Curved Beam Finite Element Research Articles

Natural frequencies of arch bridges with slab decks by the finite element method

A study of the free-vibration natural frequencies of an arch bridge is presented. The bridge consists of two structural components namely a circular arch and a flat deck, monolithically connected together at the crown of the arch. A two-dimensional mathematical model is used in the analysis; the curved component is modelled by curved-beam finite elements and the deck by straight-beam finite elements. Both symmetrical and anti-symmetrical modes of vibration are studied for such bridges when the ends of the arches and decks are either hinged or fixed to rigid abutments. The effect of varying the relative stiffnesses of the two components on the fundamental and second modes of vibration is also presented and compared with the corresponding frequencies of the arch component vibrating on its own.

P-Version two-dimensional curved beam element using piecewise hierarchical approximation for laminated composites

A three node two-dimensional laminated composite curved beam finite element formulation for linear static analysis is presented where the displacement approximation for the laminate is piecewise hierarchical and is derived based on p-version. The displacement approximation for the element is developed by establishing a hierarchical displacement approximation for each lamina of the laminate and then by imposing interlamina continuity conditions of displacement at the interfaces between the laminas. The approximation functions and the nodal variables for each lamina are derived directly from the Lagrange family of interpolation functions of order pξand pη. This is accomplished by first establishing one-dimensional hierarchical approximation functions and the corresponding nodal variable operators in the ξ and η directions for the three and one node equivalent configurations that correspond to pξ+1 and pη+1 equally spaced nodes in the ξ and η directions and then taking their products. The nodal variables for the entire laminate are derived from the nodal variables of the laminas and the interlamina continuity conditions of displacements. The element formulation ensures C0 continuity of displacement across the interelement as well as interlamina boundaries.

On trigonometric basis functions for C1 curved beam finite elements

The formulation of a finite element model for a thin curved beam which is described by the Winkler beam model is presented. A review and discussion of the literature that pertains to this type of element is included with special attention being paid to the need to be able to recover incremental rigid body motions. Three different C 1 trigonometric trial functions that allow the recovery of incremental rigid body motions are investigated. The attributes and deficiencies of the various elements are examined and discussed via several problems which have been designed to evaluate the performance of the element. The 4 U4 W element is shown to be the best choice of those elements considered here.

Vibration analysis of coil springs by means of isoparametric curved beam finite elements

An investigation is conducted on the performance of the curved isoparametric cubic beam element for analysing vibrational behaviour of coil springs. Firstly, the results of full and uniformly reduced integration are compared for three static problems. Uniformly reduced integration is shown to yield surprising accuracy, even for curved and pretwisted beams. In the latter case of a shear loaded cantilever beam, exact internal force values are obtained. Since element geometry is described by nodal co-ordinates and cross-sectional orientation only, the element proves to be ideal for modelling both helical and non-helical sections of coil springs. In addition, the formulation is easy to implement and simpler than those of previous ‘helical spring elements’. It is shown that accurate values for modal frequencies can be obtained with relatively coarse meshes.

Nonlinear Curved‐Beam Element for Arch Structures

A nonlinear curved-beam finite element is developed for three-dimensional space systems by using the principle of potential energy and polynomial functions. It is limited to elastic material with linear stress-strain relation. Warping is not considered. A major improvement in the accuracy of the element is obtained by averaging the nonlinear part of the axial strain. The method of solution used is that of the fixed Lagrange coordinates and the Newton-Raphson procedure. Comparisons of numerical results with those of various other methods indicate that, in terms of the number of elements or degrees of freedom needed for convergence, the method seems significantly more effective than most. None of the others was seen to be more effective. The problems considered included shallow and deep arches, extremely thin arches, and arches of various profiles. An application to an arch structure subjected to dynamic or cyclic (earthquake) loading is also illustrated.

Studies on performance of curved beam finite elements for analysis of thin arches

The finite element model with cubic polynomial shape functions to analyse thin arches has been modified to relieve membrane locking effects and thus to achieve better performance. Two different ways of improving the element stiffness have been studied, one by adopting the reduced integration technique and the other by adopting a least square fit to achieve field consistency for membrane strains. The curved cantilever beam of Kikuchi and two fixed circular arches of Dawe having different ratios of radius to thickness (one deep, the other shallow) were studied by using the improved models. The results obtained by the improved models are compared with those of others. The model with three point integration for membrane energy gives, as expected, identical results in comparison with field consistency. The model with two point reduced integration in membrane and four point integration for bending has been found to be superior in convergence.

Integrated Bending Field Finite Element for Curved Beams

A displacement‐based formulation for an arbitrarily shaped, thin to moderately thick curved beam finite element is presented. Independent interpolations for bending and membrane‐shear displacement fields are employed to create a bending strain kinematically independent from the coupled membrane and shear strains. A higher order field is implemented for the bending deflection by integration of the rotation field. The resulting element is free from membrane and shear locking problems common to most isoparametric elements. Numerical testing shows excellent convergence behavior for the element, even when overintegration is applied.

