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Journal articles on the topic 'Large Deflection of a Cantilever Beam'

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Published: 4 June 2021
Last updated: 15 February 2022

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1

Chen, Li Wen, Chia Yen Lee, Chien Hsiung Tsai, and Yung Chuan Chen. "Thermal Contact Residual Stress Analysis of Elastic-Plastic Bilayer Micro-Cantilevers with Platinum Electrodes." Materials Science Forum 505-507 (January 2006): 559–64. http://dx.doi.org/10.4028/www.scientific.net/msf.505-507.559.

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This paper studies the residual stress distributions and tip deflections of microfabricated bilayer cantilevers of varying beam thickness and platinum electrode length. The bilayer cantilevers discussed here are composed of low-stress silicon nitride films deposited on silicon beams. Platinum electrodes are deposited and patterned on the low-stress silicon nitride layers. A thermal elastic-plastic finite element model is utilized to calculate the residual stress distribution across the cantilever cross-section and to determine the cantilever tip deflection following heat treatment. A contact model is introduced to simulate the influence of contact on the residual stress distribution. The influences of the beam thickness and the platinum electrode length on the residual stress distribution and tip deflections are thoroughly investigated. The numerical results indicate that a smaller beam thickness leads to a larger compressive residual stress within the platinum electrode and delivers a larger tip deflection. The results also indicate that a larger platinum electrode length delivers a smaller tip deflection.
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2

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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3

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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4

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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5

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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6

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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7

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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8

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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9

Fallahpasand, Sam, and Morteza Dardel. "Piezoelectric energy harvesting from highly flexible cantilever beam." Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics 233, no. 1 (July 30, 2018): 71–92. http://dx.doi.org/10.1177/1464419318791104.

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In many studies, linear or small deflections according to Von Karman strain model are used for energy harvesting of beam’s structures. Analyses of these types are not reliable when deformations become large. In this work, an integro-differential equation of highly flexible cantilever beam with a piezoelectric layer is presented. The harvester is composed of a thin flexible beam with attached piezoceramic which undergoes large deformations. Periodic and chaotic oscillations and their effects on the quality of harvesting energy procedure are investigated. The obtained results showed that chaotic oscillations improve energy harvesting. This means that large deflections in high-flexible electromechanical systems let harvester to gather more energy from the external source in a much wider frequency domain. Fast Fourier transform shows the emerging lots of resonance peaks in the chaotic region, which give cascade of resonances for this highly nonlinear beam. Moreover, it is discussed how this mechanism and its frequency characteristics enhances the quality and quantity of energy harvesting. The present study show how increasing the flexibility of structure can lead to high deflection and obtaining broadband energy harvesting with better energy harvesting characteristics.
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10

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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11

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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12

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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13

Abu-Alshaikh, Ibrahim, Hashem S. Alkhaldi, and Nabil Beithou. "Large Deflection of Prismatic Cantilever Beam Exposed to Combination of End Inclined Force and Tip Moment." Modern Applied Science 12, no. 1 (December 27, 2017): 98. http://dx.doi.org/10.5539/mas.v12n1p98.

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The large deflection of a prismatic Euler-Bernoulli cantilever beam under a combination of end-concentrated coplanar inclined force and tip-concentrated moment is investigated. The angle of inclination of the applied force with respect to the horizontal axis remains unchanged during deformation. The cantilever beam is assumed to be naturally straight, slender, inextensible and elastic. The large deflection of the cantilever beam induces geometrical nonlinearity; hence, the nonlinear theory of bending and the exact expression of curvature are used. Based on an elliptic integral formulation, an accurate numerical solution is obtained in terms of an integration constant that should satisfy the boundary conditions associated with the cantilever beam. For some special cases this integration constant is exactly found, which leads to closed form solution. The numerical solution obtained is quite simple, accurate and involves less computational time compared with other techniques available in literature. The details of elastica and its corresponding orientation curves are presented and analyzed for extremely large load combinations. A comparative study with pre-obtained results has been made to verify the accuracy of the presented solution; an excellent agreement has been obtained.
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14

Xiao, Yi. "Large Deflection of Cantilever Beam with Uniformly Distributed Load Using Homotopy Analysis Method." Advanced Materials Research 250-253 (May 2011): 1222–25. http://dx.doi.org/10.4028/www.scientific.net/amr.250-253.1222.

