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Journal articles on the topic 'Higher order beam element'

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Author: Grafiati

Published: 14 March 2023

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1

Lim, Jae Kyoo, and Seok Yoon Han. "Development of Orthotropic Beam Element Using a Consistent Higher Order Deformation Theory." Key Engineering Materials 261-263 (April 2004): 519–24. http://dx.doi.org/10.4028/www.scientific.net/kem.261-263.519.

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In order to analyze beam structures more accurately and effectively, a two-node orthotropic beam element is proposed. This beam element is formulated using a consistent higher order deformation theory of orthotropic beams of which the transverse normal deformation can be effectively estimated. The stiffness matrix and the vector of equivalent nodal forces of the beam element are derived explicitly by the Galerkin method. In order to examine the reliability and the characteristics of the beam element, the analytical and the finite element solutions of a simple cantilevered beam are compared with each other. As a result, the following conclusions are obtained; (1) the accuracy of the suggested orthotropic beam element is very excellent and so the transverse normal deformation and shear stress of an orthotropic beam can be effectively estimated. (2) It can be used for accurately analyzing the general beam structures regardless of the Euler's or the Timoshenko's beam.

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2

Thom, Tran Thi, and Nguyen Dinh Kien. "FREE VIBRATION OF TWO-DIRECTIONAL FGM BEAMS USING A HIGHER-ORDER TIMOSHENKO BEAM ELEMENT." Vietnam Journal of Science and Technology 56, no. 3 (June 11, 2018): 380. http://dx.doi.org/10.15625/2525-2518/56/3/10754.

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Free vibration of two-directional functionally graded material (2-D FGM) beams is studied by the finite element method (FEM). The material properties are assumed to be graded in both the thickness and longitudinal directions by a power-law distribution. Equations of motion based on Timoshenko beam theory are derived from Hamilton's principle. A higher-order beam element using hierarchical functions to interpolate the displacements and rotation is formulated and employed in the analysis. In order to improve the efficiency of the element, the shear strain is constrained to constant. Validation of the derived element is confirmed by comparing the natural frequencies obtained in the present paper with the data available in the literature. Numerical investigations show that the proposed beam element is efficient, and it is capable to give accurate frequencies by a small number of elements. The effects of the material composition and aspect ratio on the vibration characteristics of the beams are examined in detail and highlighted.

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3

Nguyen, Dinh Kien, and Van Tuyen Bui. "Dynamic Analysis of Functionally Graded Timoshenko Beams in Thermal Environment Using a Higher-Order Hierarchical Beam Element." Mathematical Problems in Engineering 2017 (2017): 1–12. http://dx.doi.org/10.1155/2017/7025750.

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A higher-order finite beam element for free and forced vibration analysis of functionally graded Timoshenko beams in thermal environment is formulated by using hierarchical functions to interpolate the kinematic variables. The shear strain is constrained to constant to improve the efficiency of the element. The effect of environmental temperature is taken into account in the element derivation by considering that the material properties are temperature-dependent and the temperature is nonlinear distribution in the beam thickness. The accuracy of the derived formulation is confirmed by comparing the results obtained in the present work with the published data. Numerical investigations show that the formulated element is efficient, and it is capable of giving accurate vibration characteristics by a small number of elements. A parametric study is carried out to highlight the effect of the material inhomogeneity, temperature rise, and loading parameter on the dynamic behaviour of the beams. The influence of the aspect ratio on the dynamic behaviour of the beam is also examined and highlighted.

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4

Gara, Fabrizio, Sandro Carbonari, Graziano Leoni, and Luigino Dezi. "Finite Elements for Higher Order Steel–Concrete Composite Beams." Applied Sciences 11, no. 2 (January 8, 2021): 568. http://dx.doi.org/10.3390/app11020568.

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This paper presents finite elements for a higher order steel–concrete composite beam model developed for the analysis of bridge decks. The model accounts for the slab–girder partial interaction, the overall shear deformability, and the shear-lag phenomenon in steel and concrete components. The theoretical derivation of the solving balance conditions, in both weak and strong form, is firstly addressed. Then, three different finite elements are proposed, which are characterised by (i) linear interpolating functions, (ii) Hermitian polynomial interpolating functions, and (iii) interpolating functions, respectively, derived from the analytical solution expressed by means of exponential matrices. The performance of the finite elements is analysed in terms of the solution convergence rate for realistic steel–concrete composite beams with different restraints and loading conditions. Finally, the efficiency of the beam model is shown by comparing the results obtained with the proposed finite elements and those achieved with a refined 3D shell finite element model.

