A large torsion beam finite element model for tapered thin-walled open cross sections beams (original) (raw)
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Large torsion finite element model for thin-walled beams
Behaviour of thin-walled beams with open section in presence of large torsion is investigated in this work. The equilibrium equations are derived in the case of elastic behaviour without any assumption on torsion angle amplitude. This model is extended to finite element formulation in the same circumstances where 3D beams with two nodes and seven degrees of freedom per node are considered. Due to large torsion assumption and flexural–torsional coupling, new matrices are obtained in both geometric and initial stress parts of the tangent stiffness matrix. Incremental-iterative Newton–Raphson method is adopted in the solution of the nonlinear equations. Many applications are presented concerning the nonlinear and post-buckling behaviour of beams under torsion and bending loads. The proposed beam element is efficient and accurate in predicting bifurcations and nonlinear behaviour of beams with asymmetric sections. It is proved that the bifurcation points are in accordance with nonlinear stability solutions. The convenience of the model is outlined and the limit of models developed in linear stability is discussed.
Advances in Engineering Software, 2015
The authors have developed a beam finite element model in large torsion context for thin-walled beams with arbitrary cross sections [1]. In the model, the trigonometric functions of the twist angle h x (c = cos h x À 1 and s = sin h x ) were included as additional variables in the whole model without any assumption. In the present paper, three other 3D finite element beams are derived according to three approximations based on truncated Taylor expansions of the functions c and s (cubic, quadratic and linear). A finite element approach of these approximations is carried out. Finally, it is worth mentioning that the promising results obtained in [1,2] encourage the authors to extend the formulation of the model in order to include load eccentricity effects. Solution of the non-linear equations is made possible by Asymptotic Numerical Method (ANM) . This method is used as an alternative to the classical incremental iterative methods.
A beam finite element for non-linear analyses of thin-walled elements
Thin-Walled Structures, 2008
The aim of the present paper is to investigate a theoretical and numerical model which is able to study the behaviour of thin-walled beams with open cross section in presence of large torsion. The presented model takes into account for large torsion, linear and nonlinear warping currently named shortening effects, pre-buckling deformation and flexural-torsional coupling. In numerical analysis, a 3D beam with two nodes and seven degrees of freedom per node is adopted. The equilibrium equations and the material behaviour are derived in discrete form without assumption on torsion angle amplitude. Due to large torsion context, all the equilibrium equations are non-linear and highly coupled. The linear behaviour is made possible by disregarding non-linear terms. For non-linear behaviour and stability, the tangent stiffness matrix is carried out. Due to large torsion context, new matrices are present. The element is incorporated in a homemade finite element code. Newton-Raphson iterative methods are used with different control parameters. In order to prove the efficiency of the model many examples are presented in linear and non-linear behaviour with presence of bifurcations. r
Lateral-torsional buckling of tapered thin-walled beams with arbitrary cross-sections
Thin-Walled Structures, 2013
In this paper, a theoretical and numerical model based on the power series method is investigated for the lateral buckling stability of tapered thin-walled beams with arbitrary cross-sections and boundary conditions. Total potential energy is derived for an elastic behavior from strain energy and work of the applied loads. The effects of the initial stresses and load eccentricities are also considered in the study. The lateral-torsional equilibrium equations and the associated boundary conditions are obtained from the stationary condition. In presence of tapering, all stiffness coefficients are not constant. The power series approximation is then used to solve the fourth-order differential equations of tapered thinwalled beam with variable geometric parameters having generalized end conditions. Displacement components and cross-section properties are expanded in terms of power series of a known degree. The lateral buckling loads are determined by solving the eigenvalue problem of the obtained algebraic system. Several numerical examples of tapered thin-walled beams are presented to investigate the accuracy and the efficiency of the method. The obtained results are compared with finite element solutions using Ansys software and other available numerical or analytical approaches. It is observed that suggested method can be applied to stability of beams with constant cross-sections as well as tapered beams.
The Torsion Effects on the Non-Linear Behaviour of Thin-Walled Beams: A Finite Element Approach
Proceedings of the Eleventh International Conference on Computational Structures Technology, 2012
The authors have developed a beam finite element model for thin walled beams with arbitrary cross sections in the large torsion context . Circular functions of the torsion angle θ x (c=cosθ x -1 and s=sinθ x ) were included as variables. In this paper three other three-dimensional finite element beams are derived according to the three approximations of the circular functions c and s: cubic, quadratic and linear. A finite element approach of these approximations is carried out. Many comparison examples are considered. They concern non linear behaviour of beams under twist moment and post buckling behaviour of beams under axial loads or bending loads.
