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S.h. Farghaly - One of the best experts on this subject based on the ideXlab platform.

Hans Irschik - One of the best experts on this subject based on the ideXlab platform.

  • Dynamic response of an elastic bridge loaded by a moving elastic beam with a finite length
    Interaction and multiscale mechanics, 2010
    Co-Authors: Eugenia C. Cojocaru, Hans Irschik
    Abstract:

    The present paper is concerned with vibrations of an elastic bridge loaded by a moving elastic beam of a finite length, which is an extension of the authors` previous study where the second beam was modeled as a semi-infinite beam. The second beam, which represents a train, moves with a constant speed along the bridge and is assumed to be connected to the bridge by the limiting case of a rigid interface such that the deflections of the bridge and the train are forced to be equal. The elastic stiffness and the mass of the train are taken into account. The differential equations are developed according to the Bernoulli-Euler Theory and formulated in a non-dimensional form. A solution strategy is developed for the flexural vibrations, bending moments and shear forces in the bridge by means of symbolic computation. When the train travels across the bridge, concentrated forces and moments are found to take place at the front and back side of the train.

  • Actuator placement in static bending of smart beams utilizing Mohr’s analogy
    Engineering Structures, 2009
    Co-Authors: Hans Irschik, M. Nader
    Abstract:

    Abstract An extension of Mohr’s analogy to bending of shear-deformable beams with eigenstrain-type actuation, such as a piezoelectric actuation, is presented first. Various refined shear-deformable beam theories are included by means of a Theory-dependent parameter. The one-dimensional version of Reissner’s sixth-order plate Theory is exemplarily addressed. The Bernoulli–Euler Theory of beams rigid in shear, as well as the shear-deformable Theory of Timoshenko, are included as special cases. Afterwards, the extended Mohr analogy is applied to the bending of smart beams with piezoelectric patch actuators. The following special problem of static shape control is solved: Seek a placement of single patch actuators, such that the displacement and the cross-sectional rotation vanish at some pre-selected locations of the beam, despite the beam is loaded by external forces. Using Mohr’s analogy, it is shown that the auxiliary loading of the adjoint beam must form a self-equilibrated system of loading in order to achieve the latter goal. The high potential of the proposed actuator placement is demonstrated for the case of a cantilever beam with a single force acting at the tip. Placements of single actuators are represented such that the tip displacement and the tip cross-sectional rotation vanish. The outcomes of shear-deformable theories are compared to the Bernoulli–Euler Theory and to a Finite Element computation using piezoelectrically coupled elements.

  • Analogy between refined beam theories and the Bernoulli-Euler Theory
    International Journal of Solids and Structures, 1991
    Co-Authors: Hans Irschik
    Abstract:

    Abstract Some refinements of the classical Bernoulli-Euler Theory of the bending of beams are shown to be completely analogous to the effects produced by sources of self-stress in the Bernoulli-Euler beam. This is true for deflections, bending moments and shearing forces. They determine rotations, stresses and strains according to the specific refined Theory under consideration. Thus, by analogy, differences between the results of various refined theories, having been the object of discussions in recent literature, become accessible to a systematic classification. In an Appendix, this strategy of treating refined theories from the point of view of the classical one is put into the more general context of the Theory of Science.

Alfonso Fernández-canteli - One of the best experts on this subject based on the ideXlab platform.

  • Buckling of laminated-glass beams using the effective-thickness concept
    Composite Structures, 2016
    Co-Authors: M. López-aenlle, F. Pelayo, G. Ismael, M.a. García Prieto, A. Martín Rodríguez, Alfonso Fernández-canteli
    Abstract:

    Abstract Structural stability is one of the design requirements in laminated-glass beams and plates due their slenderness and brittleness. In this paper the equations of the classical Euler Theory for buckling of isotropic monolithic beams are extended to laminated-glass beams using the effective thickness and the effective Young modulus concepts. It is demonstrated that the dependency of the effective stiffness on boundary conditions can be considered using buckling ratios of Euler Theory corresponding to isotropic linear monolithic beams. The analytical predictions are validated by compressive experimental tests in simply supported beams. Fixed boundary conditions are difficult to reproduce in experimental tests due to the brittleness of the glass and for this reason fixed–fixed and fixed–pinned boundary conditions were validated using a finite element model.

Ertugrul Taciroglu - One of the best experts on this subject based on the ideXlab platform.

  • much ado about shear correction factors in timoshenko beam Theory
    International Journal of Solids and Structures, 2010
    Co-Authors: S B Dong, C Alpdogan, Ertugrul Taciroglu
    Abstract:

    Abstract Many shear correction factors have appeared since the inception of Timoshenko beam Theory in 1921. While rational bases for them have been offered, there continues to be some reluctance to their full acceptance because the explanations are not totally convincing and their efficacies have not been comprehensively evaluated over a range of application. Herein, three-dimensional static and dynamic information and results for a beam of general (both symmetric and non-symmetric) cross-section are brought to bear on these issues. Only homogeneous, isotropic beams are considered. Semi-analytical finite element (SAFE) computer codes provide static and dynamic response data for our purposes. Greater clarification of issues relating to the bases for shear correction factors can be seen. Also, comparisons of numerical results with Timoshenko beam data will show the effectiveness of these factors beyond the range of application of elementary (Bernoulli–Euler) Theory. An issue concerning principal shear axes arose in the definition of shear correction factors for non-symmetric cross-sections. In this method, expressions for the shear energies of two transverse forces applied on the cross-section by beam and three-dimensional elasticity theories are equated to determine the shear correction factors. This led to the necessity for principal shear axes. We will argue against this concept and show that when two forces are applied simultaneously to a cross-section, it leads to an inconsistency. Only one force should be used at a time, and two sets of calculations are needed to establish the shear correction factors for a non-symmetrical cross-section.

Jiri Dvorak - One of the best experts on this subject based on the ideXlab platform.

  • critical load of the human cervical spine an in vitro experimental study
    Clinical Biomechanics, 1998
    Co-Authors: Manohar M Panjabi, Jacek Cholewicki, Kimio Nibu, Jonathan N Grauer, Lawrence B Babat, Jiri Dvorak
    Abstract:

    OBJECTIVE: To determine the critical load of the osteoligamentous cervical spine in frontal plane. DESIGN: Whole human cervical spine specimens were loaded in axial compression with increasing force until the point of buckling. BACKGROUND: The osteoligamentous cervical spine and the surrounding muscles support the weight of the head and the external loads applied to it. Critical load is the maximum compressive force that the spinal column can sustain before buckling. Critical loads have been obtained for the osteoligamentous thoracolumbar spine (without the rib cage) and the lumbar spine. Critical load of the cervical spine has not yet been determined. METHODS: When a compressive force is applied to the cervical spine, it bends in the sagittal plane producing greater lordosis. The determination of critical load in Euler's sense requires blocking of this sagittal plane bending. A special apparatus was developed that constrained such bending in the sagittal plane, but allowed complete freedom of the spine motion in the frontal plane. Experiments were conducted to determine the axial force-lateral bending curves of whole cervical spine specimens. Critical load values were obtained from these curves. As an alternative to this method, bending stiffness in the frontal plane was experimentally determined and the critical load was computed using Euler's Theory of columns. RESULTS: Based upon the study of seven spine specimens (CO-T1), the critical load for the human cervical spine was found to be 10.5 (3.8) N obtained by direct experimentation. The average critical load calculated with the Euler Theory using bending stiffness data, was 11.9 (2.0), but there were large individual differences when compared with the experimental results. CONCLUSIONS: The critical load of the osteoligamentous human cervical spine is about one-fifth to one-quarter the weight of the average head.