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5

Gara, Fabrizio, Sandro Carbonari, Graziano Leoni, and Luigino Dezi. "Finite Elements for Higher Order Steel–Concrete Composite Beams." Applied Sciences 11, no. 2 (January 8, 2021): 568. http://dx.doi.org/10.3390/app11020568.

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This paper presents finite elements for a higher order steel–concrete composite beam model developed for the analysis of bridge decks. The model accounts for the slab–girder partial interaction, the overall shear deformability, and the shear-lag phenomenon in steel and concrete components. The theoretical derivation of the solving balance conditions, in both weak and strong form, is firstly addressed. Then, three different finite elements are proposed, which are characterised by (i) linear interpolating functions, (ii) Hermitian polynomial interpolating functions, and (iii) interpolating functions, respectively, derived from the analytical solution expressed by means of exponential matrices. The performance of the finite elements is analysed in terms of the solution convergence rate for realistic steel–concrete composite beams with different restraints and loading conditions. Finally, the efficiency of the beam model is shown by comparing the results obtained with the proposed finite elements and those achieved with a refined 3D shell finite element model.

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6

Subramanian, G., and T. S. Balasubramanian. "A higher order element for stepped rotating beam vibration." Journal of Sound and Vibration 110, no. 1 (October 1986): 167–71. http://dx.doi.org/10.1016/s0022-460x(86)80087-6.

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7

Ferradi, Mohammed Khalil, Xavier Cespedes, and Mathieu Arquier. "A higher order beam finite element with warping eigenmodes." Engineering Structures 46 (January 2013): 748–62. http://dx.doi.org/10.1016/j.engstruct.2012.07.038.

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8

Kim, Jin Gon, and Yoon Young Kim. "A new higher-order hybrid-mixed curved beam element." International Journal for Numerical Methods in Engineering 43, no. 5 (November 15, 1998): 925–40. http://dx.doi.org/10.1002/(sici)1097-0207(19981115)43:5<925::aid-nme457>3.0.co;2-m.

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9

Marur, S. R., and T. Kant. "A Higher Order Finite Element Model for the Vibration Analysis of Laminated Beams." Journal of Vibration and Acoustics 120, no. 3 (July 1, 1998): 822–24. http://dx.doi.org/10.1115/1.2893903.

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A higher order displacement model based on a cubic axial strain, cubic transverse shear strain and quadratic transverse normal strain across the thickness of the beam, to model exactly the warping of the cross section is proposed which maintains zero stress at the top and bottom of the beam with out the aid of any shear correction factor. Numerical experiments carried out clearly bring out the efficacy of this model over the first order theory for laminated beams.

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10

Zhen, Wu, and Chen Wanji. "Interlaminar stress analysis of multilayered composites based on the Hu-Washizu variational theorem." Journal of Composite Materials 52, no. 13 (September 27, 2017): 1765–79. http://dx.doi.org/10.1177/0021998317733532.

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Up to date, accurate prediction of interlaminar stresses is still a challenging issue for two-node beam elements. The postprocessing approaches by integrating the three-dimensional equilibrium equation have to be used to obtain improved transverse shear stresses, whereas the equilibrium approach requires the first-order derivatives of in-plane stresses. In-plane stresses within two-node beam element are constant, so the first-derivatives of in-plane stresses are close to zero. Thus, two-node beam elements encounter difficulties for accurate prediction of transverse shear stresses by the constitutive equation or the equilibrium equation, so a robust two-node beam element is expected. A two-node beam element in terms of the global higher-order zig-zag model is firstly developed by employing the three-field Hu-Washizu mixed variational principle. By studying the effects of different boundary conditions, stacking sequence and loading on interlaminar stresses of multilayered composite beams, it is shown that the proposed two-node beam element yields more accurate results with lesser computational cost compared to various higher-order models. It is more important that accurate transverse shear stress has active impact on displacements and in-plane stresses of multilayered composite beams.

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11

Nolde, E., A. V. Pichugin, and J. Kaplunov. "An asymptotic higher-order theory for rectangular beams." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 474, no. 2214 (June 2018): 20180001. http://dx.doi.org/10.1098/rspa.2018.0001.

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A direct asymptotic integration of the full three-dimensional problem of elasticity is employed to derive a consistent governing equation for a beam with the rectangular cross section. The governing equation is consistent in the sense that it has the same long-wave low-frequency behaviour as the exact solution of the original three-dimensional problem. Performance of the new beam equation is illustrated by comparing its predictions against the results of direct finite-element computations. Limiting behaviours for beams with large (and small) aspect ratios, which can be established using classical plate theories, are recovered from the new governing equation to illustrate its consistency and also to illustrate the importance of using plate theories with the correctly refined boundary conditions. The implications for the correct choice of the shear correction factor in Timoshenko's beam theory are also discussed.

