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Journal articles on the topic 'Castigliano theorems'

Author: Grafiati

Published: 2 June 2025

Last updated: 31 July 2025

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1

Kondo, Kyohei. "On the Castigliano Theorems." JOURNAL OF THE JAPAN SOCIETY FOR AERONAUTICAL AND SPACE SCIENCES 52, no. 606 (2004): 316–27. http://dx.doi.org/10.2322/jjsass.52.316.

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2

Marotti de Sciarra, F. "Direct and dual theorems of castigliano and clapeyron for generalized elastic models." Acta Mechanica 124, no. 1-4 (1997): 107–30. http://dx.doi.org/10.1007/bf01213021.

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3

Schoeftner, Juergen. "Extension of Castigliano’s method for isotropic beams." Acta Mechanica 231, no. 11 (2020): 4621–40. http://dx.doi.org/10.1007/s00707-020-02762-z.

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Abstract In the present contribution Castigliano’s theorem is extended to find more accurate results for the deflection curves of beam-type structures. The notion extension in the context of the second Castigliano’s theorem means that all stress components are included for the computation of the complementary strain energy, and not only the dominant axial stress and the shear stress. The derivation shows that the partial derivative of the complementary strain energy with respect to a scalar dummy parameter is equal to the displacement field multiplied by the normalized traction vector caused b

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4

Ward, J. P. "General Solutions Using the Castigliano Theorem." International Journal of Mechanical Engineering Education 25, no. 3 (1997): 205–14. http://dx.doi.org/10.1177/030641909702500305.

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The Castigliano theorem of solid mechanics is normally used to obtain displacements at specific points on the surface of an elastic body. In this work it will be shown that by using fictitious forces placed in general positions the general solution for the displacement may be found without the need to solve a differential equation. The work also uses the technique to obtain an unusual derivation of the Euler-Bernoulli equation.

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5

Rédl, Jozef. "Differentiating under integral sign in Castigliano’s theorem." Mathematics in Education, Research and Applications 5, no. 1 (2019): 30–37. http://dx.doi.org/10.15414/meraa.2019.05.01.30-37.

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6

Kurrer, K. E. "Zur Debatte um die Theoreme von Castigliano in der klassischen Baustatik." Bautechnik 75, no. 5 (1998): 311–22. http://dx.doi.org/10.1002/bate.199802590.

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7

Romero, I. "A generalization of Castigliano’s theorems for structures with eigenstrains." Archive of Applied Mechanics 87, no. 10 (2017): 1727–37. http://dx.doi.org/10.1007/s00419-017-1282-5.

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8

De Castro, Paulo. "Bi-material Flywheels and Castigliano’s Theorems: a Case Study." Journal on Mechanics of Solids 1, no. 1 (2022): 39–59. http://dx.doi.org/10.24840/2975-8262_001-001_001818.

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The analytical stress analysis of rim and spokes flywheels is revisited in this paper. A brief survey of mechanical energy storage gives a contextualization for the work. Then, the use of Castigliano’s theorems for the stress analysis of a rotating rim and spokes flywheel is recalled. The origin of widely available design formulas is elucidated and their rational is discussed. A hitherto unpublished analytical stress analysis for a bi-material flywheel is derived and a parametric solution is presented and discussed.

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9

Hu, Jun Feng, Xiang Fu Cui, and Pei Li. "Optimization Design of a Hyperbolic Flexure Hinge Based on its Closed-Form Equations." Applied Mechanics and Materials 151 (January 2012): 414–18. http://dx.doi.org/10.4028/www.scientific.net/amm.151.414.

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An optimization design method of a hyperbolic flexible hinge is presented in this paper. According to the structure feature and force exerted on the flexible hinge, the closed-form equations are formulated for compliances to characterize both the active rotation and all other in- and out-of-plane parasitic motions by using the Castigliano’s second theorem. Meanwhile, the accuracy equations of the hyperbolic flexure hinge are obtained using the Castigliano’s second theorem. The in-plane rotation angle of flexure hinge is optimization objective, and the constraints of optimization model are out-

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10

A.M. Ilkiu. "Aplicação do segundo teorema de Castigliano na solução de estruturas hiperestaticas." Engenharia Civil UM, no. 62 (December 20, 2022): 33–44. http://dx.doi.org/10.21814/ecum.4490.

