Journal articles: '3D beam element'

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Dvořáková, Edita, and Bořek Patzák. "ON COMPARISON OF 3D ISOGEOMETRIC TIMOSHENKO AND BERNOULLI BEAM FORMULATIONS." Acta Polytechnica CTU Proceedings 30 (April 22, 2021): 12–17. http://dx.doi.org/10.14311/app.2021.30.0012.

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Application of isogeometric analysis (IGA) for curved beams is very convenient for its ability of exact representation of curved geometries. Several beam formulation has been presented since the introduction of IGA. In this paper, two different beam formulations are presented: Bernoulli beam formulation of A. M. Bauer et al. [1], and Timoshenko beam element introduced by G. Zhang et al. [2]. Both beam elements are implemented and their performance is documented on the fully threedimensionalexample of helicoidal spring.

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Eskandari, Amir H., Mostafa Baghani, and Saeed Sohrabpour. "A Time-Dependent Finite Element Formulation for Thick Shape Memory Polymer Beams Considering Shear Effects." International Journal of Applied Mechanics 10, no. 04 (May 2018): 1850043. http://dx.doi.org/10.1142/s1758825118500436.

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In this paper, employing a thermomechanical small strain constitutive model for shape memory polymers (SMP), a beam element made of SMPs is presented based on the kinematic assumptions of Timoshenko beam theory. Considering the low stiffness of SMPs, the necessity for developing a Timoshenko beam element becomes more prominent. This is due to the fact that relatively thicker beams are required in the design procedure of smart structures. Furthermore, in the design and optimization process of these structures which involves a large number of simulations, we cannot rely only on the time consuming 3D finite element analyses. In order to properly validate the developed formulations, the numeric results of the present work are compared with those of 3D finite element results of the authors, previously available in the literature. The parametric study on the material parameters, e.g., hard segment volume fracture, viscosity coefficient of different phases, and the external force applied on the structure (during the recovery stage) are conducted on the thermomechanical response of a short I-shape SMP beam. For instance, the maximum beam deflection error in one of the studied examples for the Euler–Bernoulli beam theory is 7.3%, while for the Timoshenko beam theory, is 1.5% with respect to the 3D FE solution. It is noted that for thicker or shorter beams, the error of the Euler–Bernoulli beam theory even more increases. The proposed beam element in this work could be a fast and reliable alternative tool for modeling 3D computationally expensive simulations.

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Nguyen, Hoang Nam, Tran Thi Hong, Pham Van Vinh, and Do Van Thom. "An Efficient Beam Element Based on Quasi-3D Theory for Static Bending Analysis of Functionally Graded Beams." Materials 12, no. 13 (July 8, 2019): 2198. http://dx.doi.org/10.3390/ma12132198.

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In this paper, a 2-node beam element is developed based on Quasi-3D beam theory and mixed formulation for static bending of functionally graded (FG) beams. The transverse shear strains and stresses of the proposed beam element are parabolic distributions through the thickness of the beam and the transverse shear stresses on the top and bottom surfaces of the beam vanish. The proposed beam element is free of shear-looking without selective or reduced integration. The material properties of the functionally graded beam are assumed to vary according to the power-law index of the volume fraction of the constituents through the thickness of the beam. The numerical results of this study are compared with published results to illustrate the accuracy and convenience rate of the new beam element. The influence of some parametrics on the bending behavior of FGM beams is investigated.

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Chevalier, Luc, Heba Makhlouf, Benoît Jacquet-Faucillon, and Eric Launay. "Modeling the influence of connecting elements in wood products behavior: a numerical multi-scale approach." Mechanics & Industry 19, no. 3 (2018): 301. http://dx.doi.org/10.1051/meca/2018004.

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Wood furniture is often composed of simple parts that may be modeled as beams or plates. These particularities allow using simplified approaches that reduces the number of degrees of freedom (dof for short) in a finite element simulation of the furniture's behavior. Generally, connections are not taken into account in such simulations but these connections are critical in the failure process of the furniture and it worth studying it precisely. Using a multi-scale approach, this paper introduces a numerical procedure to identify the connection contribution in the furniture's stiffness. Comparing 3D finite element calculations with a Timoshenko's beam calculation on a corner of two wooden parts, we identify the specific behavior of the connection elements (pins, nut, screw… and local 3D effects) to introduce it as a punctual 0D element in the beam code. Two validations of the approach are presented here: (i) a numerical validation by comparing the result of the beam code with a complete 3D finite element simulation on a representative plane structure of wooden furniture; (ii) an experimental validation by managing a global bending test and measuring the displacement field using digital image correlation (DIC for short).

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Poorasadion, Saeid, Jamal Arghavani, Reza Naghdabadi, and Saeed Sohrabpour. "Implementation of Microplane Model Into Three-Dimensional Beam Element for Shape Memory Alloys." International Journal of Applied Mechanics 07, no. 06 (December 2015): 1550091. http://dx.doi.org/10.1142/s175882511550091x.

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In this study, a three-dimensional (3D) beam element based on Timoshenko beam theory is introduced for shape memory alloys (SMAs). Employing the microplane approach, we use a 3D SMA constitutive model extended from a 1D model proposed by Brinson. The SMA model is implemented into a user-defined subroutine (UMAT) in the nonlinear finite element software ABAQUS/Standard. Results of numerical examples show reasonable agreement with experimental data in proportional and non-proportional loadings. Furthermore, several applications (staple, spring, structure) are simulated and the results are compared with those of continuum elements. According to the results, the 3D SMA beam element can be used in the design and analysis of various SMA applications.

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Yob, Mohd Shukri, Shuhaimi Mansor, and Razali Sulaiman. "Finite Element Modelling to Predict Equivalent Stiffness of 3D Space Frame Structural Joint Using Circular Beam Element." Applied Mechanics and Materials 431 (October 2013): 104–9. http://dx.doi.org/10.4028/www.scientific.net/amm.431.104.

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In automotive industry, thin walled beam is widely used to build vehicles structure. Vehicle structure is built by joining thin walled beams using various welding techniques. The usage of thin walled structure in automotive is important to improve vehicle performance by offering better strength-to-weight ratio. However the application of thin walled structure will cause few drawbacks to vehicle structure. When thin walled beam or structure is loaded with compression load, at certain limit it will undergo local or global buckling. Another problem is when thin walled beam is joined to other thin walled beams, it will show unexpected deformation which called joint flexibility. Both phenomena will cause numerical and analytical model to predict stiffness of structure tend to deviate from experimental result. In vehicle structure fabrication 3D space frame is used a lot. As a case study for this application, area around car bulkhead where cross member, side sill and A pillar are connected to each other at right angle is studied. The intention of this research work is to produce validated finite element model to predict equivalent stiffness of 3D space frame structural joint. Finite element, shell element is most common technique used to model the joined structure. However it is known that shell model cannot produce good result. In this result work, modelling of equivalent stiffness for 3D space frame structural joint is presented. The result shows, using this model the accuracy is about 65%. New modelling technique is proposed to increase the accuracy based on solid model. By introducing circular beam elements at welding area, it is found that accuracy improves up to 90%.