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The large deflection behavior of prismatic cantilever beams subjected to uniformly distributed load is investigated. An approximate analytical solution is obtained using the homotopy analysis method (HAM). The solution is validated by the nonlinear shooting method. This reveals that the solution is accurate, efficient and convenient for cantilever beams with uniformly distributed loads.
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15

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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16

Santos, Erivelton, and Hanz Richter. "Design and Analysis of Novel Actuation Mechanism with Controllable Stiffness." Actuators 8, no. 1 (February 9, 2019): 12. http://dx.doi.org/10.3390/act8010012.

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Actuators intended for human–machine interaction systems are usually designed to be mechanically compliant. Conventional actuators are not suitable for this purpose due to typically high stiffness. Advanced powered prosthetic and orthotic devices can vary their stiffness during a motion cycle and are power-efficient. This paper proposes a novel actuator design that modulates stiffness by means of a flexible beam. A motorized drive system varies the active length of the cantilever beam, thus achieving stiffness modulation. New large deflection formulation for cantilever beams with rolling contact constraints is used to determine the moment produced by the actuator. To validate the proposed solution method, an experiment was performed to measure large static deformations of a cantilever beam with the same boundary conditions as in the actuator design. The experiments indicate excellent agreement between measured and calculated contact forces between beam and roller, from which the actuator moment is determined.
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17

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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18

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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19

Abu-Alshaikh, Ibrahim Mousa. "Closed-Form Solution of Large Deflected Cantilever Beam a gainst Follower Loading Using Complex Analysis." Modern Applied Science 11, no. 12 (November 20, 2017): 12. http://dx.doi.org/10.5539/mas.v11n12p12.

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The literature reveals that the non-conservative deflection of an elastic cantilever beam caused by applying follower tip loading was investigated and solved by various numerical methods like: Runge Kutta, iterative shooting, finite element, finite difference, direct iterative and non-iterative numerical methods. This is due to the fact that the Euler–Bernoulli nonlinear differential equation governing the problem contains the “slope at the free end”, this slope however needs special numerical treatment. On the other hand, some of these methods fail to find numerical solutions for extremely large loading conditions. Hence, this paper is aimed to obtain a closed-form solution for solving the large deflection of a cantilever beam opposed to a concentrated point follower load at its free end. This closed-form solution when compared with other conventional numerical approaches is characterized by simplicity, stability and straightforwardness in getting the beam deflection and slopes even for extremely large loading conditions. The closed-form solution is obtained by applying complex analysis along with elliptic-integral approach. Very good results were obtained when the elastica of the beam compared with that of various numerical methods which are used in analyzing similar problem.
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20

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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21

Peng, Xiao Tao, Yi Xiong, Yong Wu, and Dan Meng. "The Alignment Control of Large-Span Continuous Beam Bridge Cantilever Construction Method." Applied Mechanics and Materials 351-352 (August 2013): 1226–30. http://dx.doi.org/10.4028/www.scientific.net/amm.351-352.1226.

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One long-span bridge adopted the cantilever casting method, which is pre-stressed concrete variable cross-section continuous box girder structure. In the construction process, due to the concrete pouring, hanging basket moving, construction loads, pre-stressed tension, concrete shrinkage and creep, temperature, humidity and many other factors. There will be such problems of cantilever beam segment closed error and the bridge line-type do not coincide in design goals. In this paper, we use the bridge dedicated finite element program MIDAS / Civil procedural for modeling and structural analysis. Analyze the problems of deflection control and pre-camber adjustment of cantilever construction, in order to ensure that the bridge closure smoothly in accordance with the design standards.
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22

Chen, Ming. "Large Deflection of a Cantilever Nanobeam under a Vertical End Load." Applied Mechanics and Materials 353-356 (August 2013): 3387–90. http://dx.doi.org/10.4028/www.scientific.net/amm.353-356.3387.

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Large deflection of a cantilever nanobeam subjected to a tip-concentrated load whose verticality to the deformed axis of the beam is assumed as constant. Governing equation is analyzed by using the shearing force formulation instead of the bending moment formulation because in the case of large deflection member, the shearing force formulation possesses some computational advantages over the bending moment formulation. The condition of boundary is discussed by several ways. The different sizes of loads and time scales are used to analyze the deformation and the different by molecular dynamics.
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23

Nageswara Rao, B., and G. Venkateswara Rao. "Large deflections of a spring-hinged tapered cantilever beam with a rotational distributed loading." Aeronautical Journal 91, no. 909 (November 1987): 429–37. http://dx.doi.org/10.1017/s0001924000021667.

