An accurate nonlinear 3d Timoshenko beam element based on Hu-Washizu functional

Date

2013-09-01

Author

Soydas, Ozan
Sarıtaş, Afşin

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

184
views

0
downloads

An accurate 3d mixed beam element that is efficient especially in nonlinear analysis is presented in this paper. The mathematical theory is based on Hu-Washizu principle that uses three-fields in the variational form. The composition of the variational form ensures independent selection of displacement, stress and strain fields. Timoshenko beam theory is extended to three dimensions for deriving strains from displacement field. Numerical integration of stress strain relations along control sections is carried out for numerical analysis. The finite element approximation for the beam uses shape functions for section forces that satisfy equilibrium and discontinuous section deformations along the control sections of the beam. This form of the element permits coupling of the stress resultants and eliminates necessity of displacement components along the beam element except at the nodes. Consequently the element is free from shear-locking. Numerical examples on uniform and tapered structural members with solid and hollow circular sections demonstrate the nonlinear interaction between axial, shear force, bending moments and torsion, where the results compare well with closed form solutions and available data in literature. Furthermore, the proposed element has superior performance in both linear and nonlinear analysis compared to a locking-free higher order displacement based 3d Timoshenko beam element.

Subject Keywords

Mechanical Engineering, General Materials Science, Mechanics of Materials, Civil and Structural Engineering, Condensed Matter Physics

URI

https://hdl.handle.net/11511/45654

Journal

INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES

DOI

https://doi.org/10.1016/j.ijmecsci.2013.04.002

Collections

Department of Civil Engineering, Article

Suggestions

OpenMETU
Core

Stress resultants plasticity with general closest point projection Sarıtaş, Afşin (Elsevier BV, 2011-03-01) In this paper, general closest point projection algorithm is derived for the elastoplastic behavior of a cross-section of a beam finite element. For given section deformations, the section forces (stress resultants) and the section tangent stiffness matrix are obtained as the response for the cross-section. Backward Euler time integration rule is used for the solution of the nonlinear evolution equations. The solution yields the general closest projection algorithm for stress resultants plasticity model. Al...
A variational multiscale constitutive model for nanocrystalline materials Gürses, Ercan (Elsevier BV, 2011-03-01) This paper presents a variational multi-scale constitutive model in the finite deformation regime capable of capturing the mechanical behavior of nanocrystalline (nc) fcc metals. The nc-material is modeled as a two-phase material consisting of a grain interior phase and a grain boundary effected zone (GBAZ). A rate-independent isotropic porous plasticity model is employed to describe the GBAZ, whereas a crystal-plasticity model which accounts for the transition from partial dislocation to full dislocation m...
A new modal superposition method for nonlinear vibration analysis of structures using hybrid mode shapes Ferhatoglu, Erhan; Ciğeroğlu, Ender; Özgüven, Hasan Nevzat (Elsevier BV, 2018-07-01) In this paper, a new modal superposition method based on a hybrid mode shape concept is developed for the determination of steady state vibration response of nonlinear structures. The method is developed specifically for systems having nonlinearities where the stiffness of the system may take different limiting values. Stiffness variation of these nonlinear systems enables one to define different linear systems corresponding to each value of the limiting equivalent stiffness. Moreover, the response of the n...
A database of PIV measurements within a turbomachinery stage and sample comparisons with unsteady RANS Uzol, Oğuz; Chow, Y.-C.; Katz, J.; Meneveau, C. (Informa UK Limited, 2007-01-01) This paper describes an experimental database obtained using two-dimensional Particle Image Velocimetry (PIV) measurements within an axial turbomachinery stage, and presents sample unsteady Reynolds Averaged Navier - Stokes (RANS) simulations to illustrate its applicability for turbomachinery model validation. The experiments are performed in a refractive-index-matched facility that provides unobstructed view, and cover the entire second stage of a two-stage axial pump. The data were obtained at ten differe...
A parallel gas-kinetic Bhatnagar-Gross-Krook method for the solution of viscous flows on two-dimensional hybrid grids Ilgaz, M.; Tuncer, İsmail Hakkı (Informa UK Limited, 2009-01-01) In this study, a parallel implementation of gas-kinetic Bhatnagar-Gross-Krook method on two-dimensional hybrid grids is presented. Boundary layer regions in wall bounded viscous flows are discretised with quadrilateral grid cells stretched in the direction normal to the solid surface while the rest of the flow domain is discretised by triangular cells. The parallel solution algorithm on hybrid grids is based on the domain decomposition using METIS, a graph partitioning software. The flow solutions obtained ...

Citation Formats

O. Soydas and A. Sarıtaş, “An accurate nonlinear 3d Timoshenko beam element based on Hu-Washizu functional,” INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES, pp. 1–14, 2013, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/45654.