Journal articles: 'Large beam deflection'

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Song, Jiang Yong. "An Elliptic Integral Solution to the Multiple Inflections Large Deflection Beams in Compliant Mechanisms." Advanced Materials Research 971-973 (June 2014): 349–52. http://dx.doi.org/10.4028/www.scientific.net/amr.971-973.349.

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In this paper, a solution based on the elliptic integrals is proposed for solving multiples inflection points large deflection. Application of the Bernoulli Euler equations of compliant mechanisms with large deflection equation of beam is obtained ,there is no inflection point and inflection points in two cases respectively. The elliptic integral solution which is the most accurate method at present for analyzing large deflections of cantilever beams in compliant mechanisms.

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Zhou, Peng, Ying Liu, and Xiaoyan Liang. "Analytical Solutions for Large Deflections of Functionally Graded Beams Based on Layer-Graded Beam Model." International Journal of Applied Mechanics 10, no. 09 (November 2018): 1850098. http://dx.doi.org/10.1142/s1758825118500989.

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The objective of this paper is to investigate the large deflection of a slender functionally graded beam under the transverse loading. Firstly, by modeling the functionally graded beam as a layered structure with graded yield strength, a unified yield criterion for a functionally graded metallic beam is established. Based on the proposed yielding criteria, analytical solutions (AS) for the large deflections of fully clamped functionally graded beams subjected to transverse loading are formulated. Comparisons between the present solutions with numerical results are made and good agreements are found. The effects of gradient profile and gradient intensity factor on the large deflections of functionally graded beams are discussed in detail. The reliability of the present analytical model is demonstrated, and the larger the gradient variation ratio near the loading surface is, the more accurate the layer-graded beam model will be.

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Elvin, Niell G., and Alex A. Elvin. "Large deflection effects in flexible energy harvesters." Journal of Intelligent Material Systems and Structures 23, no. 13 (February 20, 2012): 1475–84. http://dx.doi.org/10.1177/1045389x11435434.

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The effect of large deflection on the mechanical and electrical behaviors of flexible piezoelectric energy harvesters has not been well studied. A generalized nonlinear coupled finite element circuit simulation approach is presented in this article to study the performance of energy harvesters subjected to large deflections. The method presented is validated experimentally using three test examples consisting of (a) a static case, (b) a free vibration case, and (c) a forced vibration case. Under static conditions (when the transverse tip deflection exceeds a quarter of the cantilever length), large deflections cause geometric stiffening of the structure that reduces the tip deflection of the generator when compared to linear (i.e. small-deflection) behavior. For a cantilever generator under dynamic conditions, geometric stiffening, inertial softening, and nonlinear damping effects become significant. Large deflections both shift the resonant frequency and increase damping and can thus cause a significant reduction in output voltage when compared with small-deflection linear theory. In the finite element generator model studied in this article, these nonlinear dynamic effects become significant when the transverse tip deflection exceeds 35% of the beam length.

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Tolou, N., and J. L. Herder. "A Seminalytical Approach to Large Deflections in Compliant Beams under Point Load." Mathematical Problems in Engineering 2009 (2009): 1–13. http://dx.doi.org/10.1155/2009/910896.

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The deflection of compliant mechanism (CM) which involves geometrical nonlinearity due to large deflection of members continues to be an interesting problem in mechanical systems. This paper deals with an analytical investigation of large deflections in compliant mechanisms. The main objective is to propose a convenient method of solution for the large deflection problem in CMs in order to overcome the difficulty and inaccuracy of conventional methods, as well as for the purpose of mathematical modeling and optimization. For simplicity, an element is considered which is a cantilever beam out of linear elastic material under vertical end point load. This can further be used as a building block in more complex compliant mechanisms. First, the governing equation has been obtained for the cantilever beam; subsequently, the Adomian decomposition method (ADM) has been utilized to obtain a semianalytical solution. The vertical and horizontal displacements of a cantilever beam can conveniently be obtained in an explicit analytical form. In addition, variations of the parameters that affect the characteristics of the deflection have been examined. The results reveal that the proposed procedure is very accurate, efficient, and convenient for cantilever beams, and can probably be applied to a large class of practical problems for the purpose of analysis and optimization.

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Allam, Ahmed, Ayman Nassif, and Ali Nadjai. "Behaviour of restrained steel beam at elevated temperature – parametric studies." Journal of Structural Fire Engineering 10, no. 3 (September 9, 2019): 324–39. http://dx.doi.org/10.1108/jsfe-11-2018-0036.

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Purpose This paper aims to investigate computationally and analytically how different levels of restraint from surrounding structure, via catenary action in beams, affect the survival of steel framed structures in fire. This study focuses on examining the mid-span deflection and the tensile axial force of a non-composite heated steel beam at large deflection that is induced by the catenary action during exposure to fires. The study also considers the effect of the axial horizontal restraints, load-ratio, beam temperature gradient and the span/depth ratio. It was found that these factors influence the heated steel beam within steel construction and its catenary action at large deflection. The study suggests that this may help the beam to hang to the surrounding cold structure and delay the run-away deflection when the tensile axial force of the beam has been overcome. Design/methodology/approach This paper is part one of the parametric study and discusses both the effect of the axial horizontal restraints and load-ratio on the heated steel-beam. Reliance on the prescriptive standard fire solutions may lead to an unpredicted behaviour of the structure members if the impact of potential real fires is not considered. Findings Variation of the horizontal end-restraint level has a major effect on the behaviour of the beam at high deflection, and the loading on a beam at large displacement can be carried effectively by catenary behaviour. An increase of axial horizontal stiffness helps the catenary action to prevent run-away at lower deflections. The studies also investigated the influence of varying the load ratio on the behaviour of the heated beam at large deflection and how it affects the efficacy of the catenary action. The study suggests that care should be taken when selecting the load ratio to be used in the design. Originality/value In a recent work, the large deflection behaviours of axially restrained corrugated web steel beam (CWSB) at elevated temperatures were investigated using a finite element method (Wang et al., 2014). Parameters that greatly affected behaviours of CWSB at elevated temperatures were the load ratio, the axial restraint stiffness ratio and the span–depth ratio. Other works included numerical studies on large deflection behaviours of restrained castellated steel beams in a fire where the impact of the catenary action is considered (Wang, 2002). The impact of the induced axial forces in the steel beam during cooling stage of a fire when the beam temperature decreases, if thermal shortening of the beam is restrained, large tensile forces may be induced in the beam (Wang, 2005; Allam et al., 2002). A performance-based approach is developed for assessing the fire resistance of restrained beams. The approach is based on equilibrium and compatibility principles, takes into consideration the influence of many factors, including fire scenario, end restraints, thermal gradient, load level and failure criteria, in evaluating fire resistance (Dwaikat and Kodur, 2011; Allam et al., 1998).