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No presente artigo, apresentam-se estudos de casos de análise de estruturas estaticamente indeterminadas ou hiperestáticas, utiliza-se o segundo teorema de Castigliano e o “Theorem of Last Work” na determinação das constantes hiperestáticas. Consideram-se modelos de estruturas sujeitos a carregamentos diversos onde, as condições de contorno nos apoios externos sugeridos como redundante são identificadas e as incógnitas ou constantes hiperestáticas determinadas. Destacam-se as análises das equações clássicas apresentadas por Timoshenko S.P. e Young D.H. (1965) e das teorias elásticas no desenvo

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11

José, Alfredo Ramírez-Monares, and Israel Hernández-Hernández Jesús. "Three-Bar structure optimality criterion using the linear resizing rule." Revista Facultad de Ingeniería, Universidad de Antioquia, no. 104 (August 31, 2021): 101–7. https://doi.org/10.17533/udea.redin.20210850.

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The static analysis of the indeterminate three-bar structure is developed using the Castigliano’s first theorem, taking the lengths and inclination angles as variables. Some reductions are applied in the resulting set of Equations to approximate them to the references models. From now on, the minimum mass optimization model with restrictions is established. Then, the Optimality Criterion linear resizing optimization rule algorithm for the unbounded and bounded design variables is applied in two numerical cases. The analytical and Matlab Optimization Toolbox results are also obtained and

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12

Steiner, Wolfgang. "The use of Castigliano’s theorem in Coulomb friction problems." Acta Mechanica 225, no. 9 (2014): 2471–83. http://dx.doi.org/10.1007/s00707-014-1091-7.

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13

Hu, Jun Feng, Pei Li, and Xiang Fu Cui. "Performance Analysis of a Hyperbolic Flexure Hinge Based on its Closed-Form Equations." Advanced Materials Research 421 (December 2011): 540–43. http://dx.doi.org/10.4028/www.scientific.net/amr.421.540.

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In order to the effects of structural sizes of a hyperbolic on its performance, sensitivity and accuracy analysis are performed in this paper. According to the structure feature and force exerted on the flexible hinge, the closed-form equations are formulated for compliances to characterize both the active rotation and all other in- and out-of-plane parasitic motions by using the Castigliano’s second theorem. Meanwhile, the accuracy equations are obtained using the Castigliano’s second theorem. According to the closed-form flexibility formulas, the effects of the four structural parameters, su

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14

Li, Yinfeng, Zhonghua Li, and Pizhong Qiao. "Castigliano’s Second Theorem for Deformation Determination of a Cracked Body." Journal of Aerospace Engineering 28, no. 5 (2015): 06014006. http://dx.doi.org/10.1061/(asce)as.1943-5525.0000475.

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15

Zhang, Weizhong, Wei Ye, and Chao Yang. "Elastostatic Stiffness Analysis for the US/UPS Parallel Manipulators." Mathematical Problems in Engineering 2020 (July 13, 2020): 1–9. http://dx.doi.org/10.1155/2020/1975428.

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The virtual joint method (VJM) cannot calculate the strain energy stored in each rod. In order to solve the problem, a modeling method of the elastostatic stiffness was investigated for the UP/UPS parallel manipulators (PMs), taking the example of the 6-SPS PM. The modeling method was based on screw theory, Castigliano’s theorem, and strain energy (where U, P, and S, respectively, denote universal, prismatic, and spherical joints). First, the actuator and constraint wrenches of the mechanism were obtained by screw theory. Second, compact limb stiffness matrices were obtained in terms of strain

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16

Liu, Qing Ling. "Compliances Calculation and Performance Analysis of the Novel Half Hybrid Flexure Hinge." Applied Mechanics and Materials 303-306 (February 2013): 1714–20. http://dx.doi.org/10.4028/www.scientific.net/amm.303-306.1714.

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A novel flexure hinge named right circular corner filleted half hybrid flexure hinge was advanced. Based on the Castigliano second theorem, the compliance formulas of the novel flexure hinge were formulated. The theoretical calculations and the finite element simulations were performed simultaneously, the similar results were obtained which indicated the correctness of the compliance formulas. The influence of the geometric parameters of the novel flexure hinge on its performance was analysed. Compared with right circular corner filleted double hybrid flexure hinge, the compliance and sensitiv

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17

Dong, Chensong. "Effective Elastic Modulus of Wavy Single-Wall Carbon Nanotubes." C 9, no. 2 (2023): 54. http://dx.doi.org/10.3390/c9020054.

