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Journal articles on the topic 'Higher order beam element'

Author: Grafiati

Published: 14 March 2023

Last updated: 31 July 2025

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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 wit

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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 (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 o

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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 comparin

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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 (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 funct

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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 (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 funct

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6

Shen, J., M. R. T. Arruda, A. Pagani, and M. Petrolo. "Mesh objective characteristic element length for higher-order finite beam elements." Advances in Engineering Software 195 (September 2024): 103709. http://dx.doi.org/10.1016/j.advengsoft.2024.103709.

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7

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 (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 consti

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8

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 (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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9

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 (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 classi

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10

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

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11

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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12

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 (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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13

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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14

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 (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 dir

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15

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 (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 l

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16

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 (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 spectra

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17

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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18

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 (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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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 d

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20

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 (1999): 707–21. http://dx.doi.org/10.1006/jsvi.1998.1903.

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21

Ribarić, Dragan, and Gordan Jelenić. "Higher-order linked interpolation in triangular thick plate finite elements." Engineering Computations 31, no. 1 (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 t

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22

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 (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

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23

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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24

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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25

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 (1988): 309–26. http://dx.doi.org/10.1016/0022-460x(88)90244-1.

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26

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 soluti

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27

Honickman, Hart. "An Intuitive Derivation of Beam Models of Arbitrary Order." Applied Mechanics 4, no. 1 (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 m

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28

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 (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, whi

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29

Pedersen, P. Terndrup. "Beam Theories for Torsional-Bending Response of Ship Hulls." Journal of Ship Research 35, no. 03 (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 e

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30

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

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31

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 (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

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32

Gordaninejad, F., and A. Ghazavi. "Effect of Shear Deformation on Bending of Laminated Composite Beams." Journal of Pressure Vessel Technology 111, no. 2 (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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33

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

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34

Hui, Y., G. De Pietro, G. Giunta, et al. "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

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35

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 (1988): 193–202. http://dx.doi.org/10.1016/0022-460x(88)90278-7.

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36

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 sy

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37

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 (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 compa

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38

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

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39

Feng, Yuan, Abdul Hamid Sheikh, and Guanzhen Li. "Analysis of Intact/Delaminated Composite and Sandwich Beams Using a Higher-Order Modeling Technique." Journal of Composites Science 8, no. 5 (2024): 175. http://dx.doi.org/10.3390/jcs8050175.

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A simple higher-order model (HOM) is presented in this study for the bending analysis of an intact or delaminated composite and sandwich beam. This model adopts the concept of sub-laminates to simulate multilayered structures, and each sub-laminate takes cubic variation for axial displacement and linear variation for transverse displacement through the thickness. A sub-laminate possesses displacement components at its surfaces (bottom and top) that provide a straightforward way to improve the accuracy of prediction by stacking several sub-laminates. Thus, analysts will have the flexibility to

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40

Dang, Ngoc Duyen, Ngoc Anh T. Le, and Cong Ich Le. "Size-dependent thermomechanical vibration of FGP microbeams using a higher-order shear deformable beam element." Journal of Physics: Conference Series 2949, no. 1 (2025): 012039. https://doi.org/10.1088/1742-6596/2949/1/012039.

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Abstract The thermoelastic vibration of porous microbeams is explored via a higher-order shear deformable element. The porosities are smoothly graded in the beam thickness, while the elastic moduli are temperature-dependent. The theory of third-order shear deformation is employed to formulate a size-dependent beam element, in which the theory of couple stress theory is used to model the microstructural size effect. The frequencies are predicted for microbeams with different and conditions. The performance of the formulated element is shown through a comparison study. The impacts of the size sc

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41

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

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42

Akhlaq, Adnan, Mohd Sultan Ibrahim Shaik Dawood, Mohamed Ali Jaffar Syed, and Erwin Sulaeman. "A Study on the Effect of Piezoelectric Nonlinearity on the Bending Behaviour of Smart Laminated Composite Beam." Materials 16, no. 7 (2023): 2839. http://dx.doi.org/10.3390/ma16072839.

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This paper presents a finite element analysis to model and analyze composite laminated beams with distributed piezoelectric actuators attached to the top and bottom surfaces considering nonlinear constitutive equations under a high electric field. The static response is presented for piezoelectric composite laminated beam using higher order electric field nonlinearity to assess the effect of electrostriction and elastostriction coefficient at a high electric field. A finite element approach based on higher-order shear deformation theory is applied for static analysis of composite laminated bea

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43

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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44

Sheth, Karan, and Rajendra Joshi. "Development of Higher Order Stiffened Shell Element (HOST9) for the Static Analysis of Stiffened Laminated Plates." Civil and Environmental Engineering 20, no. 1 (2024): 217–32. http://dx.doi.org/10.2478/cee-2024-0018.

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Abstract A new higher order stiffened shell element (HOST9) is developed comprising of a 9 noded flat shell element and a 3 noded stiffener element for analysis of stiffened laminated plates. The shell element is a lagrangian element. The stiffener is a beam element. The stiffness of the stiffener is computed separately and added to that of the shell element at appropriate locations. As a result, the stiffener can be located arbitrarily in the shell element. Static analysis of stiffened laminated plate is carried out using the newly developed element and is validated with the existing literatu

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45

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 (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 us

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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 (1998): 159–65. http://dx.doi.org/10.1016/s0263-8223(98)00050-6.

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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 (2005): 217–25. http://dx.doi.org/10.1007/s00466-004-0656-z.

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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 (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 formulat

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Laouche, Nassim, Ahmed Saimi, Ismail Bensaid, Mouloud Dahmane, and Hassen Ait Atmane. "A study on the crack presence effect on dynamical behavior of higher-order Quasi-3D composite steel-polymer concrete box section beams via DQFEM." Fracture and Structural Integrity 19, no. 73 (2025): 88–107. https://doi.org/10.3221/igf-esis.73.07.

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This paper presents a dynamic and critical buckling analysis of the presence of a crack of steel-polymer concrete composite beams modelled using a refined quasi 3D beam theory. The beam model is a hollow steel box section filled with a composite concrete material. The presence of the crack is assumed on both inner concrete core and outer steel layer box, incorporating its effects into the mechanical behavior of the beam. The governing equations for the box beam are derived using the Differential Quadrature Finite Element Method (DQFEM) combined with Lagrange’s principle. The study investigates

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

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