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Ghuku, Sushanta, and Kashi Nath Saha. "A Review on Stress and Deformation Analysis of Curved Beams under Large Deflection." International Journal of Engineering and Technologies 11 (July 2017): 13–39. http://dx.doi.org/10.18052/www.scipress.com/ijet.11.13.

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The paper presents a review on large deflection behavior of curved beams, as manifested through the responses under static loading. The term large deflection behavior refers to the inherent nonlinearity present in the analysis of such beam system response. The analysis leads to the field of geometric nonlinearity, in which equation of equilibrium is generally written in deformed configuration. Hence the domain of large deflection analysis treats beam of any initial configuration as curved beam. The term curved designates the geometry of center line of beam, distinguishing it from the usual straight or circular arc configuration. Different methods adopted by researchers, to analyze large deflection behavior of beam bending, have been taken into consideration. The methods have been categorized based on their application in various formats of problems. The nonlinear response of a beam under static loading is also a function of different parameters of the particular problem. These include boundary condition, loading pattern, initial geometry of the beam, etc. In addition, another class of nonlinearity is commonly encountered in structural analysis, which is associated with nonlinear stress-strain relations and known as material nonlinearity. However the present paper mainly focuses on geometric nonlinear analysis of beam, and analysis associated with nonlinear material behavior is covered briefly as it belongs to another class of study. Research works on bifurcation instability and vibration responses of curved beams under large deflection is also excluded from the scope of the present review paper.

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Saxena, A., and S. N. Kramer. "A Simple and Accurate Method for Determining Large Deflections in Compliant Mechanisms Subjected to End Forces and Moments." Journal of Mechanical Design 120, no. 3 (September 1, 1998): 392–400. http://dx.doi.org/10.1115/1.2829164.

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Compliant members in flexible link mechanisms undergo large deflections when subjected to external loads. Because of this fact, traditional methods of deflection analysis do not apply. Since the nonlinearities introduced by these large deflections make the system comprising such members difficult to solve, parametric deflection approximations are deemed helpful in the analysis and synthesis of compliant mechanisms. This is accomplished by representing the compliant mechanism as a pseudo-rigid-body model. A wealth of analysis and synthesis techniques available for rigid-body mechanisms thus become amenable to the design of compliant mechanisms. In this paper, a pseudo-rigid-body model is developed and solved for the tip deflection of flexible beams for combined end loads. A numerical integration technique using quadrature formulae has been employed to solve the large deflection Bernoulli-Euler beam equation for the tip deflection. Implementation of this scheme is simpler than the elliptic integral formulation and provides very accurate results. An example for the synthesis of a compliant mechanism using the proposed model is also presented.

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QIN, QINGHUA, MINGSHI WANG, ZHENGJIN WANG, JIANXUN ZHANG, and T. J. WANG. "A YIELD CRITERION AND PLASTIC ANALYSIS FOR PHYSICALLY ASYMMETRIC SANDWICH BEAM WITH METAL FOAM CORE." International Journal of Applied Mechanics 05, no. 04 (December 2013): 1350037. http://dx.doi.org/10.1142/s1758825113500373.

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A yield criterion for physically asymmetric sandwich cross-sections is proposed in this paper. Using the yield criterion, analytical solutions for the large deflections of fully clamped asymmetric slender sandwich beams transversely loaded by a flat punch at the midspan are derived considering the core strength effect and interaction of bending and axial stretching. Finite element (FE) method is employed to predict the large deflection behavior of the sandwich beams. Good agreement is achieved between the analytical predictions and FE results. Effects of asymmetric factor, core strength and loading punch size are also discussed. It is demonstrated that core strength and loading punch size have significant influences on the load-carrying and energy absorption capacities of physically asymmetric metal sandwich beams while the asymmetry effect could be neglected when the deflection exceeds sandwich beam depth.

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Torkamani, Morteza A. M., and Mustafa Sonmez. "Inelastic Large Deflection Modeling of Beam-Columns." Journal of Structural Engineering 127, no. 8 (August 2001): 876–87. http://dx.doi.org/10.1061/(asce)0733-9445(2001)127:8(876).

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10

Verly, Pierre G. "Low-loss liquid-crystal-clad waveguide switch with a large angular separation of the optical beams." Canadian Journal of Physics 65, no. 5 (May 1, 1987): 476–83. http://dx.doi.org/10.1139/p87-064.

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We propose a new nematic liquid-crystal-clad electrooptic waveguide beamsplitter simultaneously capable of very high beam deflections and relatively low losses. A trade-off between the deflection and the cross talk due to unswitched spatial frequencies of a realistic diverging beam is discussed with respect to waveguide materials and geometries.

