On the stability of inhomogeneously viscoelastic reinforced bars

There is investigated the stability of inhomogeneously ageing reinforced viscoelastic bars. It is assumed that the strains and stresses in the reinforcement are related by Hooke's law. The properties of the matrix material are described by equations of the theory of viscoelasticity of inhomogeneously ageing solids /1,2/. Under different boundary conditions for the ends of the bar and loading methods an expression is set up for the critical force in stability problems in an infinite time interval. The stability definition taken corresponds to the Liapunov stability definition for the motion of dynamical systems. Estimates of the critical time when the magnitude of the deflection of a viscoelastic bar reaches a given value are obtained for stability problems in a finite time interval. The formulation for the stability problem in a finite time interval starts from the definition of stability of motion of dynamical systems by taking its beginning from the Chetaev work. The dependence of the critical time on the inhomogeneity and the reinforcing parameter is investigated numerically. The stability of viscoelastic unreinforced bars was studied in /3,4/, A survey and bibliography of research associated with the stability problem for viscoelastic bars are available in /5–8/.     

A new Branch and Bound method for a discrete truss topology design problem

Our paper considers a classic problem in the field of Truss Topology Design, the goal of which is to determine the stiffest truss, under a given load, with a bound on the total volume and discrete requirements in the cross-sectional areas of the bars. To solve this problem we propose a new two-stage Branch and Bound algorithm. In the first stage we perform a Branch and Bound algorithm on the nodes of the structure. This is based on the following dichotomy study: either a node is in the final structure or not. In the second stage, a Branch and Bound on the bar areas is conducted. The existence or otherwise of a node in this structure is ensured by adding constraints on the cross-sectional areas of its incident bars. In practice, for reasons of stability, free bars linked at free nodes should be avoided. Therefore, if a node exists in the structure, then there must be at least two incident bars on it, unless it is a supported node. Thus, a new constraint is added, which lower bounds the sum of the cross-sectional areas of bars incident to the node. Otherwise, if a free node does not belong to the final structure, then all the bar area variables corresponding to bars incident to this node may be set to zero. These constraints are added during the first stage and lead to a tight model. We report the computational experiments conducted to test the effectiveness of this two-stage approach, enhanced by the rule to prevent free bars, as compared to a classical Branch and Bound algorithm, where branching is only performed on the bar areas.     

Die Knicklast des einseitig eingespannten Stabes als zweiparametriges,nichtkonservatives Eigenwertproblem

Summary The paper deals with an application of Galerkin's method to a nonconservative problem of the elastic stability of bars. It is shown that the relation between the critical loads of the two-parametric eigenvalue problem is nearly linear.     

A Stability Result for a Magnetostatic Inverse Problem

For a linearized inverse problem which models a new measurement technique for finding steel reinforcement bars in concrete, we prove a quantitative stability result under physically reasonable a-priori assumptions.     

Anwendung des Galerkinschen Verfahrens auf nichtkonservative Stabilitätsprobleme des elastischen Stabes

Summary The paper deals with the application ofGalerkin's method to non-conservative stability problems of elastic bars. Two results established byBeck andPflüger by means of other methods are verified.     

Deformation of laminated anisotropic bars in the three-dimensional statement 1. Transverse-longitudinal bending and edge compatibility condition

By using the methods of asymptotic splitting, the 3D problem on the transverse-longitudinal bending of elastic anisotropic laminated bars under the action of longitudinal and transverse loads is split into a number of plane boundary-value problems, whose solution allows one to construct asymptotic approximations for all components of the displacement vector and the strain tensor at each point in the bars. A system of ordinary differential equations of transverse-longitudinal bending is obtained for laminated bars with arbitrary anisotropy of its layers. A condition for the edge compatibility of materials in laminated orthotropic bars is deduced. Translated from Mekhanika Kompozitnykh Materialov, Vol. 45, No. 3, pp. 379-410, May-June, 2009.     

