribbon impellers. Review and Experiments

 The purpose of this paper is to extend basic information on mixing and circulation times for mixing systems equipped with helical ribbon impellers. In a first part, from a survey of existing literature, we have reviewed the different effects of the geometrical parameters of the helical mixing systems (clearance-wall, pitch size ratio, blade width, number of blades) on the mixing process. From this qualitative analysis, useful guidelines are provided on the influence of the helical impeller geometry on the mixing effectiveness. In a second part, the homogenization effectiveness of an atypical helical ribbon impeller was investigated and compared with the performance of classical helical ribbons impellers. Received: 1 December 1998/Accepted: 22 April 1999     

Tensile behaviors of pre-twisted composite strands

In this paper, we address the tensile behaviors of pre-twisted composite strands, which consists of a pre-twisted single core filament surrounded by n-helical side filaments. Based on the extensible rod with zero bending and small twisting moduli for the core filament and inextensible rod for the side filaments, we develop the analytical method of the tensile behaviors of pre-twisted composite strands. Using a numerical continuation scheme, we elucidate the effects of microscopic factors such as initial helical angle, pre-twist of core filament, ratio of elastic modulus of core to that of side filament, and the number of the side filaments on the macroscopic tensile behavior of the strand as a whole structure. As a result, we show that the behavior is not trivial, even though the filament is a linear elastic due to the interplay of both geometrical constraint and finite deformation of the strand.     

Generalized forces in the description of creep processes in beam elements

The intensity of the creep process and the time to rupture in bending and twisting of beam elements with various shapes are estimated. These estimates are compared with the use of equivalent external generalized forces.     

Flexural rigidity of honeycomb consisting of hexagonal cells

In this study,the flexural rigidity of a honeycomb consisting of regular hexagonal cells is investigated.It is found that the honeycomb bending can not be evaluated by using the equivalent elastic moduli obtained from the in-plane deformation because the moments acting on the inclined cell wall are different for in-plane deformation and bending deformation.Based on the fact that the inclined wall is twisted under the condition of the rotation angle in both connection edges being zero,a theoretical technique for calculating the flexural rigidity of honeycombs is proposed,and the validity of the present analysis is demonstrated by numerical results obtained by BFM.     

Analysis of bending, vibration and stability for thin plate on elastic foundation by the multivariable spline element method

I.IntroductionTheplatestructuresonelasticfoundationareofpracticalimportanceinwide-spreadapplicationsinengineering.Basedonrapidprogressofscienceandtechnologyaswellasengineeringconstructions,differentmodelsofeIasticfoundationaredeve1oped,sucha,Winkler,Vlazo…     

Experiments and theory in strain gradient elasticity

Conventional strain-based mechanics theory does not account for contributions from strain gradients. Failure to include strain gradient contributions can lead to underestimates of stresses and size-dependent behaviors in small-scale structures. In this paper, a new set of higher-order metrics is developed to characterize strain gradient behaviors. This set enables the application of the higher-order equilibrium conditions to strain gradient elasticity theory and reduces the number of independent elastic length scale parameters from five to three. On the basis of this new strain gradient theory, a strain gradient elastic bending theory for plane-strain beams is developed. Solutions for cantilever bending with a moment and line force applied at the free end are constructed based on the new higher-order bending theory. In classical bending theory, the normalized bending rigidity is independent of the length and thickness of the beam. In the solutions developed from the higher-order bending theory, the normalized higher-order bending rigidity has a new dependence on the thickness of the beam and on a higher-order bending parameter, b_h. To determine the significance of the size dependence, we fabricated micron-sized beams and conducted bending tests using a nanoindenter. We found that the normalized beam rigidity exhibited an inverse squared dependence on the beam's thickness as predicted by the strain gradient elastic bending theory, and that the higher-order bending parameter, b_h, is on the micron-scale. Potential errors from the experiments, model and fabrication were estimated and determined to be small relative to the observed increase in beam's bending rigidity. The present results indicate that the elastic strain gradient effect is significant in elastic deformation of small-scale structures.     