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SummaryLarge deflection problem of a spring loaded hinged nonuniform cantilever beam subjected to a rotational distributed loading is formulated by means of a second-order non-linear integro-differential equation. The problem is examined by considering the beam of rectangular cross-section with linear depth taper subjected to a uniform rotational distributed load. The elastic curves of a beam for this special case are presented.
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24

HORIBE, Tadashi, Ryou FUJIKAWA, and Kotaro MORI. "206 Large Deflection of Tapered Cylindrical Cantilever Beams." Proceedings of Ibaraki District Conference 2015.23 (2015): 107–8. http://dx.doi.org/10.1299/jsmeibaraki.2015.23.107.

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25

Chen, Li. "An integral approach for large deflection cantilever beams." International Journal of Non-Linear Mechanics 45, no. 3 (April 2010): 301–5. http://dx.doi.org/10.1016/j.ijnonlinmec.2009.12.004.

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26

OHTSUKI, Atsumi, and Tohru TSURUMI. "Analysis of Large Deflection in a Cantilever Beam with Low Support Stiffness." Transactions of the Japan Society of Mechanical Engineers Series A 62, no. 594 (1996): 493–99. http://dx.doi.org/10.1299/kikaia.62.493.

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27

Kimiaeifar, A., N. Tolou, A. Barari, and J. L. Herder. "Large deflection analysis of cantilever beam under end point and distributed loads." Journal of the Chinese Institute of Engineers 37, no. 4 (August 2013): 438–45. http://dx.doi.org/10.1080/02533839.2013.814991.

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28

Li, Xiang Fang, and Bao Lin Wang. "Bending and Fracture Properties of Small Scale Elastic Beams – A Nonlocal Analysis." Applied Mechanics and Materials 152-154 (January 2012): 1417–26. http://dx.doi.org/10.4028/www.scientific.net/amm.152-154.1417.

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Using the nonlocal elasticity theory, this paper presents a static analysis of a microbeam according to the Timoshenko beam model. A fourth-order governing differential equation is derived and a general solution is suggested. For a cantilever beam at nanoscale subjected to uniform distributed loading, explicit expressions for deflection, rotation and strain energy are obtained. The nonlocal effect decreases the deflection and maximum stress distribution. With a double cantilever beam model, the strain energy release rate of a cracked beam is evaluated, and the results obtained show that the strain energy release rate is decreased (hence an increased apparent fracture toughness is measured) when the beam thickness is several times the material characteristic length. However, in the absence of a uniformly distributed loading, the nonlocal beam theory fails to account for the size-dependent properties for static analysis. Particularly, the nonlocal Euler-Bernoulli beam can be analytically obtained from the nonlocal Timoshenko beam if the apparent shear modulus is sufficiently large.
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29

Chen, Yuhang, Maomao Zhang, Yaxuan Su, and Zhidong Zhou. "Coupling Analysis of Flexoelectric Effect on Functionally Graded Piezoelectric Cantilever Nanobeams." Micromachines 12, no. 6 (May 21, 2021): 595. http://dx.doi.org/10.3390/mi12060595.

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The flexoelectric effect has a significant influence on the electro-mechanical coupling of micro-nano devices. This paper studies the mechanical and electrical properties of functionally graded flexo-piezoelectric beams under different electrical boundary conditions. The generalized variational principle and Euler–Bernoulli beam theory are employed to deduce the governing equations and corresponding electro-mechanical boundary conditions of the beam model. The deflection and induced electric potential are given as analytical expressions for the functionally graded cantilever beam. The numerical results show that the flexoelectric effect, piezoelectric effect, and gradient distribution have considerable influences on the electro-mechanical performance of the functionally graded beams. Moreover, the nonuniform piezoelectricity and polarization direction will play a leading role in the induced electric potential at a large scale. The flexoelectric effect will dominate the induced electric potential as the beam thickness decreases. This work provides helpful guidance to resolve the application of flexoelectric and piezoelectric effects in functionally graded materials, especially on micro-nano devices.
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Beléndez, Tarsicio, Cristian Neipp, and Augusto Beléndez. "Large and small deflections of a cantilever beam." European Journal of Physics 23, no. 3 (May 1, 2002): 371–79. http://dx.doi.org/10.1088/0143-0807/23/3/317.