Nonlinear Shallow Curved‐Beam Finite Element

A geometrically nonlinear curved-beam finite element is derived and is applied to the load-deflection and buckling analysis of shallow and deep arches. The element stiffness properties are derived relative to a moving reference frame having one axis along the element chord, and they are then transformed to a global reference frame. The initial shape of the element is a shallow cubic polynomial, and its deformed shape is the exact shape caused by end actions within the context of shallow beam theory with shear deformation included. The element stiffness properties are exact within the context of that theory, and are described by explicit formulas similar to those of an initially straight element. In a global reference frame the element applies to deep arches with large rotations. Numerical applications are implemented for the second-order theory. Good results are obtained for the snap-through analysis of a shallow arch and for buckling of deep and shallow arches.

Curved beam elements to model noncircular coil shapes for tokamak reactor

AbstractThe detailed stress analysis of the toroidal field superconducting coil is needed to ensure its structural integrity, which includes conductor breakage, insulation breakage, sliding between two turns, or support structure failure. Such detailed‐analysis requires that each of the superconducting coil turns be modelled separately. In this paper, a curved beam finite element,13 having constant radius of curvature, is considered to model a turn of a noncircular toroidal field coil. Four different coil shapes subjected to electromagnetic body forces due to toroidal magnetic fields are analysed to assess the finite element models: circular, elliptic, Princeton‐D8 and compound shape9. The comparison of analytical and finite element analysis results for resultant forces, tensions and displacements suggest that the proposed approach may be extended to the detailed stress analysis of the noncircular toroidal field superconducting coil.

Nonlinear finite element computation of the equilibrium, stability and motion of the extensional beam and ring

Discrete Gauss integration of the element total potential energy is applied to the formation of a cubic-cubic C 1 extensible completely nonlinear curved beam finite element. The versatility, accuracy, effectiveness, and robustness of the element, and the Newton-Raphson technique used to solve the nonlinear algebraic stiffness equation set up with it is numerically demonstrated by computations of the nonlinear equilibrium stability and motion of beams and rings.

A laminated anisotropic curved beam and shell stiffening finite element

The details of development of the stiffness matrix of a laminated anisotropic curved beam finite element are reported. It is a 16 dof element which makes use of 1-D first order Hermite interpolation polynomials for expressing it's assumed displacement state. The performance of the element is evaluated considering various examples for which analytical or other solutions are available.

Closure to “Thin-Walled Curved Beam Finite Element”

Closure to “Thin-Walled Curved Beam Finite Element”

Comment on ‘horizontally curved beam finite element including warping’

Comment on ‘horizontally curved beam finite element including warping’

Discussion of “Thin-Walled Curved Beam Finite Element”

Discussion of “Thin-Walled Curved Beam Finite Element”

Discussion of “Thin-Walled Curved Beam Finite Element”

Discussion of “Thin-Walled Curved Beam Finite Element”

Discussion of “Thin-Walled Curved Beam Finite Element”

Discussion of “Thin-Walled Curved Beam Finite Element”

Erratum for “Thin-Walled Curved Beam Finite Element”

Erratum for “Thin-Walled Curved Beam Finite Element”

Nonlinear finite element analysis of curved beams

Abstract Mixed curved-beam finite elements are developed for the geometrically nonlinear analysis of deep arches. The analytical formulation is based on a form of the nonlinear deep-arch theory with the effects of transverse shear deformation and bending-extensional coupling included. The fundamental unknowns consist of the six internal forces and generalized displacements of the arch. The generalized stiffness matrix is obtained by using a modified form of the Hellinger-Reissner mixed variational principle. Numerical studies are presented to demonstrate the high accuracy of the solutions obtained by the mixed models and to show that their performance is considerably less sensitive to variations in the arch geometry than that of the displacement models.

Technical note: Horizontally curved beam finite element including warping

International Journal for Numerical Methods in EngineeringVolume 10, Issue 6 p. 1397-1403 Short Communication Technical note: Horizontally curved beam finite element including warping Fathalla M. El-Amin, Fathalla M. El-Amin Department of Civil Engineering, University of Assiut, Assiut, Egypt LecturerSearch for more papers by this authorD. M. Brotton, D. M. Brotton Department of Civil and Structural Engineering, University of Manchester Institute of Science and Technology, Manchester, England ProfessorSearch for more papers by this author Fathalla M. El-Amin, Fathalla M. El-Amin Department of Civil Engineering, University of Assiut, Assiut, Egypt LecturerSearch for more papers by this authorD. M. Brotton, D. M. Brotton Department of Civil and Structural Engineering, University of Manchester Institute of Science and Technology, Manchester, England ProfessorSearch for more papers by this author First published: 1976 https://doi.org/10.1002/nme.1620100618Citations: 20 AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Citing Literature Volume10, Issue61976Pages 1397-1403 RelatedInformation

Curved finite elements for the analysis of shallow and deep arches

The paper considers the analysis of shallow and deep arches by curved beam finite elements, the interest in this problem being that it forms a limiting case of the shell problem. The individual elements are assumed to be shallow with respect to a local base line and different types of strain-displacement equations are utilised. Particular attention is focussed on the choice of the displacement patterns for the elements and models based both on independently-interpolated displacement components, of up to quintic order, and on assumed strain distributions are considered. Numerical applications using the various models show that of those tested only quintic-quintic models and assumed-strain models are generally satisfactory.