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A simple method for determining the effective elastic modulus of wavy single-wall carbon nanotubes (SWCNTs) is presented in this paper. The effective modulus of curved SWCNTs is derived using Castigliano’s theorem. The effect of curvature on the effective modulus is studied. This method is verified by finite element analysis (FEA). The distributions of effective moduli are studied by Monte Carlo simulation. The effective modulus of a general wavy SWCNT is derived by considering the SWCNT as a number of curved SWCNT sections.

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18

Kiyak, Murat, and Billur Kaner. "Determination of the actual deflection of the cutting tool ın turning by the Castigliano theorem." Journal of Radiation Research and Applied Sciences 16, no. 4 (2023): 100744. http://dx.doi.org/10.1016/j.jrras.2023.100744.

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19

Hernández-Acosta, Marco Antonio, Christopher René Torres-San Miguel, Armando Josue Piña-Díaz, Juan Carlos Paredes-Rojas, Luis Antonio Aguilar-Peréz, and Guillermo Urriolagoitia-Sosa. "Numerical Study of a Customized Transtibial Prosthesis Based on an Analytical Design under a Flex-Foot® Variflex® Architecture." Applied Sciences 10, no. 12 (2020): 4275. http://dx.doi.org/10.3390/app10124275.

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This work addresses the design, analysis, and validation of a transtibial custom prosthesis. The methodology consists of the usage of videometry to analyze angular relationships between joints, moments, and reaction forces in the human gait cycle. The customized geometric model of the proposed prosthesis was defined by considering healthy feet for the initial design. The prosthesis model was developed by considering the Flex-Foot® Variflex® architecture on a design basis. By means of the analytical method, the size and material of the final model were calculated. The behavior of the prosthesis

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20

Liu, Yu. "Stiffness Calculation of the Microstructure with Crab-Leg Flexural Suspension." Advanced Materials Research 317-319 (August 2011): 1123–26. http://dx.doi.org/10.4028/www.scientific.net/amr.317-319.1123.

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The stiffness of microstructure is an important parameter of the microsensor. It is usually obtained by FEM approach, which is difficult to give an analytical expression. This paper reports on a biaxial microaccelerometer with the crab-leg flexural suspension. Its stiffness is carried out by using force method and Castigliano’s theorem. During the deduction, we neither introduce the other assumptions nor design the special dimension. So this methodology is strict in theory, and can be extended to analysis for the displacement and stiffness of the symmetric and statically indeterminate microstr

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21

Freed, Alan D., and Todd C. Doehring. "Elastic Model for Crimped Collagen Fibrils." Journal of Biomechanical Engineering 127, no. 4 (2005): 587–93. http://dx.doi.org/10.1115/1.1934145.

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A physiologic constitutive expression is presented in algorithmic format for the nonlinear elastic response of wavy collagen fibrils found in soft connective tissues. The model is based on the observation that crimped fibrils in a fascicle have a three-dimensional structure at the micron scale that we approximate as a helical spring. The symmetry of this wave form allows the force/displacement relationship derived from Castigliano’s theorem to be solved in closed form: all integrals become analytic. Model predictions are in good agreement with experimental observations for mitral-valve chordæ

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Retama Velasco, Jaime, and Ricardo Heras Cruz. "Cálculo numérico de la matriz de flexibilidades de vigas de sección variable, con elementos finitos." RDP Revista Digital de Posgrado, no. 1 (2020): 22–31. http://dx.doi.org/10.22201/fesa.rdp.2020.1.03.

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In this work, the flexibility properties of variable cross section beams are derived, through the application of the second theorem of Castigliano; considering the complementary energy by bending and share forces. To perform the integration of the flexibility coefficients, a numerical method, which considers the discretization of the beam domain with first order rectangular finite elements, in conjunction with the Gauss rule, is proposed. At the end of the work, the proposed method is applied to a tapered beam that has been discretized with a maximum of five finite elements. It is shown that t

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23

Meghdari, Ali. "A Variational Approach for Modeling Flexibility Effects in Manipulator Arms." Robotica 9, no. 2 (1991): 213–17. http://dx.doi.org/10.1017/s0263574700010262.

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SUMMARYThis paper presents a general technique to model flexible components (mainly links and joints flexibilities are considered) of manipulator arms based on Castigliano's theorem of least work. The robotic arms flexibility properties are derived and represented by the matrix of compliance coefficients. Such expressions can be used to determine the errors due to the robotic tip deformations under the application of a set of applied loads at the tip in a Cartesian space. Once these deformations are computed, they may be used to correct for the positional errors arisen from the robotic structu

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24

Dragoni, E. "A contribution to wave spring design." Journal of Strain Analysis for Engineering Design 23, no. 3 (1988): 145–53. http://dx.doi.org/10.1243/03093247v233145.