Mechanical response of fabric sheets to three-dimensional bending,twisting, and stretching

A model for the mechanics of woven fabrics is developed in the framework of two-dimensional elastic surface theory. Thickness effects are modeled indirectly in terms of appropriate constitutive equations. The model accounts for the strain of the fabric and additional effects associated with the normal bending, geodesic bending, and twisting of the constituent fibers.     

A Helical Cauchy-Born Rule for Special Cosserat Rod Modeling of Nano and Continuum Rods

We present a novel scheme to derive nonlinearly elastic constitutive laws for special Cosserat rod modeling of nano and continuum rods. We first construct a 6-parameter (corresponding to the six strains in the theory of special Cosserat rods) family of helical rod configurations subjected to uniform strain along their arc-length. The uniformity in strain then enables us to deduce the constitutive laws by just solving the warping of the helical rod’s cross-section (smallest repeating cell for nanorods) but under certain constraints. The constraints are shown to be critical in the absence of which, the 6-parameter family reduces to a well known 2-parameter family of uniform helical equilibria. An explicit formula for the 6-parameter helical map is derived which maps atoms in the repeating cell of a nanorod to their images for the purpose of repeating cell energy minimization. A scheme for the passage from nano to continuum scale is also presented to derive the constitutive laws of a continuum rod via atomistic calculations of nanorods. The bending, twisting, stretching and shearing stiffnesses of diamond nanorods and carbon nanotubes are computed to demonstrate our theory. We show that our scheme is more general and accurate than existing schemes allowing us to deduce shearing stiffness and several coupling stiffnesses of a nanorod for the first time.     

The crack tip fields of orthotropic composite plate under bending

1MechhacalModelThefractUreproblemwhichisthesameasthatinpaper[I]isfurtherdiscussedinthispaper.TheanalysisoffractUrebehavioursnearcracktipforinfinitelinearelasticorthotropiccompositeplatewithacentralthroughcrackoflengthZaiscarriedout.ThegeometryandloadingcondihonsareshowninFig.1.Tosolvesuchaproblem,weneedtosolvethepanaldifferentialequationwiththefollowingboundaryconditions:wherewisdeflectionofcoddleplane;M.andM,arebendingmoment,Ma.istwistingmoment,andstiffnessmatrixFromthetheoryofplateL'],w…     

离散多层厚壁爆炸容器抗爆炸性能试验研究

为了研究离散多层爆炸容器的动力响应和破坏特性,制造了尺寸和材料相同但钢带缠绕倾角不同的三台离散多层试验容器,并进行了一系列大药量的中心加载试验,测量了典型位置的应变。结果表明中心装药时三台试验容器的破坏都在爆心截面处,钢带缠绕倾角较小的容器能够承受更大炸药量的爆炸作用,容器具有较好的抗内爆炸性能。     

螺旋细杆的均匀扭转振动

讨论螺旋细杆的特殊形式扭转振动，即均匀扭转振动．以非圆截面杆和有原始曲率的圆截面杆为研究对象．杆作均匀扭转振动时各截面有相同的扭角变化规律，且杆中心线的几何形状不受振动过程的影响．研究表明，扭振来源于杆截面的非对称性及杆的原始曲率．杆的扭振规律与单摆运动相似，其动力学方程存在精确解．圆环杆的均匀扭振为螺旋杆的倾角为零时的特例．     

On Solutions to Euler-Lagrange Equations Governing Isotropic, Homogeneous, Naturally Curved Kirchhoff��s Elastic Rods

Motivated by the elastic rod model for DNA with intrinsic curvature, we study the solution space of the Euler-Lagrange equations governing isotropic, homogeneous, naturally curved Kirchhoff??s elastic thin rods. Our studies show that for each given total energy and twisting density, there are at most three solutions, aside from the case where the twisting density is some particular constant. We also propose in this paper a reasonable condition under which an improvement on the number of the solutions may be possible. Finally, numerical calculations are presented to support our conclusions.     