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Murín, Justín, Vladimír Kutiš, Viktor Královič, and Tibor Sedlár. "3D Beam Finite Element Including Nonuniform Torsion." Procedia Engineering 48 (2012): 436–44. http://dx.doi.org/10.1016/j.proeng.2012.09.537.

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Viet, N. V., W. Zaki, and Quan Wang. "Free vibration characteristics of sectioned unidirectional/bidirectional functionally graded material cantilever beams based on finite element analysis." Applied Mathematics and Mechanics 41, no. 12 (November 18, 2020): 1787–804. http://dx.doi.org/10.1007/s10483-020-2664-8.

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AbstractAdvancements in manufacturing technology, including the rapid development of additive manufacturing (AM), allow the fabrication of complex functionally graded material (FGM) sectioned beams. Portions of these beams may be made from different materials with possibly different gradients of material properties. The present work proposes models to investigate the free vibration of FGM sectioned beams based on one-dimensional (1D) finite element analysis. For this purpose, a sample beam is divided into discrete elements, and the total energy stored in each element during vibration is computed by considering either Timoshenko or Euler-Bernoulli beam theories. Then, Hamilton’s principle is used to derive the equations of motion for the beam. The effects of material properties and dimensions of FGM sections on the beam’s natural frequencies and their corresponding mode shapes are then investigated based on a dynamic Timoshenko model (TM). The presented model is validated by comparison with three-dimensional (3D) finite element simulations of the first three mode shapes of the beam.

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Murín, Justín, Juraj Hrabovský, and Vladimír Kutiš. "Calculation of stress in FGM beams." MATEC Web of Conferences 157 (2018): 06006. http://dx.doi.org/10.1051/matecconf/201815706006.

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Content of the paper is oriented to calculation of elastic normal stress in the Functionally Graded Beams (FGM). Spatial variation of material properties is considered in the lateral, transversal and longitudinal direction of the straight beam. The displacements and internal forces are calculated using our new FGM finite beam element. Heterogeneous material properties are homogenized by extended mixture rules, laminate theory and reference volume element (RVE). Obtained results by our approach are evaluated and compared with the ones obtained by the 3D solid finite elements.

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Wang, Yuquan. "Improved Strategy of Two-Node Curved Beam Element Based on the Same Beam’s Nodes Information." Advances in Materials Science and Engineering 2021 (September 2, 2021): 1–9. http://dx.doi.org/10.1155/2021/2093096.

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The curved beam with a great initial curvature is the typical structure and applied widely in real engineering structures. The common practice in the current literature employs two-node straight beam elements as the elementary members for stress and displacement analysis, which needs a large number of divisions to fit the curved beam shape well and increases computational time greatly. In this paper, we develop an improved accurate two-node curved beam element (IC2) in 3D problems, combining the curved Timoshenko beam theory and the curvature information calculated from the same beam curve. The strategy of calculating the curvature information from the same bean curve in the IC2 beam element and then transferring the curvature information to the two-node straight beam element can greatly enhance the accuracy of the mechanical analysis with no extra calculation burden. We then introduce the finite element implementation of the IC2 beam element and verify by the complex curved beam analysis. By comparison with simulation results from the straight two-node beam element in the MIDAS (S2-MIDAS) and the three-node curved beam element adopted in the ANSYS (C3-ANSYS), the simulation results of the typical quarter arc examples under constant or variable curvature show that the IC2 beam element based on curved beam theory is a combination of efficiency and accuracy. And, it is a good choice for analysis of complex engineering rod structure with large initial curvature.

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Staszak, Natalia, Tomasz Gajewski, and Tomasz Garbowski. "Shell-to-Beam Numerical Homogenization of 3D Thin-Walled Perforated Beams." Materials 15, no. 5 (February 28, 2022): 1827. http://dx.doi.org/10.3390/ma15051827.

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Determining the geometric characteristics of even complex cross-sections of steel beams is not a major challenge nowadays. The problem arises when openings of various shapes and sizes appear at more or less regular intervals along the length of the beam. Such alternations cause the beam to have different stiffnesses along its length. It has different bending and shear stiffnesses at the opening point and in the full section. In this paper, we present a very convenient and easy-to-implement method of determining the equivalent stiffness of a beam with any cross-section (open or closed) and with any system of holes along its length. The presented method uses the principles of the finite element method (FEM), but does not require any formal analysis, i.e., solving the system of equations. All that is needed is a global stiffness matrix of the representative volumetric element (RVE) of the 3D representation of a beam modeled with shell finite elements. The proposed shell-to-beam homogenization procedure is based on the strain energy equivalence, and allows for precise and quick determination of all equivalent stiffnesses of a beam (flexural and shear). The results of the numerical homogenization procedure were compared with the existing analytical solution and experimental results of various sections. It has been shown that the results obtained are comparable with the reference results.

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Yob, Mohd Shukri, Shuhaimi Mansor, and Razali Sulaiman. "Joint Stiffness of 3D Space Frame Thin Walled Structural Joint Considering Local Buckling Effect." Applied Mechanics and Materials 660 (October 2014): 773–77. http://dx.doi.org/10.4028/www.scientific.net/amm.660.773.

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Thin walled structure is widely used in designing light weight vehicle. For automotive industry, weight is an important characteristic to increase performance of a vehicle. Vehicle structures are built from thin walled beams by joining them using various joining methods and techniques. For a structure, its stiffness greatly depends on joint stiffness. However, stiffness of thin walled beam is difficult to predict accurately due to buckling effect. Once the beams are joined to form a structure, it will expose to joint flexibility effect. A lot of researches had been done to predict the behaviors of thin walled joint analytically and numerically. However, these methods failed to come out with satisfactory result. In this research work, finite element model for 3D space frame thin walled structural joint is developed using circular beam element by validating with experimental result. Another finite element model using rigid element is used to represent 3D space frame behavior without joint effect. The difference between these 2 models is due to joint effect. By using same modelling technique, joint stiffness for different sizes can be established. Then, the relation between joint stiffness for 3D space frame and size of beam can be obtained.