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12

Frikha, A., A. Hajlaoui, M. Wali, and F. Dammak. "A new higher order C mixed beam element for FGM beams analysis." Composites Part B: Engineering 106 (December 2016): 181–89. http://dx.doi.org/10.1016/j.compositesb.2016.09.024.

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13

Yu, Haidong, Chunzhang Zhao, Bin Zheng, and Hao Wang. "A new higher-order locking-free beam element based on the absolute nodal coordinate formulation." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 232, no. 19 (October 25, 2017): 3410–23. http://dx.doi.org/10.1177/0954406217736550.

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The beam elements based on the absolute nodal coordinate formulation are widely used in large deformation and large rotation problems. Some of them lead to shear and Poisson locking problems when the continuum mechanics method is employed to deduce the generalized elastic force of the element. To circumvent these locking problems, a new higher-order beam element is proposed that may capture the warping and non-uniform stretching distribution of the cross-section by introducing the trapezoidal cross-section deformation mode and increasing the order of interpolation polynomials in transverse direction. The curvature vectors are chosen as the nodal coordinates of the new element that improve the continuity condition at the element interface. Static and dynamic analyses are conducted to investigate the performance of the new element. Poisson locking phenomena may be eliminated effectively for the new element even when Poisson’s ratio is greater than zero. Meanwhile, the distortion deformation of the cross-section may be described directly. The new element has a better convergence performance compared with the spatial absolute nodal coordinate formulation beam element for that shear locking issue is eliminated. The results also show that the new element fulfills energy conservation and may be applied to the dynamics of both straight and initial curved structures with large deformation.

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14

KATORI, Hiroaki, and Masaki MAEDA. "Beam Element Based on a Higher-Order Shear Deformation Theory." Transactions of the Japan Society of Mechanical Engineers Series A 69, no. 685 (2003): 1374–79. http://dx.doi.org/10.1299/kikaia.69.1374.

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15

Prathap, G., and R. U. Vinayak. "Best-fit stress performance of a higher-order beam element." Communications in Numerical Methods in Engineering 12, no. 4 (April 1996): 229–34. http://dx.doi.org/10.1002/(sici)1099-0887(199604)12:4<229::aid-cnm969>3.0.co;2-0.

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16

Shi, G., and K. Y. Lam. "FINITE ELEMENT VIBRATION ANALYSIS OF COMPOSITE BEAMS BASED ON HIGHER-ORDER BEAM THEORY." Journal of Sound and Vibration 219, no. 4 (January 1999): 707–21. http://dx.doi.org/10.1006/jsvi.1998.1903.

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17

VALLALA, V. P., G. S. PAYETTE, and J. N. REDDY. "A SPECTRAL/hp NONLINEAR FINITE ELEMENT ANALYSIS OF HIGHER-ORDER BEAM THEORY WITH VISCOELASTICITY." International Journal of Applied Mechanics 04, no. 01 (March 2012): 1250010. http://dx.doi.org/10.1142/s1758825112001397.

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In this paper, a finite element model for efficient nonlinear analysis of the mechanical response of viscoelastic beams is presented. The principle of virtual work is utilized in conjunction with the third-order beam theory to develop displacement-based, weak-form Galerkin finite element model for both quasi-static and fully-transient analysis. The displacement field is assumed such that the third-order beam theory admits C0 Lagrange interpolation of all dependent variables and the constitutive equation can be that of an isotropic material. Also, higher-order interpolation functions of spectral/hp type are employed to efficiently eliminate numerical locking. The mechanical properties are considered to be linear viscoelastic while the beam may undergo von Kármán nonlinear geometric deformations. The constitutive equations are modeled using Prony exponential series with general n-parameter Kelvin chain as its mechanical analogy for quasi-static cases and a simple two-element Maxwell model for dynamic cases. The fully discretized finite element equations are obtained by approximating the convolution integrals from the viscous part of the constitutive relations using a trapezoidal rule. A two-point recurrence scheme is developed that uses the approximation of relaxation moduli with Prony series. This necessitates the data storage for only the last time step and not for the entire deformation history.

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18

Ribarić, Dragan, and Gordan Jelenić. "Higher-order linked interpolation in triangular thick plate finite elements." Engineering Computations 31, no. 1 (February 25, 2014): 69–109. http://dx.doi.org/10.1108/ec-03-2012-0056.

