Ebene Flächentragwerke

Altenbach, Johannes; Altenbach, Holm; Naumenko, Konstantin

doi:10.1007/978-3-642-58721-4

Cited by 68 publications

(39 citation statements)

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“…It is not necessary to introduce equivalent shear forces (as it is in the classical theory) and, therefore, corner forces in the case of a rectangular plate region are not present, [1].…”

Section: Second-order Approximationmentioning

confidence: 99%

“…Following the reasoning of the classical plate theory leads to the well-known corner forces for rectangular plate regions, [1,5,17]. …”

Section: First-order Approximationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…Translations, rotations, or, generally, directors are attached to each point of the material surface leading to Cosserat-or director-type theories, [20,33]. A historical review of plate theories may be found in [1,30]; the latest achievements in plate and shell theories have been discussed in [29].Any two-dimensional approximation of the governing equations of three-dimensional continuum mechanics yields errors and, possibly, contradictions. In order to assess the validity of an approximation and to indicate its range of applicability, various features have been…”

mentioning

confidence: 99%

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On consistent plate theories

Kienzler¹

2002

Archive of Applied Mechanics (Ingenieur Archiv)

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Applying the uniform-approximation technique, consistent plate theories of different orders are derived from the basic equations of the three-dimensional linear theory of elasticity. The zeroth-order approximation allows only for rigid-body motions of the plate. The first-order approximation is identical to the classical Poisson-Kirchhoff plate theory, whereas the second-order approximation leads to a Reissner-type theory. The proposed analysis does not require any a priori assumptions regarding the distribution of either displacements or stresses in thickness direction. IntroductionPlates are important elements in structural engineering and have been widely studied by engineers during the last century. A comprehensive bibliography can be found in [14,26,32]. Plates are characterized by the fact that their extension in one direction, e.g. in the thickness (characteristic length h), is considerably less than that in the other two directions (characteristic in-plane length a). The surface that bisects the plate continuum transversely is assumed to be plane and is called for short, mid-plane. Loads are applied perpendicular to the mid-plane or through moments acting around the in-plane axes. Plate theories attempt to describe the three-dimensional state of stresses and displacements in a plate continuum by two-dimensional quantities defined on a surface. Therefore, plate theories are inherently approximative.Several possibilities exist to derive plate theories. One uses polynominal expansions in the thickness direction both for the displacements and for the stresses. These series expansions have to be truncated at a specific order, and often they are complemented by a set of a priori assumptions, mostly motivated by engineering intuition, [16,22].The asymptotic method (cf. e.g.[7]) for the derivation of governing plate equations develops two sets of differential equations, one for the ''interior'' of the plate and the other one for the ''boundary layer''. Especially for dynamic problems, where the characteristic in-plane dimension, i.e. the wave length k, is much smaller than the planar extension a, this method supplies accurate results and allows for reliable error estimations; it requires, however, advanced mathematical techniques.An alternative approach ''lives'' completely on the mid-surface. Translations, rotations, or, generally, directors are attached to each point of the material surface leading to Cosserat-or director-type theories, [20,33]. A historical review of plate theories may be found in [1,30]; the latest achievements in plate and shell theories have been discussed in [29].Any two-dimensional approximation of the governing equations of three-dimensional continuum mechanics yields errors and, possibly, contradictions. In order to assess the validity of an approximation and to indicate its range of applicability, various features have been

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“…It is not necessary to introduce equivalent shear forces (as it is in the classical theory) and, therefore, corner forces in the case of a rectangular plate region are not present, [1].…”

Section: Second-order Approximationmentioning

confidence: 99%

“…Following the reasoning of the classical plate theory leads to the well-known corner forces for rectangular plate regions, [1,5,17]. …”

Section: First-order Approximationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

See 2 more Smart Citations

On consistent plate theories

Kienzler¹

2002

Archive of Applied Mechanics (Ingenieur Archiv)

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“…The product function X w n0 nX w g0 g is formulated as the elastic de¯ection function by given applied load. The procedure for the construction of such a function basing on the Vlasov-Kantorovich method and variational iterations is discussed in Altenbach et al (1998a), Altenbach et al (1998b). The functions X w ni n and X U ni n are chosen as eigenfunctions of transversely vibrating beam X w ni n sin ln À sinh ln À sin l À sinh l cos l À cosh l cos ln À cosh lnY…”

