Mechanics of Solids and Shells

Wempner, Gerald; Talaslidis, Demosthenes

doi:10.1201/9781420036428

Cited by 28 publications

(18 citation statements)

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“…At the macroscopic scale, this problem is relevant to the outer-body shells of automobiles and aircraft, which are often made from double-curved thin metal sheets. Localization in these structures can occur during collisions to cause elastic-plastic denting or crumpling [1][2][3]. The design of thin-walled structures is bounded by a need for them to be lightweight and slender, but also resistant to deformation by suppressing localization, which can cause permanent damage.…”

Section: Introductionmentioning

confidence: 99%

Localized Structures in Indented Shells: A Numerical Investigation

Nasto

Reis

2014

Journal of Applied Mechanics

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We present results from a numerical investigation of the localization of deformation in thin elastomeric spherical shells loaded by differently shaped indenters. Beyond a critical indentation, the deformation of the shell ceases to be axisymmetric and sharp structures of localized curvature form, referred to as "s-cones," for "shell-cones." We perform a series of numerical experiments to systematically explore the parameter space. We find that the localization process is independent of the radius of the shell. The ratio of the radius of the shell to its thickness, however, is an important parameter in the localization process. Throughout, we find that the maximum principal strains remain below 6%, even at the s-cones. As a result, using either a linear elastic (LE) or hyperelastic constitutive description yields nearly indistinguishable results. Friction between the indenter and the shell is also shown to play an important role in localization. Tuning this frictional contact can suppress localization and increase the load-bearing capacity of the shell under indentation.

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Section: Introductionmentioning

confidence: 99%

Localized Structures in Indented Shells: A Numerical Investigation

Nasto

Reis

2014

Journal of Applied Mechanics

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“…The displacements of the beam are expressed in the transport coordinate system S 1 , assuming Timoshenko's theory for bending [12] and Saint-Venant's theory for torsion [13], including deformation in longitudinal direction due to warping: , , , , , , , , , , , , cos , sin , , , , , sin , cos ,…”

Section: Beam Equation Of Motion In Transport Coordinate Systemmentioning

confidence: 99%

Nonlinear Vibrations of Rotating 3d Tapered Beams With Arbitrary Cross Sections

Stoykov¹,

Margenov²

2014

Proceedings of the 4th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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Abstract. The geometrically nonlinear vibrations of 3D beams that rotate about a fixed axis are investigated by the p-version finite element method. The beams are considered to be tapered, i.e. with variable thickness along its length, and with arbitrary cross sections. The beam model is based on INTRODUCTIONRotating beams are used to model and investigate the dynamics of helicopter blades, jet engine turbine blades, robot arms, wind turbine blades, etc. Many studies have been performed for modeling rotating beams about a fixed axis. The linear natural frequencies of beams that rotate with constant speed were investigated by many researchers, for example in [1][2][3][4][5]. Works that consider geometrically nonlinear models of rotating beams may be found, for example [6][7][8]. In what concerns modern wind turbine blades, most of them are constructed with load carrying box girder inside the blade and shells on the surface of the blade [9]. The purpose of the box girder is to make the blade stronger and stiffer while the shells around the box girder form the aerodynamic shape. Thus, the dynamic behavior of the wind turbine blade might be determined mainly from the load carrying box, even though the shells contribute small bending strength.In the current work, a model of beams rotating about a fixed axis with constant speed of rotation is presented. A setting angle and a rigid hub are included in the model. The equation of motion is derived in the rotating coordinate system, and the rotation is taken into account by the inertia forces [10]. The beam may vibrate in space, i.e. it may perform longitudinal, torsional and bending deformations, the model is based on Timoshenko's theory for bending and assumes that under torsion, the cross section deforms only in longitudinal direction due to warping [11]. Geometrical type of nonlinearity is considered and the equation of motion is derived by the principle of virtual work.Thin-walled box beams with linearly varying thickness and width are investigated. First, the derived model is validated by generating a fine mesh of three-dimensional finite elements. Then, the influence of the setting angle and the speed of rotation on the natural frequencies is examined. Forced vibrations of rotating beams due to harmonic forces are presented.

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“…Stated simply, for vibration at a system natural frequency, the kinetic energy at maximum velocity and zero displacement must then be stored as elastic (strain) energy at maximum displacement and zero velocity [13]. Since the strain energy and kinetic energy are respectively proportional to the squares of stress and velocity, it follows that dynamic stress, σ will be proportional to vibration velocity, v [14]. For idealized straight-beam systems, consisting of thin-walled pipe and with no contents, insulation or concentrated mass, the ratio σ/v is dependent primarily upon material properties (density ρ and modulus of elasticity E), and is remarkably independent of system-specific dimensions, natural-mode number and vibration frequency.…”

Section: Introduction and Literature Reviewmentioning

confidence: 99%

On the Dynamic Behavior of Town Gas Pipelines

El-Kafrawy¹

2012

ENG

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Pipelines have been acknowledged as the most reliable, economic and efficient means for the transportation of gas and other commercial fluids such as oil and water. The designation of pipeline system as "lifelines" signifies that their operation is essential in maintaining the public safety and well being. A pipeline transmission system is a linear system which traverses a large geographical area, and soil conditions thus, is susceptible to a wide variety of hazards. This paper is concerned with the dynamic behavior of buried town gas pipelines. A computer model with a finite number of nodes is created to simulate the behavior of the real gas pipeline. The dynamic susceptibility method is applied for twenty mode shapes of this model, which utilizes the stress per velocity method and is an incisive analytical tool for screening the vibration modes of the system. It can be readily identified, which modes, if excited, could potentially cause large dynamic stresses. This paper discusses also two of the piping dynamic analyses, namely the effect of the response spectrum of an earthquake and the time history analysis of a truck crosses the pipeline.

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Mechanics of Solids and Shells

Cited by 28 publications

References 0 publications

Localized Structures in Indented Shells: A Numerical Investigation

Localized Structures in Indented Shells: A Numerical Investigation

Nonlinear Vibrations of Rotating 3d Tapered Beams With Arbitrary Cross Sections

On the Dynamic Behavior of Town Gas Pipelines

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