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31

Jialin, Yang, and Chen Zheng. "The large deflection plastic response of a cracked cantilever beam subjected to impact." Mechanics Research Communications 19, no. 5 (September 1992): 391–97. http://dx.doi.org/10.1016/0093-6413(92)90017-5.

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32

Xu, Meng Hua, and Bao Lin Wang. "Electromechanical Analysis of a Beam Piezoelectric Transducer Energy Harvest Device." Advanced Materials Research 415-417 (December 2011): 1114–20. http://dx.doi.org/10.4028/www.scientific.net/amr.415-417.1114.

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This paper considers the vibtation problem of beam piezoelectric transducer. Traditional reasearches face difficulties in providing the analytical expression for the piezoelectric effect of the piezoelectric vibrator with a mass at its end as well as the improper model of piezoelectric vibrators which work in high-frequency band. In this paper, the nature of the current output in a large frequency range is explored. Firstly, static analysis of cantilever is conducted and the piezoelectric effect under a certain deformation were formuled. Next, the main vibration modes of the cantilever were modified so that the main modes are of orthogonality in nature and satisfy the boundary conditions. The dynamic deflection of the piezoelectric cantilever was also investigated using the modified vibration modes. Charge outputs of piezoelectric cantilever beam are also demonstrated. Finally, based on the theoretical analysis, some numerical results are given.
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33

Liu, J. H., A. G. Atkins, and A. J. Pretlove. "The Effect of Inclined Loads on the Large Deflection Behaviour of Elastoplastic Work-Hardening Straight and Pre-Bent Cantilevers." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 209, no. 2 (March 1995): 87–96. http://dx.doi.org/10.1243/pime_proc_1995_209_128_02.

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A theoretical analysis is presented to examine the effect of inclined tip load on the large deflection behaviour of an elastoplastic cantilever with linear work hardening. The cantilever is either initially straight or pre-bent to a tip angle of ø (see Fig. 1). When the load is large enough, the overall deformation of a pre-bent cantilever is smaller than that of an initially straight one as a result of the influence of the guided end. The maximum plastic region spm in the cantilever increases with the force angle ø and the plastic-elastic modulus ratio α, but decreases as the beam flexibility parameter β increases. Some unstable deformation may occur in the initially straight cantilever when ø > π/2 and this depends on the value of α and β. Reasonable agreement is obtained between the theoretical analysis and experimental results.
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34

Mondal, Soumen, Sushanta Ghuku, and Kashi Nath Saha. "Effect of Clamping Torque on Large Deflection Static and Dynamic Response of a Cantilever Beam: An Experimental Study." International Journal of Engineering and Technologies 15 (November 2018): 1–16. http://dx.doi.org/10.18052/www.scipress.com/ijet.15.1.

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The present paper reports an experimental study on the effect of finite clamping on static and dynamic characteristics of cantilever beam. The experiment is carried out with two different beams, each of which is clamped at two different locations resulting in two different geometry settings. Under each of these four settings, specimen is clamped under two different torque ratings giving rise to different finite clamping effect. Under the eight settings, coordinates of tip point under static loading are measured directly using scales and plumb at each load step; whereas, complete deflection profiles of loaded beam under each static load step are obtained through post-processing of images captured during experimentation. Such image processing is carried out manually using AutoCAD®and in-built AutoLISP®software. Strain measurements at each static load step are carried out by using strain gauge, a universal data acquisition system and the associated Catman Easy®software. To obtain loaded free vibration characteristics, loaded beam under each setting is disturbed by a rubber hammer and its dynamic response is recorded from strain gauge signal through Catman Easy®software. These dynamic strain readings of loaded beam are post-processed and FFT plots are generated in MATLAB®software and first two loaded natural frequencies of beam under each setting are obtained. Finally, effects of clamping torques on the static strain and deflection results and loaded natural frequencies for beam settings with the four different thickness to length ratios are reported in a suitable manner. The result reported may be useful as ready reference to develop a theoretical model of clamped beam like structures incorporating the effect of finite clamping.
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35

Vázquez-Leal, H., Y. Khan, A. L. Herrera-May, U. Filobello-Nino, A. Sarmiento-Reyes, V. M. Jiménez-Fernández, D. Pereyra-Díaz, et al. "Approximations for Large Deflection of a Cantilever Beam under a Terminal Follower Force and Nonlinear Pendulum." Mathematical Problems in Engineering 2013 (2013): 1–12. http://dx.doi.org/10.1155/2013/148537.