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Purpose – In this work, the authors aim to employ the so-called linked-interpolation concept already tested on beam and quadrilateral plate finite elements in the design of displacement-based higher-order triangular plate finite elements and test their performance. Design/methodology/approach – Starting from the analogy between the Timoshenko beam theory and the Mindlin plate theory, a family of triangular linked-interpolation plate finite elements of arbitrary order are designed. The elements are tested on the standard set of examples. Findings – The derived elements pass the standard patch tests and also the higher-order patch tests of an order directly related to the order of the element. The lowest-order member of the family of developed elements still suffers from shear locking for very coarse meshes, but the higher-order elements turn out to be successful when compared to the elements from literature for the problems with the same total number of the degrees of freedom. Research limitations/implications – The elements designed perform well for a number of standard benchmark tests, but the well-known Morley's skewed plate example turns out to be rather demanding, i.e. the proposed design principle cannot compete with the mixed-type approach for this test. Work is under way to improve the proposed displacement-based elements by adding a number of internal bubble functions in the displacement and rotation fields, specifically chosen to satisfy the basic patch test and enable a softer response in the bench-mark test examples. Originality/value – A new family of displacement-based higher-order triangular Mindlin plate finite elements has been derived. The higher-order elements perform very well, whereas the lowest-order element requires improvement.

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19

Sujuan, Jiao, Li Jun, Hua Hongxing, and Shen Rongying. "A Spectral Finite Element Model for Vibration Analysis of a Beam Based on General Higher-Order Theory." Shock and Vibration 15, no. 2 (2008): 179–92. http://dx.doi.org/10.1155/2008/953639.

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The spectral element matrix is derived for a straight and uniform beam element having an arbitrary cross-section. The general higher-order beam theory is used, which accurately accounts for the transverse shear deformation out of the cross-sectional plane and antielastic-type deformation within the cross-sectional plane. Two coupled equations of motion are derived by use of Hamilton's principle along with the full three-dimensional constitutive relations. The theoretical expressions of the spectral element matrix are formulated from the exact solutions of the coupled governing equations. The developed spectral element matrix is directly applied to calculate the exact natural frequencies and mode shapes of the illustrative examples. Numerical results of the thick isotropic beams with rectangular and elliptical cross-sections are presented for a wide variety of cross-section aspect ratios.

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20

Pietro, Gabriele De, Gaetano Giunta, Salim Belouettar, and Erasmo Carrera. "A static analysis of three-dimensional sandwich beam structures by hierarchical finite elements modelling." Journal of Sandwich Structures & Materials 21, no. 7 (September 27, 2017): 2382–410. http://dx.doi.org/10.1177/1099636217732907.

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A static analysis of three-dimensional sandwich beam structures using one-dimensional modelling approach is presented within this paper. A family of several one-dimensional beam elements is obtained by hierarchically expanding the displacements over the cross-section and letting the expansion order a free parameter. The finite element approximation order over the beam axis is also a formulation free parameter (linear, quadratic and cubic elements are considered). The principle of virtual displacements is used to obtain the problem weak form and derive the beam stiffness matrix and equivalent load vectors in a nuclear, generic form. Displacements and stresses are presented for different load and constraint configurations. Results are validated towards three-dimensional finite element solutions and experimental results. Sandwich beams present a three-dimensional stress state and higher-order models are necessary for an accurate description. Numerical investigations show that fairly good results with reduced computational costs can be obtained by the proposed finite element formulation.

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21

Orzechowski, Grzegorz, and Ahmed A. Shabana. "Analysis of warping deformation modes using higher order ANCF beam element." Journal of Sound and Vibration 363 (February 2016): 428–45. http://dx.doi.org/10.1016/j.jsv.2015.10.013.

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22

Geng, P. S., T. C. Duan, and L. X. Li. "An uncoupled higher-order beam theory and its finite element implementation." International Journal of Mechanical Sciences 134 (December 2017): 525–31. http://dx.doi.org/10.1016/j.ijmecsci.2017.10.041.

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23

Heyliger, P. R., and J. N. Reddy. "A higher order beam finite element for bending and vibration problems." Journal of Sound and Vibration 126, no. 2 (October 1988): 309–26. http://dx.doi.org/10.1016/0022-460x(88)90244-1.

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24

Kumar, D. V. T. G. Pavan, and B. K. Raghu Prasad. "Higher-Order Beam Theories for Mode II Fracture of Unidirectional Composites." Journal of Applied Mechanics 70, no. 6 (November 1, 2003): 840–52. http://dx.doi.org/10.1115/1.1607357.

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Mathematical models, for the stress analyses of unidirectional end notch flexure and end notch cantilever specimens using classical beam theory, first, second, and third-order shear deformation beam theories, have been developed to determine the interlaminar fracture toughness of unidirectional composites in mode II. In the present study, appropriate matching conditions, in terms of generalized displacements and stress resultants, have been derived and applied at the crack tip by enforcing the displacement continuity at the crack tip in conjunction with the variational equation. Strain energy release rate has been calculated using compliance approach. The compliance and strain energy release rate obtained from present formulations have been compared with the existing experimental, analytical, and finite element results and found that results from third-order shear deformation beam theory are in close agreement with the existing experimental and finite element results.