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Chandra, J., H. Wibowo, D. Wijaya, F. O. Purnomo, P. Pudjisuryadi, and A. Antoni. "Modeling and analysis of 3D-printed reinforced and prestressed concrete beams." IOP Conference Series: Earth and Environmental Science 907, no. 1 (November 1, 2021): 012009. http://dx.doi.org/10.1088/1755-1315/907/1/012009.

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Abstract Three-dimensional (3D)-printed concrete is believed to have a significant impact in the construction industry in the future. Some research has been conducted experimentally and analytically to investigate the structural behavior of 3D-printed concrete elements, such as beams. Previous study by the authors attempted to analytically model 3D-printed reinforced concrete (RC) beams failing in flexure that were tested by other researchers. The study was done with the aid of a finite element software. However, there are some limitations of the analytical model to simulate the failure mode of the specimens. In this study, an improvement of the analytical model is proposed in order to simulate the behavior of the 3D-printed RC beams more accurately. Furthermore, the analysis was also expanded for 3D-printed prestressed concrete (PC) beam. From the analysis results, it can be concluded that the improved analytical model is able to predict more accurately the failure mode as well as the hysteretic behavior of the 3D-printed RC beams. Nevertheless, a more sophisticated analytical model is needed to improve the accuracy of the prediction for the 3D-printed PC beam.

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Soydas, Ozan, and Afsin Saritas. "Free vibration characteristics of a 3d mixed formulation beam element with force-based consistent mass matrix." Journal of Vibration and Control 23, no. 16 (December 9, 2015): 2635–55. http://dx.doi.org/10.1177/1077546315619263.

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In this analytical study, free vibration analyses of a 3d mixed formulation beam element are performed by adopting force-based consistent mass matrix that incorporates shear and rotary inertia effects. The force-based approach takes into account the actual distribution of mass of an element in the derivation of the mass matrix. Moreover, the force-based approach enables accurate determination of free vibration frequencies of members with varying geometry and material distribution without any need for specification of different displacement shape functions for each individual case. This phenomenon is justified by comparing free vibration frequencies of cantilever beams that have circular and rectangular cross-sections and various mass distribution configurations. Vibration frequencies of the mixed formulation element are compared with the frequencies obtained from closed-form solutions and finite element analyses. Fundamental frequency is computed with only one element per member span and higher order frequencies are determined with two or four elements with considerable accuracy by employing 3d mixed element and force-based consistent mass matrix.

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Powell, Graham H., and Paul Fu‐Song Chen. "3D Beam‐Column Element with Generalized Plastic Hinges." Journal of Engineering Mechanics 112, no. 7 (July 1986): 627–41. http://dx.doi.org/10.1061/(asce)0733-9399(1986)112:7(627).

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Murín, Justín, Mehdi Aminbaghai, Vladimír Goga, Vladimír Kutiš, Juraj Paulech, and Juraj Hrabovský. "Effect of Non-Uniform Torsion on Elastostatics of a Frame of Hollow Rectangular Cross-Section." Strojnícky casopis – Journal of Mechanical Engineering 68, no. 2 (November 1, 2018): 35–52. http://dx.doi.org/10.2478/scjme-2018-0016.

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AbstractIn this paper, results of numerical simulations and measurements are presented concerning the non-uniform torsion and bending of an angled members of hollow cross-section. In numerical simulation, our linear-elastic 3D Timoshenko warping beam finite element is used, which allows consideration of non-uniform torsion. The finite element is suitable for analysis of spatial structures consisting of beams with constant open and closed cross-sections. The effect of the secondary torsional moment and of the shear forces on the deformation is included in the local finite beam element stiffness matrix. The warping part of the first derivative of the twist angle due to bimoment is considered as an additional degree of freedom at the nodes of the finite elements. Standard beam, shell and solid finite elements are also used in the comparative stress and deformation simulations. Results of the numerical experiments are discussed, compared, and evaluated. Measurements are performed for confirmation of the calculated results.

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Kagermanov, Alexander, and Paola Ceresa. "3D Fiber-Based Frame Element with Multiaxial Stress Interaction for RC Structures." Advances in Civil Engineering 2018 (August 15, 2018): 1–13. http://dx.doi.org/10.1155/2018/8596970.

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A three-dimensional fiber-based frame element accounting for multiaxial stress conditions in reinforced concrete structures is presented. The element formulation relies on the classical Timoshenko beam theory combined with sectional fiber discretization and a triaxial constitutive model for reinforced concrete consisting of an orthotropic, smeared crack material model based on the fixed crack assumption. Torsional effects are included through the Saint-Venant theory of torsion, which accounts for out-of-plane displacements perpendicular to the cross section due to warping effects. The formulation was implemented into a force-based beam-column element and verified against monotonic and cyclic tests of reinforced concrete columns in biaxial bending, beams in combined flexure-torsion, and flexure-torsion-shear.

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Xiao, Xiang, and Wei-Xin Ren. "A Versatile 3D Vehicle-Track-Bridge Element for Dynamic Analysis of the Railway Bridges under Moving Train Loads." International Journal of Structural Stability and Dynamics 19, no. 04 (April 2019): 1950050. http://dx.doi.org/10.1142/s0219455419500500.

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There has been a growing interest to carry out the vehicle–track–bridge (VTB) dynamic interaction analysis using 2D or 3D finite elements based on simplified wheel–rail relationships. The simplified or elastic wheel–rail contact relationships, however, cannot consider the lateral contact forces and geometric shapes of the wheel and rails, and even the occasional jump of wheels from the rails. This does not guarantee a reliable analysis for the safety running of trains over bridges. To consider the wheel–rail constraint and contact forces, this paper proposes a versatile 3D VTB element, consisting of a vehicle, eight rail beam elements, four bridge beam elements, and continuous springs as well as the dampers between the rail and bridge girder. With the 3D VTB element matrices formulated, a procedure for assembling the interaction matrices of the 3D VTB element is presented based on the virtual work principle. The global equations of motion of the VTB interaction system are established accordingly, which can be solved by time integration methods to obtain the dynamic responses of the vehicle, track and bridge, as well as the stability and safety indices of the moving train. Finally, an illustrative example is used to verify the proposed the versatile 3D VTB element for the dynamic interactive analysis of railway bridges under moving train loads.

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Zhang, Xun, Xiao Zhen Li, and Ya Dong Li. "Dynamic Characteristics Study of U-Beam Applied in Rail Transit." Advanced Materials Research 243-249 (May 2011): 2021–26. http://dx.doi.org/10.4028/www.scientific.net/amr.243-249.2021.