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11

Songsuwan, Wachirawit, Monsak Pimsarn, and Nuttawit Wattanasakulpong. "Dynamic Responses of Functionally Graded Sandwich Beams Resting on Elastic Foundation Under Harmonic Moving Loads." International Journal of Structural Stability and Dynamics 18, no. 09 (September 2018): 1850112. http://dx.doi.org/10.1142/s0219455418501122.

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This paper investigates the free vibration and dynamic response of functionally graded sandwich beams resting on an elastic foundation under the action of a moving harmonic load. The governing equation of motion of the beam, which includes the effects of shear deformation and rotary inertia based on the Timoshenko beam theory, is derived from Lagrange’s equations. The Ritz and Newmark methods are employed to solve the equation of motion for the free and forced vibration responses of the beam with different boundary conditions. The results are presented in both tabular and graphical forms to show the effects of layer thickness ratios, boundary conditions, length to height ratios, spring constants, etc. on natural frequencies and dynamic deflections of the beam. It was found that increasing the spring constant of the elastic foundation leads to considerable increase in natural frequencies of the beam; while the same is not true for the dynamic deflection. Additionally, very large dynamic deflection occurs for the beam in resonance under the harmonic moving load.

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Nellessen, J., J. H. Müller, K. Sengstock, and W. Ertmer. "Large-angle beam deflection of a laser-cooled sodium beam." Journal of the Optical Society of America B 6, no. 11 (November 1, 1989): 2149. http://dx.doi.org/10.1364/josab.6.002149.

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13

Park, Hyo Seon, H. M. Lee, Y. H. Kwon, J. H. Seo, and Hong C. Rhim. "Assessment Model for the Safety and Serviceability of Steel Beams Using Terrestrial LiDAR." Key Engineering Materials 321-323 (October 2006): 248–53. http://dx.doi.org/10.4028/www.scientific.net/kem.321-323.248.

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Structural monitoring is concerned with the safety and serviceability of the users of structures, especially for the case of building structures and infrastructures. When considering the safety of a structure, the maximum stress in a member due to live load, earthquake, wind, or other unexpected loadings must be checked not to exceed the stress specified in a code. Although the steel will not fail at yield, excessively large deflections will deteriorate the serviceability of a structure. Therefore, to guarantee the safety and serviceability of steel beams, the maximum stress and deflection in a steel beam must be monitored. However, no practical method has been reported to monitor both the maximum stress and deflection. In this paper, assessment model for both safety and serviceability of a steel beam is proposed. The model was tested in an experiment by comparing stress level estimated by LiDAR system and stress level directly measured from electrical or fiber optic sensors. The maximum deflection measured from LiDAR system is also compared with the maximum deflection directly measured from LVDTs. In addition to displacement measurement, the proposed system can provide information on deformed shapes of steel beams.

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Tahir, N. A., R. Schmidt, M. Brugger, A. Shutov, I. V. Lomonosov, A. R. Piriz, and D. H. H. Hoffmann. "Simulations of full impact of the Large Hadron Collider beam with a solid graphite target." Laser and Particle Beams 27, no. 3 (July 13, 2009): 475–83. http://dx.doi.org/10.1017/s0263034609990206.

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AbstractThe Large Hadron Collider (LHC) will operate with 7 TeV/c protons with a luminosity of 1034 cm−2 s−1. This requires two beams, each with 2808 bunches. The nominal intensity per bunch is 1.15 × 1011protons and the total energy stored in each beam is 362 MJ. In previous papers, the mechanisms causing equipment damage in case of a failure of the machine protection system was discussed, assuming that the entire beam is deflected onto a copper target. Another failure scenario is the deflection of beam, or part of it, into carbon material. Carbon collimators and beam absorbers are installed in many locations around the LHC close to the beam, since carbon is the material that is most suitable to absorb the beam energy without being damaged. In case of a failure, it is very likely that such absorbers are hit first, for example, when the beam is accidentally deflected. Some type of failures needs to be anticipated, such as accidental firing of injection and extraction kicker magnets leading to a wrong deflection of a few bunches. Protection of LHC equipment relies on the capture of wrongly deflected bunches with beam absorbers that are positioned close to the beam. For maximum robustness, the absorbers jaws are made out of carbon materials. It has been demonstrated experimentally and theoretically that carbon survives the impact of a few bunches expected for such failures. However, beam absorbers are not designed for major failures in the protection system, such as the beam dump kicker deflecting the entire beam by a wrong angle. Since beam absorbers are closest to the beam, it is likely that they are hit first in any case of accidental beam loss. In the present paper we present numerical simulations using carbon as target material in order to estimate the damage caused to carbon absorbers in case of major beam impact.

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Kimball, Chris, and Lung-Wen Tsai. "Modeling of Flexural Beams Subjected to Arbitrary End Loads." Journal of Mechanical Design 124, no. 2 (May 16, 2002): 223–35. http://dx.doi.org/10.1115/1.1455031.

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The analysis of compliant mechanisms is often complicated due to the geometric nonlinearities which become significant with large elastic deflections. Pseudo rigid body models (PRBM) may be used to accurately and efficiently model such large elastic deflections. Previously published models have only considered end forces with no end moment or end moment acting only in the same direction as the force. In this paper, we present a model for a cantilever beam with end moment acting in the opposite direction as the end force, which may or may not cause an inflection point. Two pivot points are used, thereby increasing the model’s accuracy when an inflection point exists. The Bernoulli-Euler beam equation is solved for large deflections with elliptic integrals, and the elliptic integral solutions are used to determine when an inflection point will exist. The beam tip deflections are then parameterized using a different parameterization from previous models, which renders the deflection paths easier to model with a single degree of freedom system. Optimization is used to find the pseudo rigid body model which best approximates the beam deflection and stiffness. This model, combined with those models developed for other loading conditions, may be used to efficiently analyze compliant mechansims subjected to any loading condition.