封闭薄壁截面空间曲杆的双力矩

讨论了各向异性材料薄壁截面空间曲杆的双力矩,给出了一般解法及平面曲杆受竖向载荷作用的双力矩公式。     

An analysis of stress wave propagation in slender bars using a discrete particle approach

In this paper, a discrete particle approach is developed for the quantitative analysis of stress wave propagation in metal bars. Though linear forces are emphasized, nonlinear forces are also considered. Cylindrical, tapered, homogeneous, and nonhomogeneous bars are studied. Computer results show most favourable agreement with available theoretical and experimental results.     

Stabilization of a platform under wind loads

The Steward platform is employed in dynamic simulation of a number of controlled mechanical systems, in control of the active surface of a telescope mirror, and other constructions. Position and orientation of this platform is regulated by changing the lengths of its supporting bars, and corresponding change of their angles relative to the base. Viable motions of the platform depend on how the bars are hinged to the base and to the platform. This paper studies dynamics and stabilization of a platform leaning on three bars of controlled length under wind loads. This problem is of interest for design of active mirror surfaces of radio telescopes. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 7, pp. 97–115, 2005.     

The Cutting Stock Problem for the Stockholder of Steel Reinforcement Bars

Journal of the Operational Research Society - The stockholder of steel reinforcement bars supplies cut lengths to its customers to be used principally in prestressed concrete. The bars which the...     

Study of posterolateral lumbar arthrodesis by means of a finite element model

Posterolateral lumbar arthrodesis consists in the fixation of the lumbar vertebrae pedicles by means of bars and screws. It is indicated in all those cases in which instability exists previous to the surgery, or in those other cases in which the instability has been caused by the need of bone resections that put the articulations structures in danger.The pedicle fixation of the lumbar arthrodesis is a great advance in the lumbar surgery. It contributes to achieve a stable and biologic fusion. The aim of the present research is the analysis of the contact problem that exists between the screw and the bone as one of the key points to control in order to achieve a good future stability of the arthrodesed spine.In order to achieve such aim, a Finite Elements Model (FEM) of the spine was performed. Such a model was obtained using a computer vision technique that creates 3D bodies using computed tomographies of the sacrum and vertebrae L4 and L5. Not only the bone bodies have been modeled, but also the intervertebral discs that act as the joints of the bones. In order to obtain a complete simulation of the lumbar region the titanium screws and bars have been modeled too.The study of the influence of the contact between bone and screw in the biomechanical behavior of the lumbar column has been studied applying several load conditions simulating different kinds of typical movements of the column. Finally, the stresses on the different elements of the lumbar structure and the relative movements between bone and screw as well as the conclusions of this research are also expounded.     

Elastic-Plastic Torsion of Heterogeneous Cylindrical Bars

Following the study by Lanchon (1974) on elastic-plastic torsionof cylindrical bars with simple or multiple connected crosssections, we give here a generalized formulation including,in particular, the case of bars reinforced by longitudinal fibres.     

Bond of FRP Reinforcement in Concrete - a Challenge

The bond of ordinary steel reinforcement in concrete depends on many factors, such as the pullout resistance, the geometry of a concrete member, the placement of a bar in the member cross section, the cover splitting, the confinement caused by concrete and the surrounding reinforcement, the order of bond-crack appearance, and the bond-stress distribution along the bond length. The bond of FRP reinforcement depends on even a greater number of factors. Moreover, the types of FRP bars are numerous. Their surface is weaker than that of steel bars and may fracture by bond forces. The surface of FRP bars is softer and does not create as high local stress concentrations in bond contact points to concrete as the harder steel bars do. This fact often delays the appearance of cover splitting cracks along the bars. However, the load necessary for developing the crack pattern of ultimate splitting failure in concrete is then very dependent on whether the bar surface is glossy or rough. The FRP reinforcement can also be used for external shear and/or flexural strengthening of existing members. For this application, FRP bars are placed in grooves cut on the surface of the member to be strengthened and are fixed there with a cement mortar or epoxy paste. In such an application, the performance of bond between the FRP rod and the mortar or resin and then between the mortar or resin and concrete is critical for the effectiveness of the technique. The presence of two interfaces increases the number of parameters needed to characterize the global joint behavior and introduces new possible failure modes. The fundament for the bond resistance estimation should be an accepted bond philosophy linked to appropriate models. A system of bond tests should provide necessary coefficients for the models.     