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In theoretical mechanics field, solution methods for nonlinear differential equations are very important because many problems are modelled using such equations. In particular, large deflection of a cantilever beam under a terminal follower force and nonlinear pendulum problem can be described by the same nonlinear differential equation. Therefore, in this work, we propose some approximate solutions for both problems using nonlinearities distribution homotopy perturbation method, homotopy perturbation method, and combinations with Laplace-Padé posttreatment. We will show the high accuracy of the proposed cantilever solutions, which are in good agreement with other reported solutions. Finally, for the pendulum case, the proposed approximation was useful to predict, accurately, the period for an angle up to179.99999999∘yielding a relative error of 0.01222747.
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36

Howell, L. L., and A. Midha. "Parametric Deflection Approximations for End-Loaded, Large-Deflection Beams in Compliant Mechanisms." Journal of Mechanical Design 117, no. 1 (March 1, 1995): 156–65. http://dx.doi.org/10.1115/1.2826101.

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Geometric nonlinearities often complicate the analysis of systems containing large-deflection members. The time and resources required to develop closed-form or numerical solutions have inspired the development of a simple method of approximating the deflection path of end-loaded, large-deflection cantilever beams. The path coordinates are parameterized in a single parameter called the pseudo-rigid-body angle. The approximations are accurate to within 0.5 percent of the closed-form elliptic integral solutions. A physical model is associated with the method, and may be used to simplify complex problems. The method proves to be particularly useful in the analysis and design of compliant mechanisms.
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37

Theinchai, Ratchata, Siriwan Chankan, and Weera Yukunthorn. "Application of ADM Using Laplace Transform to Approximate Solutions of Nonlinear Deformation for Cantilever Beam." International Journal of Mathematics and Mathematical Sciences 2016 (2016): 1–5. http://dx.doi.org/10.1155/2016/5052194.

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We investigate semianalytical solutions of Euler-Bernoulli beam equation by using Laplace transform and Adomian decomposition method (LADM). The deformation of a uniform flexible cantilever beam is formulated to initial value problems. We separate the problems into 2 cases: integer order for small deformation and fractional order for large deformation. The numerical results show the approximated solutions of deflection curve, moment diagram, and shear diagram of the presented method.
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38

He, Xiao-ting, and Shan-lin Chen. "Biparametric perturbation solutions of large deflection problem of cantilever beams." Applied Mathematics and Mechanics 27, no. 4 (April 2006): 453–60. http://dx.doi.org/10.1007/s10483-006-0404-z.

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39

Zuev, D. M., and Yu V. Zakharov. "Large deflection of a cantilever beam under transverse loading. A modification of linear theory." IOP Conference Series: Materials Science and Engineering 822 (May 22, 2020): 012039. http://dx.doi.org/10.1088/1757-899x/822/1/012039.

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TERAO, Hiroki, Tadashi HORIBE, Kotaro MORI, and Hiroshi KIMOTO. "Experimental Study on Large Deflection of Tapered Cantilever Beam Considering Axially Functionally Graded Material." Proceedings of Ibaraki District Conference 2017.25 (2017): 207. http://dx.doi.org/10.1299/jsmeibaraki.2017.25.207.

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41

Batista, Milan. "Large deflections and stability of spring-hinged cantilever beam." Journal of Mechanics of Materials and Structures 14, no. 2 (July 26, 2019): 295–308. http://dx.doi.org/10.2140/jomms.2019.14.295.

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42

Wu, Yiting, Elisa Wirthmann, Ute Klöpzig, and Tino Hausotte. "Investigation of a metrological atomic force microscope system with a combined cantilever position, bending and torsion detection system." Journal of Sensors and Sensor Systems 10, no. 2 (July 15, 2021): 171–77. http://dx.doi.org/10.5194/jsss-10-171-2021.

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Abstract. This article presents a new metrological atomic force microscope (MAFM) head with a new beam alignment and a combined one-beam detection of the cantilever deflection. An interferometric measurement system is used for the determination of the position of the cantilever, while a quadrant photodiode measures the bending and torsion of the cantilever. To improve the signal quality and reduce disturbing interferences, the optical design was revised in comparison to the systems of others (Dorozhovets et al., 2006; Balzer et al., 2011; Hausotte et al., 2012). The integration of the MAFM head in a nanomeasuring machine (NMM-1) offers the possibility of large-scale measurements over a range of 25mm×25mm×5 mm with sub-nanometre resolution. A large number of measurements have been performed by this MAFM head in combination with the NMM-1. This paper presents examples of the measurements for the determination of step height and pitch and areal measurement.
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43

Basu, Aviru Kumar, Anup Basak, and Shantanu Bhattacharya. "Geometry and thickness dependant anomalous mechanical behavior of fabricated SU-8 thin film micro-cantilevers." Journal of Micromanufacturing 3, no. 2 (September 10, 2020): 113–20. http://dx.doi.org/10.1177/2516598420930988.