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An analytical model for stamped ring wave springs is proposed, based on the theory for circular beams loaded normal to the plane of curvature. The model profits from the adoption of Castigliano's theorem as a tool for mathematical treatment. Closed-form expressions for both load—deflection and load—stress relationships are presented. Because of the particular shape of the spring in the undeformed configuration, the load—deflection curve is found to be appreciably bilinear in character. A similar but less pronounced behaviour is displayed also by the relationship between load and internal stres

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25

Hwang, Hui-Geon, Won-Jee Chung, and Dae-Young Kim. "A Study on the Deflection of Roller Axis of an Improved Mecanum Wheel Using the Castigliano Theorem." Korean Society of Manufacturing Process Engineers 19, no. 6 (2020): 61–66. http://dx.doi.org/10.14775/ksmpe.2020.19.06.061.

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26

Lu, Ye Qiang, Wen Feng Wei, and Yi Long Zhang. "Research and Simulation on Drawing Force of the Tripod Type Universal Coupling." Advanced Materials Research 482-484 (February 2012): 792–95. http://dx.doi.org/10.4028/www.scientific.net/amr.482-484.792.

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Analyzing the strain expression referring to Castigliano’s Theorem after analysis of the tripod type universal coupling under drawing force comes to the simplified mode of tripod type universal coupling. And with the help of simplified mode, it concludes that the minimum strain occurs when the radius of cross-section of the circlip equals to the depth of groove. After setting material attributes, boundary conditions, contacts of the tripod type universal coupling, and static simulation with the finite element method in SolidWorks, the strain of the universal couplings is carried out. Theoretic

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27

Jia, X., J. Liu, Y. Tian, and D. Zhang. "Stiffness analysis of a compliant precision positioning stage." Robotica 30, no. 6 (2011): 925–39. http://dx.doi.org/10.1017/s0263574711001147.

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SUMMARYIn this paper a 3-degree of freedom compliant parallel positioning stage utilizing flexure hinges is explored for nanoimprint lithography. The performance of the stage is extensively analyzed using a pseudo-rigid body model and finite element method. The position and velocity models are established. Accordingly, the stiffness at driving point of the active arm is obtained on the basis of Castigliano's first theorem. The system stiffness of the compliant stage is explored using the compliant matrix methodology and matrix transformation, and the influence of the geometry parameters on sti

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28

Yuriev, A., and L. Panchenko. "ENERGY BEGINNING IN THE THEORY OF STRUCTURE SYNTHESIS." Bulletin of Belgorod State Technological University named after. V. G. Shukhov 8, no. 10 (2023): 35–41. http://dx.doi.org/10.34031/2071-7318-2023-8-10-35-41.

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The theory of construction synthesis is based on the principle of stationary action. The fundamental beginning of the design of structure is the variational principle of structural synthesis with energy content. The increment in the energy of external forces and the potential energy of deformation depends not only on the increments of displacements and internal forces, as provided by the principles of Lagrange and Castigliano, but also on the changes of configuration body and materials modules. The influence of these factors on the potential strain energy is discussed on the example of a tensi

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Wang, Sheldon, Ebot Ndip-Agbor, and Enaho Atamenwan. "On Hierarchical Applications of Finite Element Methods and Classical Applied Mechanics Approaches for Complex Structures." Applied Mechanics 3, no. 2 (2022): 464–80. http://dx.doi.org/10.3390/applmech3020027.

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In this paper, hierarchical studies based on both analytical and computational approaches have been employed to validate and improve current structural designs of mud holding tanks for hydraulic fracturing in petroleum industries. Through detailed comparisons at different levels of approximations for both real world complex structural design problem and a simplified stiffened plate with extreme geometrical aspect ratios, proper design procedures have been reiterated and validated. It is highly recommended that low-dimensional structures with emphasis on classical mechanics principles should be

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Hu, Jun Feng, Wen Juan Xie, Pei Li, and Xiang Fu Cui. "Comparative Analysis of Parabolic and Hyperbolic Flexure Hinges Using Closed-Form Equations." Advanced Materials Research 503-504 (April 2012): 880–83. http://dx.doi.org/10.4028/www.scientific.net/amr.503-504.880.