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The Train-Track-Bridge coupling vibration theory was applied to analyze the dynamic characteristics of a U-beam serviced in Chongqing Rail Transit Line 1 in China. According to the analysis, for the U-beam form of this opening cross-section, the traditional 3D beam element model can only reflect the first-order vibration mode, but neglect the coupled local flexure and torsion vibration characteristics; the 3D beam element model overestimates the lateral stiffness of the bridge, and underestimates it’s lateral vibration; the 3D plate element model is reasonable in dynamic analysis of opening cross-section structure; the vibration of U-beam dominates in the frequency range of f < 250, which is accurate and efficient to take into account this frequency range in the analysis of noise radiated by bridge structure.

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Zhou, Ling Yuan, and Qiao Li. "Analysis of Reinforced Concrete Column Using a Beam-Column Element with a Meshed Section." Advanced Materials Research 255-260 (May 2011): 1954–58. http://dx.doi.org/10.4028/www.scientific.net/amr.255-260.1954.

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A efficient 3D reinforced-concrete beam element based on the flexibility method and distributed nonlinearity theory is proposed, The sections of the beam element are divided into the plane isoparametric elements in this formulation, the section stiffness matrices are calculated through the integration of stress-strain relations of concrete including reinforcing steel effect in the section. The flexibility matrices of the sections are calculated by inverting the stiffness matrices, and the element flexibility matrix is formed through the force interpolation functions. The element stiffness matrix is evaluated through the element flexibility matrix. Finally, the buckling behaviors of a reinforced concrete beam under various eccentric loads are analyzed with the proposed formulation to illustrate its accuracy and computational efficiency.

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Gnoli, Daniel, Sajjad Babamohammadi, and Nicholas Fantuzzi. "Homogenization and Equivalent Beam Model for Fiber-Reinforced Tubular Profiles." Materials 13, no. 9 (April 30, 2020): 2069. http://dx.doi.org/10.3390/ma13092069.

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The current work presents a study on hollow cylinder composite beams, since hollow cylinder cross-sections are one of the principal geometry in many engineering fields. In particular, the present study considers the use of these profiles for scaffold design in offshore engineering. Composite beams cannot be treated as isotropic ones due to couplings mainly present among traction, torsion, bending and shear coefficients. This research aims to present a simple approach to study composite beams as they behave like isotropic ones by removing most complexities related to composite material design (e.g., avoid the use of 2D and 3D finite element modeling). The work aims to obtain the stiffness matrix of the equivalent beam through an analytical approach which is valid for most of the laminated composite configurations present in engineering applications. The 3D Euler–Bernoulli beam theory is considered for obtaining the correspondent isotropic elastic coefficients. The outcomes show that negligible errors occur for some equivalent composite configurations by allowing designers to continue using commercial finite element codes that implement the classical isotropic beam model.

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Kalsoom, Ambreen, A. N. Shankar, Ismail Kakaravada, Prakhar Jindal, V. V. K. Lakshmi, and S. Rajeshkumar. "Investigation of dynamic properties of a three-dimensional printed thermoplastic composite beam containing controllable core under non-uniform magnetic fields." Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications 236, no. 2 (October 25, 2021): 404–12. http://dx.doi.org/10.1177/14644207211045943.

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This paper presents the dynamic responses of sandwich beams with 3D printed thermoplastic composite face sheets and multi-walled carbon nanotubes reinforced magnetorheological elastomer (MWCNT-MR elastomer) cores under non-uniform magnetic fields. A higher-order beam theory (HoBT) is employed to express the beam‘s displacement field. The governing equations of the 3D printed thermoplastic sandwich beam are derived using Lagrange‘s principle and discretized by the finite element method. The validity of the present method is confirmed through comparison with the results available in the literature. The stiffness and damping characteristics of the 3D printed thermoplastic sandwich beam are investigated in relation to support conditions, non-homogeneous magnetic flux, and core-face sheet thickness ratio.

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Xu, Hai Yong. "Numerical Analysis of Top Ring Beam for Foundation Pit." Applied Mechanics and Materials 166-169 (May 2012): 1137–40. http://dx.doi.org/10.4028/www.scientific.net/amm.166-169.1137.

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The research and application condition of top ring beam for the foundation pit engineering is introduced. A 3D finite element model of row piles and top ring beam is calculated and several major parameters of the beams are discussed. On the basic of the FEM results, a simplified method is proposed to calculate the equivalent stiffness of the beam in a typical design profile for practical engineering.

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Gajewski, Tomasz, Natalia Staszak, and Tomasz Garbowski. "Parametric Optimization of Thin-Walled 3D Beams with Perforation Based on Homogenization and Soft Computing." Materials 15, no. 7 (March 29, 2022): 2520. http://dx.doi.org/10.3390/ma15072520.

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The production of thin-walled beams with various cross-sections is increasingly automated and digitized. This allows producing complicated cross-section shapes with a very high precision. Thus, a new opportunity has appeared to optimize these types of products. The optimized parameters are not only the lengths of the individual sections of the cross section, but also the bending angles and openings along the beam length. The simultaneous maximization of the compressive, bending and shear stiffness as well as the minimization of the production cost or the weight of the element makes the problem a multi-criteria issue. The paper proposes a complete procedure for optimizing various open sections of thin-walled beam with different openings along its length. The procedure is based on the developed algorithms for traditional and soft computing optimization as well as the original numerical homogenization method. Although the work uses the finite element method (FEM), no computational stress analyses are required, i.e., solving the system of equations, except for building a full stiffness matrix of the optimized element. The shell-to-beam homogenization procedure used is based on equivalence strain energy between the full 3D representative volume element (RVE) and its beam representation. The proposed procedure allows for quick optimization of any open sections of thin-walled beams in a few simple steps. The procedure can be easily implemented in any development environment, for instance in MATLAB, as it was done in this paper.

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Schulz, Mauro. "Beam Element with a 3D Response for Shear Effects." Journal of Engineering Mechanics 144, no. 1 (January 2018): 04017149. http://dx.doi.org/10.1061/(asce)em.1943-7889.0001366.

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Teh, Lip H. "Beam element verification for 3D elastic steel frame analysis." Computers & Structures 82, no. 15-16 (June 2004): 1167–79. http://dx.doi.org/10.1016/j.compstruc.2004.03.022.

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Petrolo, Antonio Salvatore, and Raffaele Casciaro. "3D beam element based on Saint Venànt’s rod theory." Computers & Structures 82, no. 29-30 (November 2004): 2471–81. http://dx.doi.org/10.1016/j.compstruc.2004.07.004.