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25

Ayad, M., N. Karathanasopoulos, H. Reda, JF Ganghoffer, and H. Lakiss. "Dispersion characteristics of periodic structural systems using higher order beam element dynamics." Mathematics and Mechanics of Solids 25, no. 2 (October 22, 2019): 457–74. http://dx.doi.org/10.1177/1081286519880227.

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In the current work, we elaborate upon a beam mechanics-based discrete dynamics approach for the computation of the dispersion characteristics of periodic structures. Within that scope, we compute the higher order asymptotic expansion of the forces and moments developed within beam structural elements upon dynamic loads. Thereafter, we employ the obtained results to compute the dispersion characteristics of one- and two-dimensional periodic media. In the one-dimensional space, we demonstrate that single unit-cell equilibrium can provide the fundamental low-frequency band diagram structure, which can be approximated by non-dispersive Cauchy media formulations. However, we show that the discrete dynamics method can access the higher frequency modes by considering multiple unit-cell systems for the dynamic equilibrium, frequency ranges that cannot be accessed by simplified formulations. We extend the analysis into two-dimensional space computing with the dispersion attributes of square lattice structures. Thereupon, we demonstrate that the discrete dynamics dispersion results compare well with that obtained using Bloch theorem computations. We show that a high-order expansion of the inner element forces and moments of the structures is required for the higher wave propagation modes to be accurately represented, in contrast to the shear and the longitudinal mode, which can be captured using a lower, fourth-order expansion of its inner dynamic forces and moments. The provided results can serve as a reference analysis for the computation of the dispersion characteristics of periodic structural systems with the use of discrete element dynamics.

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26

Yuan, Fuh-Gwo, and Robert E. Miller. "Higher-order finite element for short beams." AIAA Journal 26, no. 11 (November 1988): 1415–17. http://dx.doi.org/10.2514/3.10059.

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27

Kant, T., and A. Gupta. "A finite element model for a higher-order shear-deformable beam theory." Journal of Sound and Vibration 125, no. 2 (September 1988): 193–202. http://dx.doi.org/10.1016/0022-460x(88)90278-7.

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28

Giunta, G., and S. Belouettar. "Higher-Order Hierarchical Models for the Free Vibration Analysis of Thin-Walled Beams." Mathematical Problems in Engineering 2015 (2015): 1–12. http://dx.doi.org/10.1155/2015/940347.

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This paper addresses a free vibration analysis of thin-walled isotropic beams via higher-order refined theories. The unknown kinematic variables are approximated along the beam cross section as aN-order polynomial expansion, whereNis a free parameter of the formulation. The governing equations are derived via the dynamic version of the Principle of Virtual Displacements and are written in a unified form in terms of a “fundamental nucleus.” This latter does not depend upon order of expansion of the theory over the cross section. Analyses are carried out through a closed form, Navier-type solution. Simply supported, slender, and short beams are investigated. Besides “classical” modes (such as bending and torsion), several higher modes are investigated. Results are assessed toward three-dimensional finite element solutions. The numerical investigation shows that the proposed Unified Formulation yields accurate results as long as the appropriate approximation order is considered. The accuracy of the solution depends upon the geometrical parameters of the beam.

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29

Pedersen, P. Terndrup. "Beam Theories for Torsional-Bending Response of Ship Hulls." Journal of Ship Research 35, no. 03 (September 1, 1991): 254–65. http://dx.doi.org/10.5957/jsr.1991.35.3.254.

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A consistent one-dimensional finite-element procedure for analysis of the coupled torsional-bending response of thin-walled beam structures such as ship hulls is presented. At each element end there are three translations, three rotations and one classical Vlasov warping degree of freedom plus possibly N degrees of freedom associated with higher order generalized warping deformation modes. These higher order warping modes are generated from an eigenvalue problem associated with the homogeneous plane stress equilibrium condition for the individual beam cross sections. The assembly of the beam elements to the global model is performed by use of transition matrices which assure compatibility between the elements in the sense of least squares. Numerical examples are included which demonstrate the accuracy of the mathematical model and the applicability of the proposed analysis procedure for calculation of torsion-horizontal bending response of a containership hull. Even if the higher order warping modes are not included in the finite element formulation it is found that the mathematical model is quite accurate for overall response analysis of hull structures.

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30

Qi, Lin, and Hai Feng Huo. "Refined Beam Element for Second Order Analysis of Latticed Shells." Advanced Materials Research 1065-1069 (December 2014): 1208–11. http://dx.doi.org/10.4028/www.scientific.net/amr.1065-1069.1208.