Ammann bars and quasicrystals

In 1988 Danzer [3] constructed a family of four tetrahedra which allows—with certain matching conditions—only aperiodic tilings. By analogy with the Ammann bars of planar Penrose tilings we define Ammann bars in space in the form of planar Penrose tilings we define Ammann bars in space in the form of plane sections of the four tetrahedra. If we require that the plane sections continue as planes across the faces of the tilings, we obtain an alternative matching condition, thus answering a question of Danzer.     

Optimal layout of cantilever trusses

For given allowable stress, Michell (Ref. 1) has investigated the optimal design of a cantilever truss that is to transmit a given load to two given fixed points of support. Disregarding the weight of the connections between the bars, he found that the truss of minimum weight is a truss-like continuum with an infinity of joints, and with bars that are mostly of infinitesimal length. In the present paper, a finite number of joints is enforced by including in the structural weight, which is to be minimized, not only the weight of the bars but also the weight of their connections, which is assumed to be proportional to the number of joints. The concept of two adjoint trusses is introduced, each of which coincides with the Maxwell diagram of the other truss. Two adjoint trusses have the same weight, and an optimal truss is therefore self-adjoint. The optimal configurations of 6-joint and 11-joint cantilever trusses are discussed, and the range of the weight of the typical joint is determined for which the 6-joint truss is optimal.     

Stability of linearly viscoelastic bars made from polymer materials of variable cross section

The critical viscoelastic forces for hinged bars made from polymer materials of variable cross section changing in accordance with a power law are obtained. It is shown that these forces are proportional to the critical elastic forces of bars of variable cross section.VMEL "Lenin," Sofia. Translated from Mekhanika Polimerov, Vol. 9, No. 3, pp. 540–546, May–June, 1973.     

Account of the Cross-Sectional Deplanation of a Composite Bar in Determining the Critical Force

A method for determining the critical force for an axially compressed composite bar with account of deplanation of its cross sections is considered. It is proposed to consider the cross-sectional deplanation, which decreases the critical force, by lowering the basic flexural stiffness of the bar by the value resulting from this effect. General relationships for calculating this value for composite bars are obtained. Numerical results are presented, which show the decrease in the critical force as a function of some parameters for transversely isotropic bars of rectangular cross section.     

Exact analytical and numerical solutions of stability problems for a straight composite bar subjected to axial compression and torsion

Based on linearized equations of the theory of elastic stability of straight composite bars with a low shear rigidity, which are constructed using the consistent geometrically nonlinear equations of elasticity theory for small deformations and arbitrary displacements and a kinematic model of Timoshenko type, exact analytical solutions of nonclassical stability problems are obtained for a bar subjected to axial compression and torsion for various modes of end fixation. It is shown that the problem of direct determination of the critical parameter of the compressive load at a given torque parameter leads to transcendental characteristic equations that are solvable only if bar ends have cylindrical hinges. At the same time, we succeeded in obtaining solutions to these equations in terms of wave formation parameters of the bar; these parameters, in turn, enabled us to find the parameter of the critical load at any boundary conditions. Also, an algorithm for numerical solution of the problems stated is proposed, which is based on reducing the problems to systems of integroalgebraic equations with Volterra-type operators and on solving these equations by the method of mechanical quadratures (finite sums). It is demonstrated that such numerical solutions exist only for certain ranges of parameters of the bar and of the parameter of torque. In the general case, they can not be obtained by the numerical method used. It is also shown that the well-known solutions of the stability problem for a bar subjected to torsion or to compression with torsion are in correct. Translated from Mekhanika Kompozitnykh Materialov, Vol. 45, No. 2, pp. 167–200, March–April, 2009.     

Tiling a simply connected figure with bars of length 2 or 3

Let F be a simply connected figure formed from a finite set of cells of the planar square lattice. We first prove that if F has no peak (a peak is a cell of F which has three of its edges in the contour of F), then F can be tiled with rectangular bars formed from 2 or 3 cells. Afterwards, we devise a linear-time algorithm for finding a tiling of F with those bars when such a tiling exists.