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Rahman, Ridwan, Ilham Akbar, and Rofriantona Rofriantona. "3D Finite Element Model for Shear-dominant Failure of Reinforced Concrete Beams." Journal of Applied Materials and Technology 3, no. 1 (January 28, 2022): 12–21. http://dx.doi.org/10.31258/jamt.3.1.12-21.

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This study explores the 3D FE modelling approach in determining the behaviour of shear-dominant responses of RC beams. Five RC beams (A1, A2, B1, C2 and C3) with different cross-sections, amount of tension reinforcement area, amount of shear reinforcement and the length of the span was analysed and the results were compared with the results of the experiment and 2D analysis available in published literature. RC beams analysed in this FE study were constructed as a discrete model using ABAQUS software. The concrete and the plate for loading as well as for supports were modelled using the C3D8R element while longitudinal steel bars and stirrups were modelled with the T3D2 element. The interaction between the steel bar and the concrete in the FE model was assumed perfectly bond. The material behaviour of concrete was modelled with the damage plasticity model where the yield or failure of the material was governed by the tensile cracking and the compressive crushing of the concrete by introducing the hardening variables. The results showed that crack propagation in the FE analysis matched the cracks observed in the test. The crack pattern on Beam A1, A2, B1 and C2 indicated that the specimens experienced flexure and shear failure while Beam C3 experienced less brittle behaviour. Estimates of strength and the load–deformation response of 3D analysis were certainly achieved with reasonable accuracy compared to that of 2D analysis. The difference of experiment-to-2D strength (Pu,exp - Pu,2D / Pu,exp) had a mean of 4.53 whereas the difference of experiment-to-3D strength (Pu,exp - Pu,3D / Pu,exp) had a mean of 1.83. Furthermore, the displacements at ultimate load gained in the 3D analysis were comparable to those of experiments. The difference of experiment-to-2D (du,exp - du,2D / du,exp) and experiment-to-3D (du,exp - du,3D / du,exp) midspan displacement had a mean of 19.91 and 10.89, respectively.

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Jovanović, Đorđe, Drago Žarković, Zoran Brujić, and Đorđe Lađinović. "Fiber beam-column element implementation in academic CAD software Matrix 3D." Gradjevinski materijali i konstrukcije 60, no. 2 (2017): 57–77. http://dx.doi.org/10.5937/grmk1702057j.

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Yang, Dong Quan, and Hong Peng. "Elasto-Plastic Analysis of Frame Structures under Large Displacement-Rotation Deformations." Advanced Materials Research 243-249 (May 2011): 5968–74. http://dx.doi.org/10.4028/www.scientific.net/amr.243-249.5968.

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A finite element program for elasto-plastic analysis of 3D beams and frame structures under large displacement/rotations is developed. The element is Timoshenko beam element based on mechanics of continuum. Constitutive equations for large displacements/rotations in elastic stage are expressed in an explicit way which is suitable for programming. The modification of constitutive equation is presented for the analysis of elasto-plastic problems. A fiber model is adopted for the calculation of stiffness matrix and internal forces. For solution of nonlinear finite element equations, general displacement control method and semi-modified stiffness matrix method is adopted. The results of numerical experimentation show that the program work well for 3D beams and frame structures under elasto-plastic large displacement/rotations.

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31

Malik, Pravin, and Ravikiran Kadoli. "Nonlinear bending and free vibration response of SUS316-Al2O3 functionally graded plasma sprayed beams: theoretical and experimental study." Journal of Vibration and Control 24, no. 6 (July 20, 2016): 1171–84. http://dx.doi.org/10.1177/1077546316659422.

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Functionally graded SUS316-Al2O3 beams with ceramic content varying from 0 to 40% were prepared by a plasma spraying technique. Nonlinear finite element analysis was used to obtain the static deflection and free vibration of a clamped-free functionally graded beam. Von Kármán geometric nonlinearity and power law variation in material gradation through the beam thickness are considered in the analysis. The maximum error between the experimental and nonlinear finite element results for deflection is 6.68% and 14.31% on the fundamental frequency. Numerical results have also been attempted using ANSYS 3D solid element and they compare more closely with the experimental results.

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32

Sergei N. Nazarenko and Galina A. Grudcina. "Method of the Finite-Element Model Formation Containing the 3D Elements for Structural Calculations of the Reinforced Concrete Structures Considering the Crack Opening." Communications - Scientific letters of the University of Zilina 23, no. 1 (January 4, 2021): D15—D25. http://dx.doi.org/10.26552/com.c.2021.1.d15-d25.

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This article presents the 3D computational modeling method for reinforced concrete structures. An example of calculation of the reinforced concrete beam, using the Finite Element Method in SCAD++ following proposed algorithm, is given. Results comparison to the analytical calculation of the model with selected reinforcement is presented. For concrete, the 3D solid Finite Elements are used and the 3D beam elements for reinforcement. The model is formed using AutoCAD and AutoLISP, which creates a text data file in SCAD format for the description of model. In addition, computation of the 3D model of the crossbar with a crack is performed. Crack sizes are set in the stretched zone based on data from initial calculation. Graphic results obtained in SCAD++ are presented.

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Hu, Zhengzhou, and Minger Wu. "Large displacement geometrically nonlinear finite element analysis of 3D Timoshenko fiber beam element." Structural Engineering and Mechanics 51, no. 4 (August 25, 2014): 601–25. http://dx.doi.org/10.12989/sem.2014.51.4.601.

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De Gaetano, G., D. Mundo, F. I. Cosco, C. Maletta, and S. Donders. "Concept Modelling of Vehicle Joints and Beam-Like Structures through Dynamic FE-Based Methods." Shock and Vibration 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/303567.

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This paper presents dynamic methodologies able to obtain concept models of automotive beams and joints, which compare favourably with the existing literature methods, in terms of accuracy, easiness of implementation, and computational loads. For the concept beams, the proposed method is based on a dynamic finite element (FE) approach, which estimates the stiffness characteristics of equivalent 1D beam elements using the natural frequencies, computed by a modal analysis of the detailed 3D FE model of the structure. Concept beams are then connected to each other by a concept joint, which is obtained through a dynamic reduction technique that makes use of its vibration normal modes. The joint reduction is improved through the application of a new interface beam-to-joint element, able to interpolate accurately the nodal displacements of the outer contour of the section, to obtain displacements and rotations of the central connection node. The proposed approach is validated through an application case that is typical in vehicle body engineering: the analysis of a structure formed by three spot-welded thin-walled beams, connected by a joint.