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Based on equilibrium equation of beam, the displacement interpolating functions with shear effect of spatial beam elements which are used to simulate the structure members of latticed shells are deduced. The different displacement interpolating functions in compression and tension spatial beam-column elements are unified by the method of Maclaurin series expansion, and the unified expressions which are used to simulate structure members are equivalent to those expressed by stability functions. Numerical analyses results indicate that the second-order elastic analysis method for beam structures proposed in this paper, which can perfectly incarnate the second-order effects and the geometrical nonlinearity of the single-layer cylindrical reticulated shell, is of better accurateness and higher effectiveness.

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31

Li, Peng Fei, Yuan Yuan, and Hong Zhao Liu. "Beam Element Considering the Warping Effect of Cross Section in Large Displacement Finite Element Analysis." Applied Mechanics and Materials 152-154 (January 2012): 958–63. http://dx.doi.org/10.4028/www.scientific.net/amm.152-154.958.

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A simple two-dimensional shear deformable finite beam element is developed in order to examine the effect of the high order interpolation on the modes of deformation of the beam cross section using the ANCF finite element. The new element allows for effect of warping that cannot be captured using previously introduced ANCF beam elements, and relaxes the assumption of planar cross section. The displacement field of the new element is assumed to be cubic in the axial direction and quadratic in the transverse direction. Using this displacement field, new shape functions are formulated and include the quadratic of the transverse direction instead of the linear expression. The displacement gradient and transverse strain component obtained using the new higher order element are introduced. Numerical example is presented in order to compare the results obtained using the new finite element and the results obtained using previously developed ANCF finite element. The results reveal that the cross section remains as a curve surface not a planar one.

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32

Honickman, Hart. "An Intuitive Derivation of Beam Models of Arbitrary Order." Applied Mechanics 4, no. 1 (January 28, 2023): 109–40. http://dx.doi.org/10.3390/applmech4010008.

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This article presents a new beam model that employs a recursive derivation procedure that enables the user to set the order of the governing differential equations as an input parameter, without the need for ad hoc assumptions or methodologies. This article employs a novel system of kinematic variables, section constants, and section functions that facilitate the development of higher-order beam models that retain a clear philosophical link to classical beam models such as Euler–Bernoulli beam theory and Timoshenko beam theory. The present beam model is a type of equivalent single layer beam model, wherein section constants are used to model the global stiffness characteristics of the beam, and section functions are used to recover sectional fields of displacements, strains, and stresses. The present beam model is solved for several example beams, and the results are compared to the results of finite element analyses. It is shown that the present beam model can accurately predict the deformed shapes and stress fields of each of the example beams. This article also reveals an interesting peculiarity of the elastic potential energy that pertains to any unidimensional beam model that is governed by differential equations that are of finite order.

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33

Sharifnia, Mahdi. "A higher-order nonlinear beam element for planar structures by using a new finite element approach." Acta Mechanica 233, no. 2 (January 23, 2022): 495–511. http://dx.doi.org/10.1007/s00707-021-03076-4.

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34

Pölöskei, Tamás, and András Szekrényes. "Dynamic Stability of a Structurally Damped Delaminated Beam Using Higher Order Theory." Mathematical Problems in Engineering 2018 (June 6, 2018): 1–15. http://dx.doi.org/10.1155/2018/2674813.

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The static and dynamic stability of the composite beam with a single delamination are investigated using the Timoshenko beam theory. The mechanical model is discretized using the finite element method and the equation of motion is obtained using Hamilton’s principle. The coefficients of the mass and stiffness matrix for the damping matrix are determined using experimental modal analysis. The effect of harmonic excitation on the dynamic stability of a single delaminated composite beam is investigated using Bolotin’s harmonic balance method. The stability boundaries of the damped and undamped system are compared for different static load values and delamination lengths on the excitation frequency-excitation force amplitude parameter field.

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35

Savino, Pierclaudio, Francesco Tondolo, Marco Gherlone, and Alexander Tessler. "Application of Inverse Finite Element Method to Shape Sensing of Curved Beams." Sensors 20, no. 24 (December 8, 2020): 7012. http://dx.doi.org/10.3390/s20247012.

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Curved beam, plate, and shell finite elements are commonly used in the finite element modeling of a wide range of civil and mechanical engineering structures. In civil engineering, curved elements are used to model tunnels, arch bridges, pipelines, and domes. Such structures provide a more efficient load transfer than their straight/flat counterparts due to the additional strength provided by their curved geometry. The load transfer is characterized by the bending, shear, and membrane actions. In this paper, a higher-order curved inverse beam element is developed for the inverse Finite Element Method (iFEM), which is aimed at reconstructing the deformed structural shapes based on real-time, in situ strain measurements. The proposed two-node inverse beam element is based on the quintic-degree polynomial shape functions that interpolate the kinematic variables. The element is C2 continuous and has rapid convergence characteristics. To assess the element predictive capabilities, several circular arch structures subjected to static loading are analyzed, under the assumption of linear elasticity and isotropic material behavior. Comparisons between direct FEM and iFEM results are presented. It is demonstrated that the present inverse beam finite element is both efficient and accurate, requiring only a few element subdivisions to reconstruct an accurate displacement field of shallow and deep curved beams.