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SU-8 micro-cantilever arrays consisting of V- and M-shaped structures fabricated using a simplified single hard mask step. Bending tests were performed under similar peak loads (ranging 2–10 µN), with thickness ranging between micron (3.5 µm) and sub-micron (0.2 µm) scales. Various mechanical properties such as stiffness and hysteresis are determined from the load versus deflection curves. When the thickness of the V-shaped beam is decreased from 2 µm to 0.2 µm, the stiffness increases by a factor of 2.7, which is in contradiction with the classical beam theory according to which the stiffness for 0.2 µm beam should be three orders of magnitude less than that of 2 µm beam. Micropolar elasticity theory with a variable-intrinsic length scale (thickness dependant) is used to explain such an anomalous response. Experimentally obtained stiffness of two M-shaped beams of thickness 2 µm and 0.2 µm are almost identical. Reason behind this contradictory result is that the thicker beam has a residual strain with a large plastic deformation which usually increases the cross-linking network density, leading to increase in elastic modulus, hardness and thus stiffness of polymers. But the thinner beam has undergone an elastic deformation. The size effect of V- and M-shaped cantilever beams is discussed.
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44

Nageswara Rao, B., and G. Venkateswara Rao. "Large deflection analysis of cantilever beams of symmetrical cross-section subjected to a rotational distributed loading including the effect of material nonlinearity." Aeronautical Journal 92, no. 916 (July 1988): 230–34. http://dx.doi.org/10.1017/s0001924000016171.

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AbstractCombined effects of geometrical and material non-linearities on a cantilever beam having symmetrical cross-section about its central axis with a rotational distributed loading are studied. It is assumed that the stress-strain relation in compression is identical to that in tension. Due to this, the neutral axis coincides with the central axis of the beam. The problem is formulated by means of an integral equation which is suitably converted to a system of nonlinear ordinary differential equations which are solved using a simple and accurate numerical method. Details of the load deflection characteristics for an I-beam and for a beam of rectangular cross-section are presented.
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45

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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46

Xi, F., F. Liu, and Q. M. Li. "Large deflection response of an elastic, perfectly plastic cantilever beam subjected to a step loading." International Journal of Impact Engineering 48 (October 2012): 33–45. http://dx.doi.org/10.1016/j.ijimpeng.2011.05.006.

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47

Oguibe, Chuks N., and David C. Webb. "Large deflection analysis of multilayer cantilever beams subjected to impulse loading." Computers & Structures 78, no. 4 (December 2000): 537–47. http://dx.doi.org/10.1016/s0045-7949(00)00042-0.

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48

Rao, B. Nageswara, and G. Venkateswara Rao. "On the Large Deflection of Cantilever Beams with End Rotational Load." ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 66, no. 10 (1986): 507–9. http://dx.doi.org/10.1002/zamm.19860661027.

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49

Zhiming, Ye, and Yeh Kaiyuan. "A Study of Belleville Spring and Diaphragm Spring in Engineering." Journal of Applied Mechanics 57, no. 4 (December 1, 1990): 1026–31. http://dx.doi.org/10.1115/1.2897621.

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This paper deals with the static response of a Belleville spring and a diaphragm spring by using the finite rotation and large deflection theories of a beam and conical shell, and an experimental method as well. The authors propose new mechanical analysis mathematical models. The exact solution of a variable width cantilever beam is obtained. By using the integral equation method and the iterative method to solve the simplified equations and Reissner’s equations of finite rotation and large deflection of a conical shell, this paper has calculated a great number of numerical results. The properties of loads, strains, stresses and displacements, and the distribution rules of strains and stresses of diaphragm springs are investigated in detail by means of the experimental method. The unreasonableness of several assumptions in traditional theories and calculating method is pointed out.
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50

Kang, Ying-An, and Xian-Fang Li. "Large Deflections of a Non-linear Cantilever Functionally Graded Beam." Journal of Reinforced Plastics and Composites 29, no. 12 (July 2, 2009): 1761–74. http://dx.doi.org/10.1177/0731684409103340.

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