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35

Boso, D. P., P. Litewka, B. A. Schrefler, and P. Wriggers. "A 3D beam-to-beam contact finite element for coupled electric-mechanical fields." International Journal for Numerical Methods in Engineering 64, no. 13 (December 7, 2005): 1800–1815. http://dx.doi.org/10.1002/nme.1427.

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36

Guldberg, R. E., S. J. Hollister, and G. T. Charras. "The Accuracy of Digital Image-Based Finite Element Models." Journal of Biomechanical Engineering 120, no. 2 (April 1, 1998): 289–95. http://dx.doi.org/10.1115/1.2798314.

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Digital image-based finite element meshing is an alternative approach to time-consuming conventional meshing techniques for generating realistic three-dimensional (3D) models of complex structures. Although not limited to biological applications, digital image-based modeling has been used to generate structure-specific (i.e., nongeneric) models of whole bones and trabecular bone microstructures. However, questions remain regarding the solution accuracy provided by the digital meshing approach, particularly at model or material boundaries. The purpose of this study was to compare the accuracy of digital and conventional smooth boundary models based on theoretical solutions for a two-dimensional (2D) compression plate and a 3D circular cantilever beam. For both the plate and beam analyses, the predicted solution at digital model boundaries was characterized by local oscillations, which produced potentially high errors within individual boundary elements. Significantly, however, the digital model boundary solution oscillated approximately about the theoretical solution. A marked improvement in solution accuracy was therefore achieved by considering average results within a region composed of several elements. Absolute errors for Von Mises stress averaged over the beam cross section, for example, converged to less than 4 percent, and the predicted free-end displacement of the cantilever beam was within 1 percent of the theoretical solution. Analyses at several beam orientations and mesh resolutions suggested a minimum discretization of three to four digital finite elements through the beam cross section to avoid high numerical stiffening errors under bending.

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Montero, Jorge A., and Ghadir Haikal. "Modeling Beam–Solid Finite Element Interfaces: A Stabilized Formulation for Contact and Coupled Systems." International Journal of Applied Mechanics 10, no. 09 (November 2018): 1850094. http://dx.doi.org/10.1142/s1758825118500941.

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A number of engineering applications involve contact with bodies modeled using specialized theories of solid mechanics like beams or shells. While computational models for contact in 2D and 3D solid mechanics have been extensively developed in the literature, problems involving contact with beams or shells have received less attention. When modeling contact between a solid body represented with beam or shell theory and a domain discretized with solid finite elements, the contact model faces the typical challenges of enforcing geometric compatibility and the transfer of a complete pressure field along the contact interface, with the added complications stemming from the different underlying mathematical formulations and finite element discretizations in the connecting domains. Resultant-based beam and shell theories do not provide direct estimates of surface tractions, therefore rendering the issue of pressure transfer on beam–solid and shell–solid interfaces more problematic. In the absence of specialized contact formulations for solid–beam and solid–shell interfaces, contact models have relied almost exclusively on the Node-To-Surface (NTS) geometric compatibility approach. This formulation suffers from well-known drawbacks, including instability, surface locking and incomplete pressure fields on the interface. The NTS approach, however, remains the method most readily applicable to contact with beam or shell elements among the vast variety of available methods for computational contact modeling using finite elements. The goal of this paper is to bridge the gap in the literature on coupling domains with beam and solid finite element discretizations. We propose an interface formulation for beam–solid interfaces that ensures the transfer of a complete pressure field while enforcing geometric compatibility using standard NTS constraints. The formulation uses a stabilization approach, based on a special form of the Discontinuous Galerkin method, to enforce weak continuity between the stress fields on the solid side of the interface, and the moment and shear resultants in the contacting beam. We show that the proposed formulation is a robust approach for satisfying compatibility constraints while ensuring the transfer of a complete pressure field on beam–solid finite element interfaces that can be used with bilinear and quadratic interpolations in the solid, and Euler or Timoshenko formulations for the beam.

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38

Mohammed, Tesfaye Alemu, and Tensae Alebachew. "NUMERICAL INVESTIGATION OF AS-BUILT AND CARBON FIBER REINFORCED POLYMER RETROFITTED REINFORCED CONCRETE BEAM WITH WEB OPENINGS UNDER IMPACT LOADING." ASEAN Engineering Journal 12, no. 1 (February 28, 2022): 173–82. http://dx.doi.org/10.11113/aej.v12.17521.

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It is not uncommon to provide openings in beams due to utility needs such as mechanical, electrical and sewerage passages. However, no clear guidelines are available in code of practice to handle beam web openings and presence of openings in beams changes behavior of Reinforced Concrete beam into a more complicated one. This research work investigates response of RC beam with openings under impact loading and proposes application of carbon fiber reinforced polymer (CFRP) composites to restore lost beam performance due to the presence of web openings. 3D nonlinear finite element software LS-DYNA is used for model development, validation and parametric finite element analysis work. The accuracy of the nonlinear finite element models are verified using experimental results from literature. Further parametric studies are performed to optimize beam web openings on opening location, size and CFRP no. of layers and fiber orientation. Numerical results showed as compared to control, large opening cutouts in RC beam decreased impact resistance of a beam by 54%. Also, RC beam exhibited poor impact loading resistance close to loading point (mid span) and performed good near shear zone. As compared to control as-built RC beam, Carbon Fiber Reinforced Polymer (CFRP) composites strengthening reduced mid span deflection by 74% and improved beams brittle failure mode. Also, 900 fiber orientation complete wrapping resulted in reduction of shear cracking around opening however exhibited low overall impact resistance as compared with 0º fiber orientation.

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Balasubramanian, K. R., T. Suthakar, K. Sankaranarayanasamy, and G. Buvanashekaran. "Laser Welding Simulations of Stainless Steel Joints Using Finite Element Analysis." Advanced Materials Research 383-390 (November 2011): 6225–30. http://dx.doi.org/10.4028/www.scientific.net/amr.383-390.6225.

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Laser beam welding (LBW) is a fusion joining process that uses the energy from a laser beam to melt and subsequently crystallize a metal, resulting in a bond between parts. In this study, finite element method (FEM) is used for predicting the weld bead profile of laser welding butt, lap and T-joints. A three-dimensional finite element model is used to analyze the temperature distribution weld bead shape for different weld configurations produced by the laser welding process. In the model temperature-dependent thermo physical properties of AISI304 stainless steel, effect of latent heat of fusion and convective and radiative boundary conditions are incorporated. The heat input to the FEM model is assumed to be a 3D conical Gaussian heat source. The finite element software SYSWELD is employed to obtain the numerical results. The computed weld bead profiles for butt, lap and T-joints are compared with the experimental profiles and are found to be in agreement.