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The comparative analysis of a parabolic and hyperbolic flexible hinges were presented. The closed-form compliance equations in the working and non-working plane can be derived by using the Castigliano’s second theorem. In order to compare the relative performance of parabolic and hyperbolic flexure hinges, a ratio function between specific compliances of the two hinges is defined. We analyzed the non-dimensional ratios of working plane and non-working plane compliance to show the relative properties of parabolic versus hyperbolic flexure hinges. The analysis results has showed compared to a hy

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Kong, Jianyi, Zhao Huang, Xiaodong Xian, Yingrui Wang, and Puliang Yu. "Generalized model for conic-V-shaped flexure hinges." Science Progress 103, no. 4 (2020): 003685042098121. http://dx.doi.org/10.1177/0036850420981211.

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This paper presents a new class of flexure hinges, namely, conic-V-shaped flexure hinges (CFHs), which can be used as a generalized model for flexure hinges with profiles such as parabolic-V-shape, elliptical-V-shape, and hyperbolic-V-shape. Compliance and precision equations for the CFHs were derived as a set of nonlinear equations using Castigliano’s second theorem. The parameters of the nonlinear equations inputted to the compliance and precision matrices were based on the generalized equations used for conic curves in polar coordinates. Furthermore, the compliance equations were verified b

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32

Jingjing, Ling, Li Ruiqin, and Zhang Qisheng. "Flexibility Calculation of Like-U Type Flexure Hinge." Open Mechanical Engineering Journal 9, no. 1 (2015): 532–39. http://dx.doi.org/10.2174/1874155x01509010532.

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A new like-U type flexure hinge structure is proposed, based on Castigliano’s second theorem and calculus theory. Taking the centrifugal angle parameters as the integration variable, and defining the intermediate parameters, it deduces the analytic computational formula for the like-U type flexure hinge flexibility. By changing the structural parameter of the flexure hinge, it is able to transform four different structure flexure hinges, and the deduced analytic computation formula can be applied to all of these four structures flexure hinges. After the twelve flexure hinges of different struc

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Elliotis, Miltiades, Petros Christou, and Antonis Michael. "Analysis of Tensegrity Structures with Redundancies, by Implementing a Comprehensive Equilibrium Equations Method with Force Densities." Advances in Numerical Analysis 2016 (December 25, 2016): 1–12. http://dx.doi.org/10.1155/2016/4815289.

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A general approach is presented to analyze tensegrity structures by examining their equilibrium. It belongs to the class of equilibrium equations methods with force densities. The redundancies are treated by employing Castigliano’s second theorem, which gives the additional required equations. The partial derivatives, which appear in the additional equations, are numerically replaced by statically acceptable internal forces which are applied on the structure. For both statically determinate and indeterminate tensegrity structures, the properties of the resulting linear system of equations give

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Li, Hua, Yannan Wu, Haochen Ye, and Yan Xu. "Thermal Actuation Analysis of Twisted and Coiled Polymer Actuators." International Journal of Applied Mechanics 12, no. 08 (2020): 2050092. http://dx.doi.org/10.1142/s1758825120500921.

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Twisted and coiled polymer actuators (TCPAs), an emerging class of artificial muscles, exhibit the advantages of large stroke, low hysteresis, low cost, etc. The effect of design parameters on thermal actuation is important for the effective design of TCPAs. In this study, a new model has been developed to describe the effect of geometrical parameters on thermal actuation based on Castigliano’s second theorem. In this model, an equivalent modulus based on its radial bias angle has been introduced from the twisted polymer actuator (TPA)’s equivalent model. The proposed model provides a simple a

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35

Žiga, Alma, and Josip Kačmarčik. "Plywood Cantilever Deflection." Drvna industrija 74, no. 1 (2023): 81–91. http://dx.doi.org/10.5552/drvind.2023.0053.

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In this paper, the elastic behaviour in bending of three-layer plywood cantilever beams is analysed. Deflections of straight and half-circle cantilevers, loaded with a force at free end is determined experimentally and calculated using analytical and finite element method approach. The analytical calculation of deflection for the strait cantilever is obtained using a transformed cross section. The deflection of half-circle cantilever is determined by the classical laminated plate theory and Castigliano’s theorem. Loads and cantilever dimensions are varied in the study using the design of exper

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Hu, Jun Feng, Pei Li, and Xiang Fu Cui. "Optimum Design of a Parabolic Flexure Hinge Based on Compliance Closed-Form Equations." Advanced Materials Research 424-425 (January 2012): 299–303. http://dx.doi.org/10.4028/www.scientific.net/amr.424-425.299.

