Influence of in-Plane Deformation in Higher Order Beam Theories

Abstract

Comparing Euler-Bernoulli or Tismoshenko beam theory to higher order beam theories, an essential difference can be depicted: the additional degrees of freedom accounting for out-of plane (warping) and in-plane (distortional) phenomena leading to the appearance of respective higher order geometric constants. In this paper, after briefly overviewing literature of the major beam theories taking account warping and distortional deformation, the influence of distortion in the response of beams evaluated by higher order beam theories is examined via a numerical example of buckling drawn from the literature.

On the Importance of Cross-Sectional Distortions and their Inclusion in an Efficient GBT-Formulation

“…1 where torsional vibration is studied in a quite slender shaft, indicating that CBM does not even come close to continuum (or shell) results since in-plane distortions influence the mechanical properties significantly [1, 4] 1 ). These effects are also observed by Sapountzakis et al [5,6] where also buckling analyses are considered. In order to circumvent the insufficient accuracy of CBM in thin-walled single or multi-cell box type cross-sections, however, maintaining a moderate number of global degrees of freedom, a Generalized Beam Theory (GBT) can be applied (see [1] and [5] for a comprehensive literature review and a discussion of main contributions in that field).…”

“…These effects are also observed by Sapountzakis et al [5,6] where also buckling analyses are considered. In order to circumvent the insufficient accuracy of CBM in thin-walled single or multi-cell box type cross-sections, however, maintaining a moderate number of global degrees of freedom, a Generalized Beam Theory (GBT) can be applied (see [1] and [5] for a comprehensive literature review and a discussion of main contributions in that field). After all, GBT is a two-step algorithm consisting of a cross-sectional analysis defining warping and distortional fields, followed by a member analysis, where those deformation fields are weighed axially along the beam.…”

A Minimal GBT Model for Distortional-Twist Elastic Analysis of Box-Girder Bridges

“…Recently, higher-order theories of one-dimensional beams have been used, in which some added kinematic descriptors account for warping and distortion of the beam. An overview of different models in the literature is provided in Reference [10]. In this class of papers falls, e.g., References [11,12], in which warping and ovalization of a multi-layered beam is analyzed, and References [13][14][15], where nonlinear effects are accounted for.…”

Free Vibration Analysis of Simply Supported P-FGM Nanoplate Using a Nonlocal Four Variables Shear Deformation Plate Theory

“…Functionally graded materials (FGM) can be characterized by the gradual variation of material properties in the thickness. A new type of composite materials is developed recently (Abdelbaki et al [1]; Arnab Choudhury et al [2]; Abdelbaki et al [3]; Ebrahimi and Barati [4]; Ebrahimi and Heidari [5]; Elmerabet et al [6]; Elmossouess et al [7]; Houari et al [8]; Karami et al [9]; Mahjoobi and Bidgoli [10]; Mohamed et al [11]; Mokhtar et al [12]; Mokhtar et al [13]; Sadoun et al [14]; Salari et al [15]; Shafiei and Setoodeh [16]; Shokravi [17]; Tlidji et al [18]; Tounsi et al [19]; Tu et al [20]; Bocko, J et al [21]; Jozef, B et al [22]; Stephan, K et al [23]; Murín, J et al [24]; Sapountzakis, E et al [25]).…”