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Bettaïeb, M. N., P. Velex, and M. Ajmi. "A Static and Dynamic Model of Geared Transmissions by Combining Substructures and Elastic Foundations—Applications to Thin-Rimmed Gears." Journal of Mechanical Design 129, no. 2 (February 6, 2006): 184–94. http://dx.doi.org/10.1115/1.2406088.

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The present work is aimed at predicting the static and dynamic behavior of geared transmissions comprising flexible components. The proposed model adopts a hybrid approach, combining classical beam elements, elastic foundations for the simulation of tooth contacts, and substructures derived from three-dimensional (3D) finite element grids for thin-rimmed gears and their supporting shafts. The pinion shaft and body are modeled via beam elements which simulate bending, torsion and traction. Tooth contact deflections are described using time-varying elastic foundations (Pasternak foundations) connected by independent contact stiffness. In order to account for thin-rimmed gears, a 3D finite element model of the gear (excluding teeth) is set up and a pseudo-modal reduction technique is used prior to solving the equations of motion. Depending on the gear structure, the results reveal a potentially significant influence of thin rims on both quasi-static and dynamic tooth loading.

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Bergin, M., T. A. Myles, A. Radić, C. J. Hatchwell, S. M. Lambrick, D. J. Ward, S. D. Eder, A. Fahy, M. Barr, and P. C. Dastoor. "Complex optical elements for scanning helium microscopy through 3D printing." Journal of Physics D: Applied Physics 55, no. 9 (November 26, 2021): 095305. http://dx.doi.org/10.1088/1361-6463/ac3a3e.

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Abstract Developing the next generation of scanning helium microscopes requires the fabrication of optical elements with complex internal geometries. We show that resin stereolithography (SLA) 3D printing produces low-cost components with the requisite convoluted structures whilst achieving the required vacuum properties, even without in situ baking. As a case study, a redesigned pinhole plate optical element of an existing scanning helium microscope was fabricated using SLA 3D printing. In comparison to the original machined component, the new optical element minimised the key sources of background signal, in particular multiple scattering and the secondary effusive beam.

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Pocratsky, Ryan M., and Maarten P. de Boer. "Self-tensioning Support Post Design to Control Residual Stress in MEMS Fixed-Fixed Beams." MRS Proceedings 1659 (2014): 55–61. http://dx.doi.org/10.1557/opl.2014.99.

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ABSTRACTFixed-fixed beams are ubiquitous MEMS structures that are integral components for sensors and actuation mechanisms. However, residual stress inherent in surface micromachining can affect the mechanical behavior of fixed-fixed structures, and even can cause buckling. A self-tensioning support post design that utilizes the compressive residual stress of trapped sacrificial oxide to control the stress state passively and locally in a fixed-fixed beam is proposed and detailed. The thickness and length of the trapped oxide affects the amount of stress in the beam. With this design, compression can be reduced or even converted into tension. An analytical model and a 3D finite element model are presented. The analytical model shows relatively good agreement with a 3D finite element model, indicating that it can be used for design purposes. A series of fixed-fixed beams were fabricated to demonstrate that the tensioning support post causes a reduction in buckling amplitude, even pulling the beam into tension. Phase shifting interferometry deflection measurements were used to confirm the trends observed from the models. Controlling residual stress allows longer fixed-fixed beams to be fabricated without buckling, which can improve the performance range of sensors. This technique can also enable local stress control, which is important for sensors.

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43

Huang, Dengpeng, and Sigrid Leyendecker. "An electromechanically coupled beam model for dielectric elastomer actuators." Computational Mechanics 69, no. 3 (November 25, 2021): 805–24. http://dx.doi.org/10.1007/s00466-021-02115-0.

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AbstractIn this work, the Cosserat formulation of geometrically exact beam dynamics is extended by adding the electric potential as an additional degree of freedom to account for the electromechanical coupling in the dielectric elastomer actuators. To be able to generate complex beam deformations via dielectric actuator, a linear distribution of electric potential on the beam cross section is proposed. Based on this electric potential, the electric field and the strain-like electrical variable are defined for the beam, where the strain-like electrical variable is work-conjugated to the electric displacement. The electromechanically coupled strain energy for the beam is derived consistently from continuum electromechanics, which leads to the direct application of the material models in the continuum to the beam model. The electromechanically coupled problem in beam dynamics is first spatially semidiscretized by 1D finite elements and then solved via variational time integration. By applying different electrical boundary conditions, different deformations of the beam are obtained in the numerical examples, including contraction, shear, bending and torsion. The damping effect induced by the viscosity as well as the total energy of the beam are evaluated. The deformations of the electromechanically coupled beam model are compared with the results of the 3D finite element model, where a good agreement of the deformations in the beam model and that in the 3D finite element model is observed. However, less degrees of freedom are required to resolve the complex deformations in the beam model.

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Diro, Gemechu Abdissa, and Worku Feromsa Kabeta. "Finite Element Analysis of Key Influence Parameters in Reinforced Concrete Exterior Beam Column Connection subjected to Lateral Loading." European Journal of Engineering Research and Science 5, no. 6 (June 15, 2020): 689–97. http://dx.doi.org/10.24018/ejers.2020.5.6.1947.

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Beam column connection is the most critical zone in a reinforced concrete frame. The strength of connection affects the overall behavior and performance of RC framed structures subjected to lateral load and axial loads. The study of critical parameters that affects the overall joint performances and response of the structure is important. Recent developments in computer technology have made possible the use of Finite element method for 3D modeling and analysis of reinforced concrete structures. Nonlinear finite element analysis of reinforced concrete exterior beam column connection subjected to lateral loading was performed in order to investigate joint shear failure mode in terms of joint shear capacity, deformations and cracking pattern using ABAQUS software. A 3D solid shape model using 3D stress hexahedral element type (C3D8R) was implemented to simulate concrete behavior. Wire shape model with truss shape elements (T3D2) was used to simulate reinforcement’s behavior. The concrete and reinforcement bars were coupled using the embedded modeling technique. In order to define nonlinear behavior of concrete material, the concrete damage plasticity (CDP) was applied to the numerical model as a distributed plasticity over the whole geometry. The study was to investigate the most influential parameters affecting joint shear failure due to column axial load, beam longitudinal reinforcement ratio, joint panel geometry and concrete compressive strength. The Finite Element Model (FEM) was verified against experimental test of exterior RC beam column connection subjected to lateral loading. The model showed good comparison with test results in terms of load-displacement relation, cracking pattern and joint shear failure modes. The FEA clarified that the main influential parameter for predicting joint shear failure was concrete compressive strength.