Section: Creep-damage Of Plates In Bendingmentioning

confidence: 99%

On the accuracy of creep-damage predictions in thinwalled structures using the finite element method

Altenbach

Kolarow²,

Morachkovsky

et al. 2000

Computational Mechanics

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The constitutive model with a single damage parameter describing creep-damage behaviour of metals with respect to the different sensitivity of the damage process due to tension and compression is incorporated into the ANSYS ®nite element code by modifying the user de®ned creep material subroutine. The procedure is veri®ed by comparison with solutions for beams and rectangular plates in bending based on the Ritz method. Various numerical tests show the sensitivity of long-term predictions to the mesh sizes and element types available for the creep analysis of thinwalled structures. IntroductionEngineering structures operating at elevated temperatures such as fossil power plants, chemical plants, reactors, etc. are designed with respect to increased requirements of safety and assurance of long-term reliability. One of the main factors which must be considered in the long-term structural analysis is time-dependent material behaviour coupled with damage evolution (Roche et al., 1992). A powerful tool for the lifetime prediction is the continuum damage mechanics approach which is based on the formulation of constitutive and evolution equations for inelastic strains and material damage. Incorporating these material models into the ®nite element code predictions of time-dependent stress, strain and damage ®elds can be performed by numerical solution of nonlinear initialboundary value problems (e.g. . The ®rst problem arising by creep damage analysis is the formulation of a phenomenological material model that is able to describe the sensitivity of creep strain and damage rate to the stress level, stress state, temperature level, environmental effects, etc. Such a model must be able to extrapolate the experimental creep data usually available from uniaxial short-term creep tests and realised for narrow stress ranges to the in-service loading conditions in the real structure. The second problem can be related to the quality of the ®nite element predictions particularly by analysis of structures with complex shapes.The structural analysis of thinwalled components (pressure vessels, pipes, pipe bends, etc.) can be performed using the mechanical models of plane stress (strain) states or equations of shell theory. In the case of plane stress (strain) problems numerous ®nite element simulations considering creep damage effects has been made because of experimental data available for veri®ca-tion. Examples are discussed by Saanouni et al. Since these examples con®rm the ability of ®nite element simulations to predict stress redistributions and failure times with accuracy enough for engineering applications and can be used as benchmark tests by development of user de®ned material subroutines incorporating damage evolution a little effort has been made for the analysis of transversely loaded thinwalled structures. Numerical results for rupture times of rectangular plates in bending are given by Bodnar and Chrzanowski (1994), Bialkiewicz and Mika (1995) based on in-house ®nite element codes and Altenbach and Naumenko (1997) for re...

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Surface Softness Tuning with Arch‐Forming Active Hydrogel Elements

Ehrenhofer

Wallmersperger

2023

Adv Eng Mater

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Thin active elements can be added to rigid surfaces for the tuning of mechanical contact properties. The deformation of the active structures leads to the forming of arches. Depending on the forming of the arch, the force–displacement curve for contact becomes more or less steep. This can be understood as changing the interaction property between soft and hard. Herein, this concept is presented with hydrogels inside the active elements. Analytical derivations and finite‐element simulation results for actuation and contact, based on the stimulus expansion model, are shown. This modeling approach appropriately captures the stimulus‐dependent swelling properties of the material and can be easily applied in commercial finite‐element tools. Special considerations are taken for the encapsulation of the active materials. A thin encapsulation foil allows 1) the use of swelling agents, such as water, without contaminating the contact objects. Furthermore, 2) appropriate water reservoirs for the swelling process can be included. The simulation results show that a surface softness tuning can be realized. The presented active material and dimensions are exemplary; the concept can be applied to other active materials for tuning surface interactions.

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Ebene Flächentragwerke

Cited by 68 publications

References 0 publications

On consistent plate theories

On consistent plate theories

On the accuracy of creep-damage predictions in thinwalled structures using the finite element method

Surface Softness Tuning with Arch‐Forming Active Hydrogel Elements

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