Analysis of bending and buckling of pre-twisted beams: A bioinspired study

Twisting chirality is widely observed in artificial and natural materials and structures at different length scales. In this paper, we theoretically investigate the effect of twisting chiral morphology on the mechanical properties of elas- tic beams by using the Timoshenko beam model. Particular attention is paid to the transverse bending and axial buckling of a pre-twisted rectangular beam. The analytical solution is first derived for the deflection of a clamped-free beam under a uniformly or periodically distributed transverse force. The critical buckling condition of the beam subjected to its self- weight and an axial compressive force is further solved. The results show that the twisting morphology can significantly improve the resistance of beams to both transverse bending and axial buckling. This study helps understand some phenomena associated with twisting chirality in nature and provides inspirations for the design of novel devices and structures.     

Analytical solution for bending stress intensity factor in an orthotropic elastic plate containing a crack and subjected to concentrated moments

The problem of estimating the bending stress distribution in the neighborhood of a crack located on a single line in an orthotropic elastic plate of constant thickness subjected to out-of-plane concentrated moments is examined. Using classical plate theory and integral transform techniques, the general formulae for the bending moment and twisting moment in an elastic plate containing cracks located on a single line are derived. The solution is obtained in a closed form for the case in which there is a single crack in an infinite plate subjected to symmetric concentrated moments.     

Steady-state whirling motions of thin filaments

The steady-state whirling motion of linear elastic filaments under self-weight with rotary excitation at one end and free at the other is examined; specifically, the effect of bending rigidity is investigated both theoretically and experimentally. Similarities between the problem of a perfectly flexible string and filament with non-negligible bending stiffness are exploited in identifying the possible modes of oscillation. The theoretical predictions have been compared with the experimental results for thin filaments with different bending rigidities to demonstrate the effect of bending directly.     

Integral Solution of a Problem with Non-Standard Boundary Conditions in an Enhanced Theory of Bending of Elastic Plates

A modified boundary integral equation method is used to solve a specific type of mixed boundary value problem in an enhanced theory of bending of elastic plates in which the effects of transverse shear deformation and transverse normal strain are taken into account. The problem considered is characterized by the fact that a combination of transverse displacement and bending and twisting moments is prescribed on the curve which bounds the middle surface of the plate. Both interior and exterior problems are formulated and the corresponding existence and uniqueness results derived.     

Solitary waves in longitudinally wrinkled and creased helicoids

Elastic ribbons subjected to twist and stretch handle multiple morphological instabilities, amongst others, the longitudinally wrinkled and creased helicoids are investigated in the present paper as promising periodic nonlinear waveguides. Modeling the ribbon by isogeometric Kirchhoff–Love shells, the first longitudinal buckling mode is recovered numerically and used into the Bloch–Floquet method to obtain dispersion curves. After analyzing the effects of the buckling pattern on the different wavemodes, it is shown that classical linear axial waves interact with bending ones and become dispersive. Additionally, as buckling involves geometrical nonlinearities, the structure is expected to host stable nonlinear waves. Indeed, clear supersonic rarefaction trains are observed experimentally and their characteristics are found in agreement with the weakly nonlinear Boussinesq model.     

Stress analysis of a semi-infinite plate with an oblique edge crack

Summary A semi-infinite plate with an oblique edge crack is analyzed as a thin plate bending problem and a plane elastic problem. The rational mapping function of the sum of fractional expressions and the complex variable method are used. Closed solutions are obtained for these respective problems. Stress distributions, stress intensity factors are investigated for loads causing transverse bending, twisting and uniform tension. The relations between the stress intensity factors and the angle of the oblique edge crack are also investigated.

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Übersicht Eine halbunendliche Platte mit schrägem Anriß wird als Platten- und Scheiben-Problem analysiert. Es werden die Abbildungsfunktionen als die Summe von Partialbruchzerlegungen und die Methode komplexer Veränderlicher zur Analyse verwendet. Damit lassen sich geschlossene Lösungen ausrechnen. Die Lastfälle Querbiegung, Torsion und gleichförmiger Zug werden bezüglich Spannungsverteilung und Spannungsintensitätsfaktor untersucht. Der Zusammenhang zwischen Spannungsintensitätsfaktor und Winkellage des Anrisses wird hergestellt.