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Wang, Wei Dong, Xiang Ji, and Xiang Yu Niu. "Research on Dynamic Coupling Characteristics of Electrostatic Actuated Micro Beam Considering Gas Film Damping." Advanced Materials Research 411 (November 2011): 437–41. http://dx.doi.org/10.4028/www.scientific.net/amr.411.437.

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It has been proved by large number of experiments that gas film damping has great influence on MEMS structures. Based on the elastic and material mechanics, this paper built a linear-vibration model for the electrostatic actuated micro-beam. According to the rarefied gas dynamics theory, a kind of modified Reynolds equation is adopted in the system modeling. In view of the study on small deflection of micro-beam has been investigated already by many researchers, this paper focus the research on large beam deflections, i.e. the mid-point deflection can be compared with the thickness of the gas film. The dynamic characteristics of micro-beam are investigated through coupling the dynamic vibration equation with the modified Reynolds equation. Through the finite difference method, the discrete form of the coupled dynamic equations has been obtained.

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Davoodinik, A. R., and G. H. Rahimi. "Large deflection of flexible tapered functionally graded beam." Acta Mechanica Sinica 27, no. 5 (September 27, 2011): 767–77. http://dx.doi.org/10.1007/s10409-011-0476-2.

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Pomraning, G. C. "Large deflection beam transport with screened Rutherford scattering." Progress in Nuclear Energy 34, no. 4 (January 1999): 377–86. http://dx.doi.org/10.1016/s0149-1970(98)00018-3.

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Pomraning, G. C., and A. K. Prinja. "A large deflection Fermi–Eyges pencil beam formula." Annals of Nuclear Energy 26, no. 7 (May 1999): 595–609. http://dx.doi.org/10.1016/s0306-4549(98)00076-0.

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Guo, Chao, Jing Zhang, Jun Zhang, Wenjun Ge, Bo Yao, and Feng Lin. "Scanning system development and digital beam control method for electron beam selective melting." Rapid Prototyping Journal 21, no. 3 (April 20, 2015): 313–21. http://dx.doi.org/10.1108/rpj-11-2012-0106.

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Purpose – The purpose of this paper is to correct the beam deflection errors and beam defocus by using a digital scanning system. Electron beam selective melting (EBSM) is an additive manufacturing technology for metal parts. Beam deflection errors and beam defocus at large deflection angles would greatly influence the accuracy of the built parts. Design/methodology/approach – The 200 × 200 mm2 scanning area of the electron beam is discretized into 1001 × 1001 points arranged in array, based on which a digital scanning system is developed. To correct the deflection errors, the electron beam scans a 41 × 41 testing grid, and the corrective algorithm is based on the bilinear transformation from the grid points’ nominal coordinates to their measured coordinates. The beam defocus is corrected by a dynamic focusing method. A three-dimensional testing part is built with and without using the corrective algorithm, and their accuracies are quantitatively compared. Findings – The testing grid scanning result shows that the accuracy of the corrected beam deflection system is better than ± 0.2 mm and beam defocus at large deflection angles is eliminated visibly. The testing part built with using the corrective algorithm is of greater accuracy than the one built without using it. Originality/value – Benefiting from the digital beam control method, the model-to-part accuracy of the system is effectively improved. The digital scanning system is feasible in rapid manufacturing large and complex three-dimensional metal parts.

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Xiang, Xin Mei, and Guo Xing Lu. "Dynamic Deflection of a Beam on Metal Foam." Key Engineering Materials 535-536 (January 2013): 481–84. http://dx.doi.org/10.4028/www.scientific.net/kem.535-536.481.

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An analytic model is developed to obtain the dynamic response of beams with initial velocities of the upper beam which is clamped at both ends and fully supported by metal foam, as a representative arrangement for protective structures. In large deflection, plastic bending and stretching in deforming regions are considered and the membrane factor method is introduced in the model to take into account the effect of axial force in the yielding. The relationships between the final displacement of the center in the beam and the dimensionless parameters are obtained. This model can predict the dynamic effects of different initial velocities and beams with different lengths, thickness and yield strength of cores.

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Ghane, M., T. Ghahraman, M. Sheikhzadeh, and A. M. Halabian. "Determination of the Bending Modulus for Fabrics Using Simply Supported Beam Systems." Research Journal of Textile and Apparel 15, no. 3 (August 1, 2011): 131–38. http://dx.doi.org/10.1108/rjta-15-03-2011-b015.

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A fabric can be modeled as an elastic beam supported by simple supports subjected to its own weight. The maximum deflection in the middle can be measured accurately. Different types of fabrics are tested and the bending modulus of the fabrics is then calculated in both small and large deflection cases. In the case of large deflection, the finite element method is used to solve the governing differential equation. The difference between the values of the bending modulus obtained from the small and large deflection cases increases as the length of the bent fabric is increased. The reason is less accuracy of the small deflection equations in longer lengths of the beam. However, the results reveal that even in the longest length of the tested beam (fabric), the differences between the values of the bending modulus from small and large deflection cases are in an acceptable range. It can be concluded that the case of the small deflection can be used to calculate the bending modulus of the fabrics in a simply supported beam method with an acceptable accuracy.

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Panza, Michael J. "Mathematical Model for Large Deflection Dynamics of a Compliant Beam Device." Journal of Dynamic Systems, Measurement, and Control 123, no. 2 (September 29, 1999): 283–88. http://dx.doi.org/10.1115/1.1367266.

