Equivariant Sternberg–Chen Theorem

Smooth (C ) vector fields with linear symmetries and anti-symmetries are considered. We prove that provided symmetry group is compact then a smooth conjugacy in Sternberg–Chen Theorem can be chosen symmetric.     

In General There Are No Unsheared Tetrads

Suppose the principal stretches are all different at a point P in a deformed body. In this case, it has been shown [1] that generally there is an infinity of non coplanar infinitesimal material line elements at P which remain unsheared following the deformation – that is, the angle between the arms of each pair of material line elements forming the triad remains unchanged. Here it is shown that in this case when all three principal stretches at P are different, there is no set of four infinitesimal material line elements, no three of which are coplanar, and such that the angle between each pair of the six pairs of material line elements is unchanged following the deformation. It is only when all three principal stretches at P are equal to each other, that there are unsheared tetrads at P, and in that case all tetrads are unsheared. This revised version was published online in June 2006 with corrections to the Cover Date.     

Termination of the starting problem of dynamic expansion of a spherical cavity in an infinite elastic-perfectly-plastic medium

Perhaps the simplest non-trivial problem in small deformation dynamic plasticity is expansion of a spherical cavity in an infinite elastic-perfectly-plastic medium. Here, example problems are considered with two boundary conditions at the cavity's surface: constant velocity and constant pressure. Attempts to obtain analytical solutions are complicated by the fact that, in general, the elastic-plastic boundary propagates with variable speed. However, it is known that the elastic-plastic boundary propagates at constant speed for the starting problem when the shocks due to the applied loads are large enough to cause inelastic response at the instant they are applied. When the value of the applied pressure equals the shock pressure due to the applied velocity the solutions of the two boundary value problems are initially identical and can be compared. The objective of this paper is to review the literature and to examine the termination conditions for the starting problem. Specifically, the starting problem terminates when either the jump in radial stress at the elastic-plastic boundary or the loading condition for plasticity vanishes there. These termination conditions depend on the applied load and on Poisson's ratio.     

Dynamic analysis of geometrically nonlinear robot manipulators

In this paper, a method for the dynamic analysis of geometrically nonlinear elastic robot manipulators is presented. Robot arm elasticity is introduced using a finite element method which allows for the gross arm rotations. A shape function which accounts for the combined effects of rotary inertia and shear deformation is employed to describe the arm deformation relative to a selected component reference. Geometric elastic nonlinearities are introduced into the formulation by retaining the quadratic terms in the strain-displacement relationships. This has lead to a new stiffness matrix that depends on the rotary inertia and shear deformation and which has to be iteratively updated during the dynamic simulation. Mechanical joints are introduced into the formulation using a set of nonlinear algebraic constraint equations. A set of independent coordinates is identified over each subinterval and is employed to define the system state equations. In order to exemplify the analysis, a two-armed robot manipulator is solved. In this example, the effect of introducing geometric elastic nonlinearities and inertia nonlinearities on the robot arm kinematics, deformations, joint reaction forces and end-effector trajectory are investigated.     

单壁碳纳米管中稳态机械波的激发条件研究

通过分子动力学模拟,对单壁碳纳米管中稳态机械波的激发条件进行了详细的研究.利用所施加的周期性机械外力,使单壁碳纳米管产生局部径向形变,该形变将以单壁碳纳米管的管壁为弹性媒质传播开去,从而在单壁碳纳米管中形成机械波;机械波产生的条件依赖于单壁碳纳米管波动系统能量的维持和受迫振动区域形变方向的控制;稳定机械波形成的最佳条件是碳纳米管的形变度和受迫振动频率之间的最优匹配,以及由此形成的单壁碳纳米管在周期性外力作用下产生的共振.     

A novel 2nd-order shape function based digital image correlation method for large deformation measurements

Compared with the traditional forward compositional matching strategy, the inverse compositional matching strategy has almost the same accuracy, but has an obviously higher efficiency than the former in digital image correlation (DIC) algorithms. Based on the inverse compositional matching strategy and the auxiliary displacement functions, a more accurate inverse compositional Gauss-Newton (IC-GN2) algorithm with a new second-order shape operator is proposed for nonuniform and large deformation measurements. A theoretical deduction showed that the new proposed second-order shape operator is invertible and can steadily attain second-order precision. The result of the numerical simulation showed that the matching accuracy of the new IC-GN2 algorithm is the same as that of the forward compositional Gauss-Newton (FC-GN2) algorithm and is relatively better than in IC-GN2 algorithm. Finally, a rubber tension experiment with a large deformation of 27% was performed to validate the feasibility of the proposed algorithm.     

Inequivalent Quantization in the Field of a Ferromagnetic Wire

We argue that it is possible to bind neutral atom (NA) to the ferromagnetic wire (FW) by inequivalent quantization of the Hamiltonian. We follow the well known von Neumann’s method of self-adjoint extensions (SAE) to get this inequivalent quantization, which is characterized by a parameter Σ∈ℝ(mod2π). There exists a single bound state for the coupling constant η ²∈[0,1). Although this bound state should not occur due to the existence of classical scale symmetry in the problem. But since quantization procedure breaks this classical symmetry, bound state comes out as a scale in the problem leading to scaling anomaly. We also discuss the strong coupling region η ²<0, which supports bound state making the problem re-normalizable.     

On the evolution of isotropic and kinematic hardening with finite plastic deformation Part I: compression/tension loading of OFHC copper cylinders

Compression tests followed by tension tests after re-machining were performed on annealed oxygen-free-high-conductivity copper cylinders. These tests were conducted at nine levels of maximum strain ranging from 5 to 50%. From this data, isotropic and kinematic hardening were calculated using 50, 1000 and 2000 microstrain offset definitions. Both isotropic and kinematic hardening were found to depend on the yield definition. Isotropic hardening, which increased with plastic strain with no signs of saturation, also increased with larger offset definition of yield. Kinematic hardening, which increased to 40% strain and appeared to saturate thereafter, decreased with higher offset definitions of yield.     

Finite element modelling of cold drawing for high-precision tubes

Cold tube drawing is a metal forming process that allows manufacturers to produce high-precision tubes. The dimensions of the tube are reduced by pulling it through a conical converging die with or without inner tool. In this study, finite element modelling has been used to give a better understanding of the process.This paper presents a model that predicts the final dimensions of the tube with very high accuracy. It is validated thanks to experimental tests. Moreover, five studies are performed with this model, such as investigating the influence of the die angle on the drawing force or the influence of relative thickness on tube deformation.