Torsional rigidity of arbitrarily shaped composite sections by hybrid finite element approach (original) (raw)
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An effective curved composite beam finite element based on the hybrid-mixed formulation
Computers & Structures, 1994
A laminated curved-beam finite element with six displacement degrees of freedom and three stress parameters is derived and evaluated. Both thermal and hygrothermal effects are included. The element is based on the Hellinger-Reissner principle and the hybrid-mixed formulation. The Timoshenko beam theory and classical lamination theory are employed in the finite element description. Within an element linear displacement interpolation is used; the generalized stresses are interpolated by either stress functions based on the equilibrium equations (P,) or constant stress approximation (PJ The beam element stiffness is obtained explicitly and numerical results show very good displacement prediction compared to analytical solutions. Generalized stresses are predicted accurately at the mid-point of the finite element only for constant stress interpolation. The P,-type element yields more accurate displacement and stress prediction.
A mixed finite element formulation for the stress analysis of composite structures
Computers & Structures, 1992
The mixed formulation based on the Hellinger-Reissner variational principle is used to analyse structures with dissimilar materials. In this formulation, both stresses and displacements are taken as independent unknowns of the problem and are continuous at the element boundaries. The formulation is then modified in order to allow the required discontinuity of some stress components along bimaterial interfaces. A finite element program of this formulation has been developed for the analysis of two-dimensional and axisymmetric bodies. A number of validation tests have been carried out to assess the performance of the mixed method in the stress analysis of both homogeneous structures and those consisting of highly dissimilar materials. The computed results are compared with those using conventional displacement method, other published techniques, and analytical solutions. The mixed formulation based on the Hellinger-Reissner theorem has been demonstrated to have a satisfactory degree of accuracy, especially in view of the observed inability of the conventional compatible method to yield reliable stress values
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The present article proposes an alternative way to compute the torsional stiffness based on three-dimensional continuum mechanics instead of applying a specific theory of torsion. A thin, representative beam slice is discretized by solid finite elements. Adequate boundary conditions and coupling conditions are integrated into the numerical model to obtain a proper answer on the torsion behaviour, thus on shear center, shear stress and torsional stiffness. This finite element approach only includes general assumptions of beam torsion which are independent of cross-section geometry. These assumptions essentially are: no in-plane deformation, constant torsion and free warping. Thus it is possible to achieve numerical solutions of high accuracy for arbitrary cross-sections. Due to the direct link to three-dimensional continuum mechanics, it is possible to extend the range of torsion analysis to sections which are composed of different materials or even to heterogeneous beams on a high s...
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Torsional evaluation of Tapered Composite Cone using Finite Element Analysis
Composite material is one of the most important and economical material for the various application due to its favorable properties .Recently many researches are going on the various properties of the these materials .In this paper an anisotropic behavior of the composite tube is to be modeled and analysis is to be performed under torsional loading conditions. Torsion is a tricky phenomenon in composite cylinders as the twist effects and their interactions with composite shells induce complex stress patterns. The objective behind the study is to understand interaction of conical angle, length of tube and torsional moment .it also includes comparative analysis of deformation and stresses developed in tapered composite cone due to use of various materials like steel, orthotropic composite and laminated composite etc. The effect of taper angle, thickness of the tube and fiber orientations in case of laminated composite is studied by using finite element analysis (ANSYS software). The finite element analysis is especially versatile and efficient for the analysis of complex structural behavior of the composite laminated structures. It is found that deformation in case of laminated composite and deformation in between steel and laminated composite cone. At membrane stresses are observed at the middle of cone in length direction for three materials.
Shear deformable hybrid finite element formulation for buckling analysis of composite columns
Canadian Journal of Civil Engineering, 2018
The objective of this study to develop a shear deformable hybrid finite element formulation for the flexural buckling analysis of fiber-reinforced laminate composite columns with doubly symmetric cross-sections. The hybrid finite element formulation is developed by using the Hellinger-Reissner functional which is obtained by introducing the conditions of compatibility as auxiliary conditions to the potential energy functional. The shear deformation effects due to bending are included by equilibrating shear stress. In comparison to the displacement-based formulations the current hybrid formulation has the advantage of incorporating the shear deformation effects easily by using the strain energy of the shear stress field without modifying the basic kinematic assumptions of the beam theory. The agreement with Engesser formulation for flexural buckling analysis of columns with shear-weak cross-sections shows the applicability and accuracy of the current hybrid finite element method for composite structural elements. The applicability of the developed method herein to sandwich and built-up columns are also illustrated.
Modal analysis of laminated composite plates by a new hybrid assumed strain finite element
Proceedings of AIMETA National Conference: XXI Congresso Associazione Italiana di Meccanica Teorica ed Applicata (AIMETA), Torino, 09/17-20 (2013), co-authored with Antonio Cazzani , 2013
Fibre reinforced plates and shells are funding an increasing interest in engineering applications; in most cases dynamic phenomena need to be taken into account. Consequently effective and robust computational tools are sought in order to provide reliable results for the analysis of such structural models. In this paper the laminate hybrid assumed-strain plate element presented in [1], and used there in a static analysis, has been extended to the dynamic realm. This model is derived within the framework of the so called First-order Shear Deformation Theory (FSDT) [2], [3]. What is peculiar in this assumed strain finite element is the direct modelling of the in-plane strain components; the corresponding stress components are deduced via constitutive law. By enforcing the equilibrium equations for each lamina, account taken of continuity requirements, the out-of-plane shear stresses are computed and, finally, constitutive law provides the corresponding strains. The resulting global strain field depends on a fixed number of parameters, regardless of the total number of layers. Since the proposed element is not locking prone even in the thin plate limit and provides an accurate description of inter-laminar stresses, an extension to the dynamic range seems to be particularly attractive. The same kinematic assumptions will lead to the formulation of a consistent mass matrix. The element, developed in this way, has been extensively tested for several lamination sequences and comparison with analytical solutions are presented.
Computers & Structures, 1995
A finite element formulation for arbitrarily curved orthotropic composite plate and shell analyses is presented here by using a higher order, partial hybrid stress method. The governing equation of the laminated plate is variationally derived from the Hellinger-Reissner principle. The flexural stress components are separated from the transverse shear stress components so that the continuity of interlaminar stress is enforced in the transverse shear stresses only. A general formulation is developed by using the shell geometry to suitably transform the plate equations into the shell equations. The partial hybrid stress method satisfies interface traction continuity conditions exactly in the transverse shear stress, and avoids the complexity of formulation that the normal hybrid stress method has. The validity of this method is demonstrated in various static deformation and free vibrations of plates and shells.
Study of Pure Torsion in Open Thin Walled Sections using Finite Element Analysis
2017
Generally, Open Thin Walled (OTW) cross sections are susceptible to torsional instability, due to their low torsional rigidity. Several analytical methods have been proposed to calculate the torsional deformation (warping) along the direction perpendicular to the cross section of such OTW sections when subjected to torsion. In this paper, we have analysed the warping in the OTW sections to validate that in case of pure torsion of such bars having free ends, the warping is uniform throughout the whole length of the bar and any line parallel to centroidal axis can be taken as axis of rotation. The finite element analysis using ABAQUS has been done to analyse the warping of such sections when subjected to pure torsion. This paper also represents the comparative study of warping distribution in OTW sections using the theoretical approach and Finite Element Modeling (FEM). KeywordsPure Torsion, Warping, Open Thin Walled Section, ABAQUS, Finite Element Method.