Large torsion analysis of thin-walled open sections beams by the Asymptotic Numerical Method
Engineering Structures, 2014
This paper presents a continuation algorithm based on the Asymptotic Numerical Method (ANM) to study instability phenomena of large torsion of thin-walled open sections beams under various external loadings. The proposed algorithm connects perturbation techniques with a discretization principle and a continuation method without the use of a correction process. In the model, the equilibrium and material constitutive equations are established without any assumption on torsion angle amplitude. In presence of eccentric loads and large torsion context, the right hand side of the equilibrium equations is highly nonlinear and contributes to the tangent stiffness matrix. A 3D beam element having two nodes with seven degrees of freedom is considered in mesh process. Several numerical examples from buckling of thin-walled open sections beams are analyzed to assess the efficiency and the reliability of the method. Comparisons are made with known commercial software. The proposed ANM algorithm is more reliable and less time consuming than other iterative classical methods.
International Journal of Mechanical Sciences, 2011
In this paper, lateral-torsional buckling behavior of open-section thin-walled beams is investigated based on a geometrically nonlinear formulation, which considers the effects of shear deformations. A finite element numerical solution along with an incremental-iterative solution procedure is adopted to trace the pre-buckling as well as the post-buckling equilibrium paths. Formulation is applicable to a general type of open-section and load position effects are also included. Numerical results are validated through comparisons with experimental results and those based on other formulations presented in the literature. Comparisons have also been made between the results based on fully nonlinear analysis and linearized buckling analysis in order to illustrate the effects of pre-buckling deformations as well as the shear deformations on the buckling load predictions. Examples illustrate the influence of beam slenderness and moment gradient on the effects of pre-buckling deformations in predicting bucking loads.
Development of a consistent design procedure for lateral–torsional buckling of tapered beams
Journal of Constructional Steel Research, 2013
Eurocode 3 provides several methods for the stability verification of members and frames. However, several inconsistencies and difficulties have been noticed in the case of non-uniform members regarding in what concerns stability verification. In this paper, the case of web-tapered beams is studied. In a first step, available methods for stability verification of web-tapered beams are discussed. A second order analytical model based on an Ayrton-Perry approach is then derived for the case of tapered beams with uniform bending moment and further extended to other bending moment distributions. Several consistent simplifications are carried out in order to build a simple but coherent design model for the stability verification of tapered beams subject to linear bending moment distributions and to parabolic bending moment. More than 3000 numerical simulations are carried out for calibration and analysis of the results. Throughout the paper, specific issues such as the presence of shear or the codified imperfections for welded cross-sections are brought in and taken into account. Finally, it is noted that the proposed model is consistent with recently proposed design models for the stability verification of prismatic beams.
Computers & Structures, 2007
This paper assesses the global performance and the underlying assumptions of a recently developed one-dimensional model characterising the elastic lateral-torsional buckling behaviour of singly symmetric tapered thin-walled open beams, which is able to account for the influence of the pre-buckling deflections. A comparative study involving the critical load factors and buckling modes yielded by (i) the one-dimensional model and (ii) two-dimensional shell finite element analyses (reference results) is presented and discussed. The results concern I-section cantilevers and simply supported beams (i) with uniform or linearly tapered webs, (ii) equal or unequal uniform flanges and (iii) acted by point loads applied at the free end or mid-span sections, respectively. In general, the one-dimensional predictions are found to agree well with the shell finite element results. Some significant discrepancies are also recorded (for the shorter beams), which are due to the occurrence of relevant cross-section distortion or localised buckling phenomena.
Static, dynamic and stability analysis of structures composed of tapered beams
Computers & Structures, 1983
A new numerical method is proposed for the static, dynamic and stability analysis of linear elastic plane structures consisting of beams with constant width and variable depth. It is a finite element method based on an exact flexural and axial stiffness matrix and approximate consistent mass and geometric stiffness matrices for a linearly tapered beam element with constant width. Use of this method provides the exact solution of the static problem with just one element per member of a structure with linearly tapered beams and excellent approximate solutions of the dynamic and stability problems with very few elements per member of the structure in a computation~iy very efticient way. Very detailed comp~ison studies of the proposed method against a number of other known finite element methods with respect to accuracy and compu~tionai elllciency for cantilever tapered beams of rectangular and I cross section clearly favor the proposed method. A continuous beam, a gable frame and a portal frame consisting of tapered members are analyzed by the proposed method as well as by other known methods to illustrate the use of the method to structures composed of tapered beams.