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A two‐node beam element including transverse shear and transverse normal deformations
Author(s) -
Tessler Alexander
Publication year - 1991
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620320507
Subject(s) - transverse plane , finite element method , orthotropic material , boundary value problem , displacement field , beam (structure) , timoshenko beam theory , geometry , bending stiffness , mechanics , materials science , mathematics , classical mechanics , mathematical analysis , physics , structural engineering , optics , engineering
A variational higher‐order theory for bending and stretching of linearly elastic orthotropic beams including the deformations due to transverse shearing and stretching of the transverse normal fibre is presented. The theory assumes a linear distribution for the longitudinal displacement and a parabolic variation of the transverse displacement across the thickness. Additionally, independent expansions are introduced for the through‐thickness displacement gradients with the requirement of a least‐square compatibility for the transverse strains and the satisfaction of exact stress boundary conditions at the top/bottom beam surfaces. The theory is shown to be well suited for finite element development requiring simple C 0 ‐ and C −1 ‐ continuous displacement interpolation fields. To demonstrate the computational utility of the theory, a simple two‐node stretching‐bending finite element is formulated. The analytic and finite element results are obtained for a simple bending problem for which an exact elasticity solution is available. It is shown that the inclusion of the transverse normal deformation in the present theory enables improved displacement, strain and stress predictions, particularly, in the analysis of deep beams.