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A mathematical model for the large deflection dynamics of a compliant beam device is presented. The device simulates the motion of a slider-crank device. The system contains a highly flexible beam that provides the compliant motion from a sliding mass at one end to a rotating hinge point at the other end. Basic models for friction and beam dissipation effects are included. A nonlinear integro-partial differential equation is derived for the complete beam/mass system in the curved space of the deformed beam. The resulting equation is cast into a generalized nondimensional form suitable for studying system behavior for a broad range of system sizes. The dynamic equation is solved in curved space by applying a spatial solution that closely represents the large static deflection measured for the beam. The nonlinear system dynamics are simulated for an initial large deflection of the system and compared to experimental results for an actual physical system.

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Wang, Zhao Qing, Jian Jiang, Bing Tao Tang, and Wei Zheng. "High Precision Numerical Analysis of Nonlinear Beam Bending Problems under Large Deflection." Applied Mechanics and Materials 638-640 (September 2014): 1705–9. http://dx.doi.org/10.4028/www.scientific.net/amm.638-640.1705.

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The high precision numerical method for solving nonlinear bending problems of large deflection beam is presented. The governing equation of large deflection beam is a strongly nonlinear ordinary differential equation. Using the solution of linear bending beam as an initial guess function, the nonlinear bending equation of beam can be transferred into a linear differential equation. The improvement solution of nonlinear bending beam is obtained by solving the linearized bending equation using barycentric interpolation collocation method. Then, the solution of nonlinear bending beam can be given by iterative method. Some examples demonstrate the validity and computational accuracy of proposed method.

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Torres, David, Sarah Dooley, and LaVern A. Starman. "Large Out-of-Plane Deflection MEMS Actuators for Optical Applications." Proceedings 2, no. 13 (November 30, 2018): 1072. http://dx.doi.org/10.3390/proceedings2131072.

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The design and fabrication of an electrothermal MEMS actuation structure which is capable of producing large out-of-plane deflection is presented. The actuators are used to move a 1 mm2 mirror structure, where the large deflection allows one to achieve large beam steering angles. The electrothermal actuators are designed to operate via joule heating with a monolithically integrated heater. The proposed design was analyzed using finite element method simulation software (COMSOL 5.3a), to determine the thickness of each material layer, the initial out-of-plane upward deflections, the configuration of the heating element to achieve the desired actuation deformations, and the overall steady-state temperature distribution through the actuation structure due to Joule heating. Finally, the actuation assemblies were fabricated, released, tested and compared with our simulation results.

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Zhang, Jian Xun, Qing Hua Qin, Wei Long Ai, Zheng Jin Wang, and Tie Jun Wang. "Large Deflection of a Pin-Supported Slender Geometrically Asymmetric Sandwich Beam under Transverse Loading." Key Engineering Materials 535-536 (January 2013): 405–8. http://dx.doi.org/10.4028/www.scientific.net/kem.535-536.405.

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The objective of this work is to study the large deflection of a pin-supported slender geometrically asymmetric metal foam core sandwich beam under transverse loading by a flat punch. Based on the yield criterion for geometrically asymmetric metal foam core sandwich structure, analytical solution for the large deflection of a pin-supported slender sandwich beam is obtained, in which the interaction of bending and stretching induced by large deflection is considered. The finite element results confirm the accuracy of the analytical solutions. The effects of asymmetric factor and boundary condition on the structural response of the asymmetric sandwich beam are discussed in detail. It is shown that the axial stretching induced by large deflection plays an important role in the load-carrying and energy absorption capacities of geometrically asymmetric sandwich structure.

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Bui Thi Thu, Hoai. "LARGE DEFLECTION OF CANTILEVER FUNCTIONALLY GRADED SANDWICH BEAM UNDER END FORCES BASED ON A TOTAL LAGRANGE FORMULATION." Vietnam Journal of Science and Technology 57, no. 6A (March 20, 2020): 32. http://dx.doi.org/10.15625/2525-2518/57/4a/14008.

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A two-node beam element for large deflection analysis of cantilever functionally graded sandwich (FGSW) beams subjected to end forces is formulated in the context of total Lagrange formulation. The beams consist of three layers, a homogeneous core and two functionally graded layers with material properties varying in the thickness direction by a power gradation law. Linear functions are adopted to interpolate the displacement field and reduced integral technique is applied to evaluate the element formulation. Newton-Raphson based iterative algorithm is employed in combination with arc-length control method to compute equilibrium paths of the beams. Numerical investigations are given for the beam under a transverse point load and a moment to show the accuracy of the element and to illustrate the effects of material inhomogeneity and the layer thickness ratio on the large deflection behavior of the FGSW beams.

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Bui Thi Thu, Hoai. "LARGE DEFLECTION OF CANTILEVER FUNCTIONALLY GRADED SANDWICH BEAM UNDER END FORCES BASED ON A TOTAL LAGRANGE FORMULATION." Vietnam Journal of Science and Technology 57, no. 6A (March 25, 2020): 32. http://dx.doi.org/10.15625/2525-2518/57/6a/14008.

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A two-node beam element for large deflection analysis of cantilever functionally graded sandwich (FGSW) beams subjected to end forces is formulated in the context of total Lagrange formulation. The beams consist of three layers, a homogeneous core and two functionally graded layers with material properties varying in the thickness direction by a power gradation law. Linear functions are adopted to interpolate the displacement field and reduced integral technique is applied to evaluate the element formulation. Newton-Raphson based iterative algorithm is employed in combination with arc-length control method to compute equilibrium paths of the beams. Numerical investigations are given for the beam under a transverse point load and a moment to show the accuracy of the element and to illustrate the effects of material inhomogeneity and the layer thickness ratio on the large deflection behavior of the FGSW beams.

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Nicholson, D. W. "Large Deformation Analysis of an Elastic-Plastic Cantilevered Beam." Journal of Pressure Vessel Technology 111, no. 3 (August 1, 1989): 312–15. http://dx.doi.org/10.1115/1.3265680.