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45

Diro, Gemechu Abdissa, and Worku Feromsa Kabeta. "Finite Element Analysis of Key Influence Parameters in Reinforced Concrete Exterior Beam Column Connection subjected to Lateral Loading." European Journal of Engineering and Technology Research 5, no. 6 (June 15, 2020): 689–97. http://dx.doi.org/10.24018/ejeng.2020.5.6.1947.

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Beam column connection is the most critical zone in a reinforced concrete frame. The strength of connection affects the overall behavior and performance of RC framed structures subjected to lateral load and axial loads. The study of critical parameters that affects the overall joint performances and response of the structure is important. Recent developments in computer technology have made possible the use of Finite element method for 3D modeling and analysis of reinforced concrete structures. Nonlinear finite element analysis of reinforced concrete exterior beam column connection subjected to lateral loading was performed in order to investigate joint shear failure mode in terms of joint shear capacity, deformations and cracking pattern using ABAQUS software. A 3D solid shape model using 3D stress hexahedral element type (C3D8R) was implemented to simulate concrete behavior. Wire shape model with truss shape elements (T3D2) was used to simulate reinforcement’s behavior. The concrete and reinforcement bars were coupled using the embedded modeling technique. In order to define nonlinear behavior of concrete material, the concrete damage plasticity (CDP) was applied to the numerical model as a distributed plasticity over the whole geometry. The study was to investigate the most influential parameters affecting joint shear failure due to column axial load, beam longitudinal reinforcement ratio, joint panel geometry and concrete compressive strength. The Finite Element Model (FEM) was verified against experimental test of exterior RC beam column connection subjected to lateral loading. The model showed good comparison with test results in terms of load-displacement relation, cracking pattern and joint shear failure modes. The FEA clarified that the main influential parameter for predicting joint shear failure was concrete compressive strength.

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Li, Xing Quan, Xiao Yan Sun, and Ya Wei Li. "Study on Three-Point Bending Numerical Tests of CFRP Reinforced Concrete Beam with Initial Crack." Advanced Materials Research 838-841 (November 2013): 639–43. http://dx.doi.org/10.4028/www.scientific.net/amr.838-841.639.

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Based on extended finite element method (XFEM) of the finite element software platform-ABAQUS, three-point bending numerical simulation of CFRP reinforced concrete beam with initial crack has been made to predict the 3D crack propagation path. The numerical tests present the crack propagation path under ultimate load and crack damage modes of non-CFRP and some different CFRP plies. The results show that the strength of CFRP reinforced concrete beam is obviously improved and the crack which previous penetrate through doesnt penetrate through concrete beam under CFRP reinforce based on multiple optometric numerical simulation results. The results of this paper can also provide some foundations for damage mode, the ultimate load and CFRP overlay design of reinforced concrete beams.

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Sucharda, Oldrich. "Selected Approaches to Numerical Modeling and Analysis of Fiber Reinforced Concrete Beam." Solid State Phenomena 309 (August 2020): 174–79. http://dx.doi.org/10.4028/www.scientific.net/ssp.309.174.

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The paper presents research focused on modeling of lightweight concrete beams combining reinforced and fiber concrete. The paper solves the selected case of the RC beam, which was experimentally tested. The advanced numerical model and calculation used for an experiment into account the non-linear behavior and collapse of the beam. For the experiment, a specific cross-section with an opening that relieves the beam is selected. Non-linear analysis in combination with the finite element method is used for numerical modeling. Specifically, 3D calculation model and fracture-plastic material for concrete are used.

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Justín, Murín, Hrabovský Juraj, Aminbaghai Mehdi, Kutiš Vladimír, Paulech Juraj, and Kugler Stephan. "Extension of the FGM Beam Finite Element by Warping Torsion." Strojnícky časopis - Journal of Mechanical Engineering 69, no. 2 (June 1, 2019): 57–76. http://dx.doi.org/10.2478/scjme-2019-0017.

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AbstractIn the contribution, our 3D FGM Timoshenko beam finite element with 12x12 stiffness and mass matrices for doubly symmetric open and closed cross-section [1] is extended by warping torsion effect (non-uniform torsion) to 14x14 finite element matrices. A longitudinal continuous variation of effective material properties is considered by the finite element equations derivation, which can be obtained by homogenization of the spatial varying material properties in real FGM beam. Results of numerical elastostatic non-uniform torsional analysis of the FGM cantilever beam of I-cross-section are presented and the accuracy and effectiveness of the new FGM beam finite element is discussed and evaluated.

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Wan, Jia, Qing Fang Niu, Guan Feng Qiao, and Tie Ying Li. "Finite Element Analysis of Chinese Traditional Hall-Style Timber Structure." Advanced Materials Research 1008-1009 (August 2014): 1201–4. http://dx.doi.org/10.4028/www.scientific.net/amr.1008-1009.1201.

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This paper uses general finite element software Abaqus to simulate three Chinese traditional hall-style structures recorded in the book <<Yingzao Fashi>>. With Abaqus having an advantage in dealing with contact problems, three hall-style timber structure finite element analysis models have been established within the 3D solid element which is used to model beams, columns, brackets and other structural members in the modeling. Contact pairs also have been used to simulate the interaction between the structure members like beam-column contact pair, column-foot foundation contact pair and dougong-bracket beam contact pair and so on. In the modeling process, some simplifying assumptions have been used for many complex structural members and interactions between them being used in Chinese hall-style structure. The model was finally tested by gravity load and vertical load.

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Hu, Ning, Kazuhiko Nunoya, and Hisao Fukunaga. "Compressive Instability of Carbon Nanotubes." Key Engineering Materials 353-358 (September 2007): 2187–90. http://dx.doi.org/10.4028/www.scientific.net/kem.353-358.2187.

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Based on both molecular mechanics and computational structural mechanics, a three-dimensional (3D) equivalent beam element is developed to model a C-C covalent bond on carbon nanotubes (CNTs) whereas the van der Waals forces between atoms in the different walls of multi-walled CNTs are described using a rod element. The buckling characteristics of CNTs are conveniently analyzed by using the traditional finite element method (FEM) of a 3D beam and rod model, termed as molecular structural mechanics approach (MSMA). Moreover, to model the CNTs with large length or large diameter, the validity of Euler’s beam buckling theory and a shell model with proper properties defined from the results of MSMA is investigated. The predicted results by this simple continuum mechanics approach agree well with the reported experimental data.

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Journal articles on the topic '3D beam element'

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