A group-theoretic approach to the geometry of elastic rings

Summary All globally possible solutions of a twisted, homogeneous, elastic ring with circular cross section and no external load are characterized by their symmetry groups. The symmetry group of the untwisted, trivial solution is identified as _S ^t0 = O(2) ×Z ₂, and symmetry groups for the nontrivial solutions are found among the subgroups of _S ^t0 .     

A dynamic programming approach to the optimization of elastic trusses

The optimal design of elastic trusses is discussed from a dynamic programming point of view. Emphasis is placed on minimum volume design of statically determinate trusses with displacement and stress constraints in the discrete case, i.e., when the cross-sectional areas of the bars are available from a discrete set of values. This, a design constraint usually very difficult to handle with standard nonlinear programming algorithms, is naturally incorporated in the present formulation. In addition, the functional equation approach is shown to furnish a direct solution to the problem of determining a design, among all possible ones satisfying certain volume and displacement constraints, for which the maximum stress is a minimum. A successive approximation approach is briefly indicated as an extension of the method to solve statically indeterminate trusses. Finally, several numerical examples are presented and the main features of the methods are briefly exposed.     

On the augmented Lagrangian approach to Signorini elastic contact problem

Summary. The Signorini problem describes the contact of a linearly elastic body with a rigid frictionless foundation. It is transformed into a saddle point problem of some augmented Lagrangian functional and then discretized by finite element methods. Optimal error estimates are obtained for general smooth domains which are not necessarily convex. The key ingredient in the analysis is a discrete inf-sup condition which guarantees the existence of the saddle point. Received January 29, 1999 / Revised version received May 2, 2000 / Published online December 19, 2000     

Structural characteristics of a four-boson system and effect of symmetries

With four-body model theory the energy spectra of a four-boson system and the distribution of the wavefunctions of low-lying states in coordinate space are investigated. On the basis of the analysis for low-lying states, the effect of the symmetries is studied. Various structural characteristics are determined by symmetries. Project supported by the Doctor Fund of the National Educational Committee of China and the Special Fund for the Scholastic Backbone of the Institutes of Guangzhou City.     

An elastic beam approach to predictive vehicle motion planning

Vehicle guidance systems are among the latest automotive developments. Examples are A daptive C ruise C ontrol (ACC), lane departure warning and active lane keeping. However, the rapid development of environmental sensor systems such as radar, lidar and video technologies in combination with data fusion of the single sensor signals enables further applications as for example lane changing assistance, collision avoidance or even autonomous driving. For all of these functions, trajectories have to be planned and, depending on the application, to be communicated to the driver. Recently, methods originally developed in robotics as for example so-called elastic bands are adapted for road vehicle applications. Here an virtual elastic beam is proposed to guide the vehicle. The beam is deflected by virtual potential fields generated by obstacles in the traffic space. In doing so, the elastic beam avoids obstacles and provides collision-free trajectories, while its bending stiffness counteracts the curvature of the trajectory. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An approach to constructing models of multiphase elastic porous media

A novel approach to describing the behaviour of multiphase elastic porous media is proposed. The average values of the physical quantities needed to describe the motions of porous media are formulated using an integral relation. The validity of this relation is taken as the fundamental hypothesis. The integral definition of the average values enables integral relations to be devised for the average values from the integral laws of conservation of mass, momentum and energy and the increase in entropy. Along with the average values, the integral relations contain new variables that can be identified with generalized thermodynamic forces, which can be used to take into account the phase interaction in a porous medium. The integral relations are used to derive differential equations for the rate of entropy change and Gibbs relations for a porous medium as a basis for obtaining the constitutive relations. Relationships between the thermomechanical parameters of the model are established from the Gibbs relations under additional assumptions. The equation for the rate of entropy change can be used to establish relations between the generalized thermodynamic forces and fluxes. A complete system of differential equations in the defining parameters, which describes the motion of multiphase elastic porous media, is finally obtained.     

A new cluster-expansion approach to the calculation of the energy structure of crystals

We propose a new approach to the calculation of energy spectra for strongly compressed or imperfect crystals in the case where the localized orbitals (LO) of atoms with different space positions overlap considerably. This approach is based on the exact orthogonalization of the LO for all atoms according to Lövdin's method and on the cluster expansion (CE). In all nth orders of the CE, we take into account the overlapping integrals (OI) of the LO for atoms belonging to the same n-particle cluster. For every n, such clusters comprise the whole crystal. For n ; , the CE converges exponentially to the OI. The two-particle cluster expansion is discussed in detail.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 106, No. 3, pp. 498–512, March, 1996.Translated by M. V. Chekhova.     

A projection approach to optimal control of elastic beam dynamics

Controlled lateral motions of an elastic beam – extended body with a cuboid shape – are studied. A generalized statement of the initial-boundary value problem is given in the frame of 3D linear elasticity based on the integral formulation of constitutive relations. A numerical approach relying on the Fourier method and semi-discretization technique is proposed to design the optimal boundary control that moves the beam to a given final state and minimizes a quadratic cost function. Some results of numerical simulation and quality analysis are presented and discussed. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Singular approximation for the calculation of the elastic properties of reinforced systems

A method has been developed, based on the random field theory, for the calculation of the elastic properties of reinforced media. The solution is obtained in the form of an operator series, each term of which is based on the formal component of the second derivative of Green's tensor of incompatibility equations. The zero (singular) approximation of such a series takes into account the local part of interactions between the inhomogeneity grains. The singular approximation was used to calculate the elasticity moduli of unidirectionl reinforced materials.Moscow Institute of Electronics. Translated from Mekhanika Polimerov, Vol. 9, No. 3, pp. 502–506, May–June, 1973.     

Vibration characteristics of single-walled carbon nanotubes based on an anisotropic elastic shell model including chirality effect

Single-walled carbon nanotubes (SWCNTs) exhibit remarkable chirality-dependent mechanical phenomena. In present paper, an anisotropic elastic shell model is developed to study the vibration characteristics of chiral SWCNTs. Analytical solution is presented by using the Flügge shell theory and complex method. The suggested model is justified by a good agreement between the present results and some experimental and numerical available data in literature. Furthermore, the model is used to elucidate the effect of tube chirality on the frequencies of SWCNTs. Finally, the influences of the externally applied mid-face axial force and torque on longitudinal, radial and torsional frequencies of SWCNTs are investigated.     

Numerical calculation of the effect of Coulomb forces on physical characteristics of the charged particle beam in a linear accelerator

An algorithm Is proposed for numerical calculation of the effect of Coulomb repulsion forces on the physical characteristics of a high-current linear accelerator with asymmetric phase-variable focusing. The problem of maximizing the initial particle trapping region is considered.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 60, pp. 70–73, 1986.     

Variational approach to scattering of plane elastic waves by diffraction gratings

The scattering of a time‐harmonic plane elastic wave by a two‐dimensional periodic structure is studied. The grating profile is given by a Lipschitz curve on which the displacement vanishes. Using a variational formulation in a bounded periodic cell involving a nonlocal boundary operator, existence of solutions in quasiperiodic Sobolev spaces is investigated by establishing the Fredholmness of the operator generated by the corresponding sesquilinear form. Moreover, by a Rellich identity, uniqueness is proved under the assumption that the grating profile is given by a Lipschitz graph. The direct scattering problem for transmission gratings is also investigated. In this case, uniqueness is proved except for a discrete set of frequencies. Copyright © 2010 John Wiley & Sons, Ltd.