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This study concerns the analysis of the deflection of an elastic-plastic cantilevered beam. Three regions of solution are treated: (i) purely elastic response at low loads; (ii) elastic-plastic response without a hinge, for intermediate loads; and (iii) elastic-plastic response with a hinge for loads corresponding to the fully plastic bending moment at the built-in end. Most existing solutions for this type of problem involve various approximations avoided here, for example, ignoring the elastic part of the strain or using upper bounds based on limit analysis. By avoiding such approximations, the solution given here may be useful as a benchmark for validating finite element codes in the large deformation elastic-plastic regime. Several aspects of the solution are analyzed: (i) the load-deflection relation; (ii) the growth of the elastic-plastic zone; (iii) limiting cases; (iv) the residual configuration; (v) the small bending configuration. A numerical procedure based on Runge-Kutta methods is used, leading to the load-deflection relation in graphical form.

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Seveno, Raynald, Benoit Guiffard, and Jean-Pierre Regoin. "Ultra large deflection of thin PZT/aluminium cantilever beam." Functional Materials Letters 08, no. 05 (September 29, 2015): 1550051. http://dx.doi.org/10.1142/s1793604715500514.

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Flexible piezoelectric cantilever beam has been realized by depositing lead zirconate titanate (PZT) thin film (4.5 μm) by chemical solution deposition (CSD) onto very thin aluminium foil (16 μm). The tip deflection of the beam has been measured as a function of the frequency of the applied sinusoidal voltage to the PZT film for different amplitudes. Resonance curves have been compared to a classical model of an oscillating system under sinusoidal stress with a very good agreement. Despite of weak ferroelectric properties (remnant polarization: 13 μC/cm2), ultra-large deflection amplitudes have been measured under very moderate applied voltage values: 750 μm@10 V for quasi-static mode and 5 mm@10 V at the resonance frequency (~12 Hz), which makes this PZT/aluminium composite film very promising for highly flexible actuation applications where large displacements are wanted.

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31

Singhal, D., and V. Narayanamurthy. "Large and Small Deflection Analysis of a Cantilever Beam." Journal of The Institution of Engineers (India): Series A 100, no. 1 (November 13, 2018): 83–96. http://dx.doi.org/10.1007/s40030-018-0342-3.

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Zhou, Yi Qing, Zhi Fang Liu, and Shan Yuan Zhang. "Solitary Waves and Chaotic Behavior in Large-Deflection Beam." Applied Mechanics and Materials 29-32 (August 2010): 28–34. http://dx.doi.org/10.4028/www.scientific.net/amm.29-32.28.

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The motion equation of nonlinear flexural wave in large-deflection beam is derived from Hamilton's variational principle using the coupling of flexural deformation and midplane stretching as key source of nonlinearity and taking into account transverse, axial and rotary inertia effects. The system has homoclinic or heteroclinic orbit under certain conditions, the exact periodic solutions of nonlinear wave equation are obtained by means of Jacobi elliptic function expansion. The solitary wave solution and shock wave solution is given when the modulus of Jacobi elliptic function in the degenerate case. It is easily thought that the introduction of damping and external load can result in break of homoclinic (or heteroclinic) orbit and appearance of transverse homoclinic point. The threshold condition of the existence of transverse homoclinic point is given by help of Melnikov function. It shows that the system has chaos property under Smale horseshoe meaning.

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33

Yu, Bao Chu, and Gong Dong Wang. "The Analysis of the Composite Beam in the Earthquake Response by the Finite Element." Advanced Materials Research 1049-1050 (October 2014): 342–45. http://dx.doi.org/10.4028/www.scientific.net/amr.1049-1050.342.

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By large-scale finite element software ANSYS, the seismic response of large span steel - concrete composite beams were analyzed, to get the change rule of the deflection and stress of the design. And analysis of the extension of design parameters for influence factors, such as concrete grade, reinforcement ratio, the height of steel beam, is to get their effect of the seismic responses of the composite beam deflection and stress, and provide powerful basis for optimal design of composite beams. For the model in the interface by setting the three direction spring element to simulate the interface slip and vertical uplift, and choosing three directions of EI Centro seismic wave including relatively rich spectrum as input, the result of analysis is relatively accurate.

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34

Sherbourne, A. N., and F. Lu. "DEFLECTION OF A FLEXURAL CANTILEVER BEAM." Transactions of the Canadian Society for Mechanical Engineering 17, no. 1 (March 1993): 29–43. http://dx.doi.org/10.1139/tcsme-1993-0003.

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The behaviour of a flexural elasto-plastic cantilever beam is investigated in which geometric nonlinearities are considered. The result of an elastica analysis by Frisch-Fay [1] is extended to include post-yield behaviour. Although a closed-form solution is not possible, as in the elastic case, simple algebraic equations are derived involving only one unknown variable, which can also be expressed in the standard form of elliptic integrals if so desired. The results, in comparison with those of the small deflection analyses, indicate that large deflection analyses are necessary when the relative depth of the beam is very small over the length. The present exact solution can be used as a reference by those who resort to a finite element method for more complicated problems. It can also serve as a building block to other beam problems such as a simply supported beam or a beam with multiple loads.

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CHENG, Hong, Hong-tao LI, Yan-jun HAN, Chang-zheng SUN, Zhi-biao HAO, Bing XIONG, Lai WANG, Jian WANG, and Jia-dong YU. "Near-infrared beam deflector with broadband and large deflection angle based on dielectric metasurface." Optics and Precision Engineering 28, no. 9 (2020): 1873–80. http://dx.doi.org/10.37188/ope.20202809.1873.