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Gordaninejad, F., and A. Ghazavi. "Effect of Shear Deformation on Bending of Laminated Composite Beams." Journal of Pressure Vessel Technology 111, no. 2 (May 1, 1989): 159–64. http://dx.doi.org/10.1115/1.3265652.

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A higher-order shear deformation beam theory is utilized to analyze the bending of thick laminated composite beams. This theory accounts for parabolic distribution of shear strain through the thickness of the beam. The predicted displacements show improvement over the Bresse-Timoshenko beam theory. Mixed finite element results are obtained for those cases where closed-form solutions are not available. The finite element and exact solutions are in close agreement. Numerical results are presented for single, two and three-layer beams under uniform and sinusoidal distributed transverse loadings.

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He, Guanghui, and Xiao Yang. "Finite element analysis for buckling of two-layer composite beams using Reddy’s higher order beam theory." Finite Elements in Analysis and Design 83 (June 2014): 49–57. http://dx.doi.org/10.1016/j.finel.2014.01.004.

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Jang, G. W., and Y. Y. Kim. "Mixed state-vector finite element analysis for a higher-order box beam theory." Computational Mechanics 36, no. 3 (February 28, 2005): 217–25. http://dx.doi.org/10.1007/s00466-004-0656-z.

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Yuan, Fuh-Gwo, and Robert E. Miller. "A higher order finite element for laminated beams." Composite Structures 14, no. 2 (January 1990): 125–50. http://dx.doi.org/10.1016/0263-8223(90)90027-c.

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Hui, Y., G. De Pietro, G. Giunta, S. Belouettar, H. Hu, E. Carrera, and A. Pagani. "Geometrically Nonlinear Analysis of Beam Structures via Hierarchical One-Dimensional Finite Elements." Mathematical Problems in Engineering 2018 (November 27, 2018): 1–22. http://dx.doi.org/10.1155/2018/4821385.

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The formulation of a family of advanced one-dimensional finite elements for the geometrically nonlinear static analysis of beam-like structures is presented in this paper. The kinematic field is axiomatically assumed along the thickness direction via a Unified Formulation (UF). The approximation order of the displacement field along the thickness is a free parameter that leads to several higher-order beam elements accounting for shear deformation and local cross-sectional warping. The number of nodes per element is also a free parameter. The tangent stiffness matrix of the elements is obtained via the Principle of Virtual Displacements. A total Lagrangian approach is used and Newton-Raphson method is employed in order to solve the nonlinear governing equations. Locking phenomena are tackled by means of a Mixed Interpolation of Tensorial Components (MITC), which can also significantly enhance the convergence performance of the proposed elements. Numerical investigations for large displacements, large rotations, and small strains analysis of beam-like structures for different boundary conditions and slenderness ratios are carried out, showing that UF-based higher-order beam theories can lead to a more efficient prediction of the displacement and stress fields, when compared to two-dimensional finite element solutions.

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Shi, G., K. Y. Lam, and T. E. Tay. "On efficient finite element modeling of composite beams and plates using higher-order theories and an accurate composite beam element." Composite Structures 41, no. 2 (February 1998): 159–65. http://dx.doi.org/10.1016/s0263-8223(98)00050-6.

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TURAN, Muhittin, and Mahmut İlter HACIOĞLU. "Buckling Analysis of Functionally Graded Beams Using the Finite Element Method." Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi 15, Special Issue 1 (December 23, 2022): 98–109. http://dx.doi.org/10.18185/erzifbed.1199454.

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This study developed a finite element model according to higher-order shear deformation beam theory (HSDT) for the buckling analysis of functionally graded (FG) beams. Equilibrium equations of the FG beam are obtained from Lagrange’s equations. The beam element to be discussed within the scope of the study has 5 nodes and 16 degrees of freedom (DOF). As a result of the buckling analysis, the critical buckling load of the beam was obtained for various boundary conditions, power-law index (p), and slenderness (L/h). When the critical buckling loads obtained as a result of the analysis were compared with the literature, it was seen that they were quite compatible.