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36

Shi, Qi Yin, Chun Zhao, Chun Wang, and Qing Li. "Finite Element Analysis on the Crack Width and Deflection of a Local Corroded Reinforced Concrete Beam." Advanced Materials Research 663 (February 2013): 219–24. http://dx.doi.org/10.4028/www.scientific.net/amr.663.219.

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In this paper, the crack width and deflection of a local corroded reinforced concrete beam is investigated. The influence of the rebar corrosion on a concrete beam is analyzed first. Based on the constitutive relationship of the corroded reinforced concrete, the corroded reinforced concrete is regarded as a bond-slip composite beam which is comprised of corroded rebar and concrete. By using the large-scale finite element software ANSYS, a separate reinforced concrete beam model is developed after selecting the reasonable element. By using the proposed model, the positions of the cracks are determined. Moreover, the cracks width and the deflection of the beam at the corroded segment are calculated through using formula and extracting the results data from ANSYS. At last, the results by the standard design of concrete structures (GB50010-2010) and EN1992-1-1:2004[1] are compared through the list, which show the crack width and deflection of the local corroded reinforced concrete beams calculated by ANSYS is feasible.

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37

Soleimani, Ali. "Large Deflection of Various Functionally Graded Beam Using Shooting Method." Applied Mechanics and Materials 110-116 (October 2011): 4705–11. http://dx.doi.org/10.4028/www.scientific.net/amm.110-116.4705.

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The equation of large deflection of functionally graded beam subjected to arbitrary loading condition is derived. In this work assumed that the elastic modulus varies by exponential and power function in longitudinal direction. The nonlinear derived equation has not exact solution so shooting method has been proposed to solve the nonlinear equation of large deflection. Results are validated with finite element solutions. The method will be useful toward the design of compliant mechanisms driven by smart actuators. Finally the effect of different elastic modulus functions and loading conditions are investigated and discussed.

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Xiao, Yi. "Large Deflection of Tip Loaded Beam with Differential Transformation Method." Advanced Materials Research 250-253 (May 2011): 1232–35. http://dx.doi.org/10.4028/www.scientific.net/amr.250-253.1232.

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This paper deals with large deflection problem of a cantilever beam with a constant section under the action of a transverse tip load. The differential transformation method (DTM) is used to solve the nonlinear differential equation governing the problem. An approach treats trigonometric nonlinearity is used in DTM. The results obtained from DTM are compared with those results obtained by the finite difference method and they agree well.

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Miyazaki, Yoko, and Hiroshi Furuya. "Two-Dimensional Large Deflection Analysis of Beam with Initial Shape." JOURNAL OF THE JAPAN SOCIETY FOR AERONAUTICAL AND SPACE SCIENCES 53, no. 618 (2005): 308–15. http://dx.doi.org/10.2322/jjsass.53.308.

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Borboni, Alberto, Diego De Santis, Luigi Solazzi, Jorge Hugo Villafañe, and Rodolfo Faglia. "Ludwick Cantilever Beam in Large Deflection Under Vertical Constant Load." Open Mechanical Engineering Journal 10, no. 1 (March 28, 2016): 23–37. http://dx.doi.org/10.2174/1874129001610010023.

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41

Borboni, Alberto, Diego De Santis, Luigi Solazzi, Jorge Hugo Villafañe, and Rodolfo Faglia. "Ludwick Cantilever Beam in Large Deflection Under Vertical Constant Load." Open Mechanical Engineering Journal 10, no. 1 (March 28, 2016): 23–37. http://dx.doi.org/10.2174/1874155x01610010023.

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The aim of this paper is to calculate the horizontal and vertical displacements of a cantilever beam in large deflections. The proposed structure is composed with Ludwick material exhibiting a different behavior to tensile and compressive actions. The geometry of the cross-section is constant and rectangular, while the external action is a vertical constant load applied at the free end. The problem is nonlinear due to the constitutive model and to the large deflections. The associated computational problem is related to the solution of a set of equation in conjunction with an ODE. An approximated approach is proposed here based on the application Newton-Raphson approach on a custom mesh and in cascade with an Eulerian method for the differential equation.

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42

Cornil, Marie-Blanche, Laurent Capolungo, Jianmin Qu, and Vivek A. Jairazbhoy. "Free vibration of a beam subjected to large static deflection." Journal of Sound and Vibration 303, no. 3-5 (June 2007): 723–40. http://dx.doi.org/10.1016/j.jsv.2007.02.016.

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Nallathambi, Ashok Kumar, C. Lakshmana Rao, and Sivakumar M. Srinivasan. "Large deflection of constant curvature cantilever beam under follower load." International Journal of Mechanical Sciences 52, no. 3 (March 2010): 440–45. http://dx.doi.org/10.1016/j.ijmecsci.2009.11.004.

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44

Lim, In-Gyu, and In Lee. "Aeroelastic Analysis of Bearingless Rotors Using Large Deflection Beam Theory." AIAA Journal 45, no. 3 (March 2007): 599–606. http://dx.doi.org/10.2514/1.26635.

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45

Al-Manaseer, A. A., and K. W. Nasser. "Analysis of beams with large openings using nonlinear finite element procedure." Canadian Journal of Civil Engineering 14, no. 3 (June 1, 1987): 302–7. http://dx.doi.org/10.1139/l87-048.

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The object of this paper was to use a nonlinear plane stress finite element procedure to predict the behaviour of simply supported reinforced concrete beams with a large opening, under mid-span static loading. In the finite element analysis, parabolic isoparametric elements were used in conjunction with the discrete bar formulation. A smeared cracking approach was included and concrete under different states of stress was modelled by using individual models that were incorporated to represent a biaxial state of stress. Reinforcing steel was modelled by using a uniaxial elastoplastic strain-hardening curve. Test results showed that the above approach was found to be satisfactory in predicting the load–deflection curves, crack patterns, and ultimate loads for this type of beam. Key words: beams, cracking, endochronic theory, finite element method, load deflection, nonlinear analysis, openings, reinforced concrete, ultimate load.