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WEN, Y., and Q. Y. ZENG. "A HIGH-ORDER FINITE ELEMENT FORMULATION FOR VIBRATION ANALYSIS OF BEAM-TYPE STRUCTURES." International Journal of Structural Stability and Dynamics 09, no. 04 (December 2009): 649–60. http://dx.doi.org/10.1142/s0219455409003223.

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A high-order finite element model is presented to perform the vibration analysis of beams. The equations of motion are formulated by applying the principle of total potential energy in elastic dynamic system and the "set-in-right-position" rule for the construction of system matrices first proposed by the author. The primary advantage of the principle and rule lies in its simplicity and efficiency in solving the modeling problem of complex dynamic system. The requirement of strain continuity has certainly not being met at element interfaces with the use of conventional cubic Hermitian formulation. Hence, it is difficult to predict the dynamic responses of beams accurately. In order to overcome this problem, a beam element with simple higher-order interpolation function is chosen as the analysis model. Although the number of nodal degrees of freedom is increased herein, usually a coarse mesh will suffice. The present formulation is able to provide results of high accuracy with low computational effort. For the purpose of illustration, the dynamic characteristics analysis and dynamic response analysis are carried out on beam models. The solutions obtained for all the examples are in good agreement with the exact solutions found by fundamental theory of vibration.

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Ibrahim, S. M., Y. A. Al-Salloum, and H. Abbas. "Dynamic Analysis of Tapered Plates Based on Higher Order Beam Theory." Advanced Materials Research 919-921 (April 2014): 79–82. http://dx.doi.org/10.4028/www.scientific.net/amr.919-921.79.

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Modal solutions of plates with uniformly varying cross section using unified beam theory are presented. The results are given in the form of Euler-Bernoulli, Timoshenko and quasi 3D solutions. Numerical results for cantilever and CFCF supported rectangular planform plates are presented. Different types of modes, i.e. axial, bending and torsional modes are observed. The frequency values are in good agreement with 3D finite element results as well as published literature. Due to uniform taper in plate cross section, bending vibration modes become asymmetric along the longitudinal axis of the structure. Further, it can also be noticed that the vibration behavior of thick tapered plates is characterized by the appearance of significant number of axial and torsional modes at lower frequency values.

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KONDOH, Kazuo, Tomohiko TAKAYA, and Masami HANAI. "HYBRID STRESS FINITE ELEMENT BASED ON HIGHER-ORDER SHEAR DEFORMATION BEAM-COLUMN THEORY : (Part 1) Basic formulation for plane beam-column element." Journal of Structural and Construction Engineering (Transactions of AIJ) 61, no. 488 (1996): 57–66. http://dx.doi.org/10.3130/aijs.61.57_3.

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Li, Wenxiong, Haitao Ma, and Wei Gao. "A higher-order shear deformable mixed beam element model for accurate analysis of functionally graded sandwich beams." Composite Structures 221 (August 2019): 110830. http://dx.doi.org/10.1016/j.compstruct.2019.04.002.

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Khonina, Svetlana N., Sergey V. Karpeev, and Sergey V. Alferov. "Polarization converter for higher-order laser beams using a single binary diffractive optical element as beam splitter." Optics Letters 37, no. 12 (June 12, 2012): 2385. http://dx.doi.org/10.1364/ol.37.002385.

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Ta Duy, Hien, Nguyen Dang Diem, Giap Van Tan, Vu Van Hiep, and Nguyen Van Thuan. "Stochastic Higher-order Finite Element Model for the Free Vibration of a Continuous Beam resting on Elastic Support with Uncertain Elastic Modulus." Engineering, Technology & Applied Science Research 13, no. 1 (February 5, 2023): 9985–90. http://dx.doi.org/10.48084/etasr.5456.

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This paper deals with a continuous beam resting on elastic support with elastic modulus derived from a random process. Governing equations of the stochastic higher-order finite element method of the free vibration of the continuous beam were derived from Hamilton's principle. The random process of elastic modulus was discretized by averaging random variables in each element. A solution for the stochastic eigenvalue problem for the free vibration of the continuous beam was obtained by using the perturbation technique, in conjunction with the finite element method. Spectral representation was used to generate a random process and employ the Monte Carlo simulation. A good agreement was obtained between the results of the first-order perturbation technique and the Monte Carlo simulation.

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Surana, K. S., and S. H. Nguyen. "Two-dimensional curved beam element with higher-order hierarchical transverse approximation for laminated composites." Computers & Structures 36, no. 3 (January 1990): 499–511. http://dx.doi.org/10.1016/0045-7949(90)90284-9.

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Chen, Wanji, and Zhen Wu. "A new higher-order shear deformation theory and refined beam element of composite laminates." Acta Mechanica Sinica 21, no. 1 (February 2005): 65–69. http://dx.doi.org/10.1007/s10409-005-0011-4.

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