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Xu, Xin Sheng, Hong Da Zhang, and Xiao Da Xu. "Characteristics and Influencing Factors of Deflection in Concrete Beams Reinforced with FRP Bars." Applied Mechanics and Materials 166-169 (May 2012): 1818–23. http://dx.doi.org/10.4028/www.scientific.net/amm.166-169.1818.

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The low modulus of elasticity of the FRP bars and their non-yielding characteristics results in large deflection and wide cracks in concrete beams reinforced with FRP bars. Consequently, in many cases, serviceability requirements may govern the design of such members. Based on the experiment studies of 5 beams of 2 groups under vertical loads at three-dividing point, the characteristics of FRP reinforced concrete beams was researched. At the same time, the experimental beams are modeled and the influencing factors of deflection of FRP bars concrete beam are analyzed using ANSYS program.

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Chiang, An-Chung, Yuan-Yao Lin, Shou-Tai Lin, and Yen-Yin Lin. "A Broadband High-Diffraction-Efficiency Electro-Optic Bragg Deflector Based on Monolithic Dual-Grating Periodically-Poled Lithium Niobate." Photonics 8, no. 7 (June 28, 2021): 242. http://dx.doi.org/10.3390/photonics8070242.

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Electro-optic (EO) Bragg deflectors have been extensively used in a variety of applications. Recent developments show that bandwidths and deflection efficiencies, as well as angular bandwidths, would significantly limit the utilization of EO Bragg deflectors, especially for applications which need strong focusing, such as intra-cavity applications. In this paper, we introduce a broadband EO Bragg deflector based on periodically-poled lithium niobate with a monolithic dual-grating design. We analyzed the deflection properties of this device by using a modified coupled wave theory and showed that this device can be still efficient for a small beam radius under strong focusing, whereas a single-grating one becomes very inefficient. Using a 1064-nm laser beam with a 100-μm beam radius, we obtained a 74% deflection efficiency with a 190-V bias voltage with a 0.5-mm-thick and 7.5-mm-long dual-grating sample. The acceptance angle for the Bragg condition of this device is as large as a few tens of mrad. The potential bandwidth of this device exceeds 500 nm if the proper operation region is chosen.

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Tuan Ya, T. M. Y. S., Reza Alebrahim, Nadziim Fitri, and Mahdi Alebrahim. "Analysis of Cantilever Beam Deflection under Uniformly Distributed Load using Artificial Neural Networks." MATEC Web of Conferences 255 (2019): 06004. http://dx.doi.org/10.1051/matecconf/201925506004.

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In this study the deflection of a cantilever beam was simulated under the action of uniformly distributed load. The large deflection of the cantilever beam causes the non-linear behavior of beam. The prupose of this study is to predict the deflection of a cantilever beam using Artificial Neural Networks (ANN). The simulation of the deflection was carried out in MATLAB by using 2-D Finite Element Method (FEM) to collect the training data for the ANN. The predicted data was then verified again through a non linear 2-D geometry problem solver, FEM. Loads in different magnitudes were applied and the non-linear behaviour of the beam was then recorded. It was observed that, there is a close agreement between the predicted data from ANN and the results simulated in the FEM.

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Li, Chong, Hui-Shen Shen, and Hai Wang. "Nonlinear Vibration of Sandwich Beams with Functionally Graded Negative Poisson’s Ratio Honeycomb Core." International Journal of Structural Stability and Dynamics 19, no. 03 (March 2019): 1950034. http://dx.doi.org/10.1142/s0219455419500342.

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This paper investigates the nonlinear flexural vibration of sandwich beams with functionally graded (FG) negative Poisson’s ratio (NPR) honeycomb core in thermal environments. The novel constructions of sandwich beams with three FG configurations of re-entrant honeycomb cores through the beam thickness direction are proposed. The temperature-dependent material properties of both face sheets and core of the sandwich beams are considered. 3D full-scale finite element analyses are conducted to investigate the nonlinear vibration, and the variation of effective Poisson’s ratio (EPR) of the sandwich beams in the large deflection region. Numerical simulations are carried out for the sandwich beam with FG-NPR honeycomb core in different thermal environmental conditions, from which results for the same sandwich beam with uniform distributed NPR honeycomb core are obtained as a basis for comparison. The effects of FG configurations, temperature changes, boundary conditions, and facesheet-to-core thickness ratios on the nonlinear vibration ratio curves and EPR–deflection curves of sandwich beams are discussed in detail.

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Qin, Qing Hua, and Tie Jun Wang. "Analytical Solution for the Large Deflection of Fully Clamped Metallic Foam Sandwich Beam." Advanced Materials Research 33-37 (March 2008): 559–66. http://dx.doi.org/10.4028/www.scientific.net/amr.33-37.559.

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A unified yield criterion is proposed in this paper, which is valid for the metallic sandwich sections with various core strength and geometrical dimensions and can reduce to the classical yield criteria for solid monolithic section and sandwich section with weak core, respectively. Then, the unified yield criterion is used to derive the analytical solution for the large deflection of fully clamped metallic sandwich beam subject to a transversely concentrated load, in which the interaction of bending and stretching is considered. Comparisons of the present solutions with experimental results are carried out and good agreements are found. It is seen that the axial stretching induced by large deflection has a significant effect on the deflection of sandwich structure in the post-yield regime, and the load carrying capacity of metallic foam core sandwich beam may be underestimated as the core strength is neglected in analysis.

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Journal articles on the topic 'Large beam deflection'

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