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Considering the increasingly wider applications of flexible hinge in the fields of micro-electromechanical and micro-positioning etc., the optimal design method of a parabolic flexible hinge is presented. According to the structure feature and force exerted on the flexible hinge, the closed-form flexibility expressions in the working and non-working plane can be derived by using the Castigliano’s second theorem. Meanwhile, the accuracy analysis of the parabolic flexure hinge is performed. The rotation angle of flexure hinge in the working plane is treated as objective function, and the constra

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Bilal, Diyar Khalis, Mustafa Unel, Mehmet Yildiz, and Bahattin Koc. "Realtime Localization and Estimation of Loads on Aircraft Wings from Depth Images." Sensors 20, no. 12 (2020): 3405. http://dx.doi.org/10.3390/s20123405.

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This paper deals with the development of a realtime structural health monitoring system for airframe structures to localize and estimate the magnitude of the loads causing deflections to the critical components, such as wings. To this end, a framework that is based on artificial neural networks is developed where features that are extracted from a depth camera are utilized. The localization of the load is treated as a multinomial logistic classification problem and the load magnitude estimation as a logistic regression problem. The neural networks trained for classification and regression are

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38

Nguyen, Nghia-Huu, Moo-Yeon Lee, Ji-Soo Kim, and Dong-Yeon Lee. "Compliance Matrix of a Single-Bent Leaf Flexure for a Modal Analysis." Shock and Vibration 2015 (2015): 1–10. http://dx.doi.org/10.1155/2015/672831.

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We present a compliance matrix for a single-bent leaf flexure (SBLF) that shows the relationships between the deformations and the six-axis loads applied to the SBLF. Higher-order beam theory that considers the variable shear and warping effect is considered in bending. The partially restrained warping at the junction between elements is also considered in torsion. The total strain energy is calculated, and the complete compliance matrix is derived by using Castigliano’s second theorem. Sensitivity analyses over the compliance elements are performed and verified via finite element analysis (FE

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Enferadi, Javad, and Alireza Akbarzadeh Tootoonchi. "Accuracy and stiffness analysis of a 3-RRP spherical parallel manipulator." Robotica 29, no. 2 (2010): 193–209. http://dx.doi.org/10.1017/s0263574710000032.

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SUMMARYIn this paper, accuracy and stiffness analysis of a 3-RRP spherical parallel manipulator (SPM) (Enferadi and Tootoonchi, A novel spherical parallel manipulator: Forward position problem, singularity analysis and isotropy design, Robotica, vol. 27, 2009, pp. 663–676) with symmetrical geometry is investigated. At first, the 3-RRP SPM is introduced and its inverse kinematics analysis is performed. Isotropic design, because of its design superiority, is selected and workspace of the manipulator is obtained. The kinematics conditioning index (KCI) is evaluated on the workspace. Global condit

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40

Lin, Zifeng. "Theoretical Design and Modeling of a Novel Composite Flexible Mechanism." Applied and Computational Engineering 141, no. 1 (2025): 225–33. https://doi.org/10.54254/2755-2721/2025.22056.

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To enhance the comprehensive performance of flexible motion platforms in terms of precise positioning and large displacement amplification, this paper designs and investigates a novel composite mechanism that combines a rhombic amplification mechanism with a parallelogram-based flexible structure. Based on the Euler-Bernoulli beam theory and Castiglianos second theorem, the displacement amplification ratio and stiffness analytical model of the rhombic flexible mechanism are derived, and the Lagrangian equation is employed to establish an analytical model for the natural frequency of the flexib

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41

Elsisy, Moataz M., Mustafa H. Arafa, Chahinaz A. Saleh, and Yasser H. Anis. "Modeling of a Symmetric Five-Bar Displacement Amplification Compliant Mechanism for Energy Harvesting." Sensors 21, no. 4 (2021): 1095. http://dx.doi.org/10.3390/s21041095.

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This paper presents an analytical model to determine a closed form mathematical representation for the output displacement of a displacement amplification compliant mechanism used for energy harvesting. A symmetric five-bar compliant mechanism with right-circular and corner-filleted flexure hinges was mathematically modeled and its displacement was determined using the Castigliano energy theorem. The stresses within the flexure joints, the weakest points in the mechanism body, were calculated. The mathematical model expresses both the displacement amplification and the stresses as functions of

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Li, K., X. L. Gao, and A. K. Roy. "Micromechanics model for three-dimensional open-cell foams using a tetrakaidecahedral unit cell and Castigliano's second theorem." Composites Science and Technology 63, no. 12 (2003): 1769–81. http://dx.doi.org/10.1016/s0266-3538(03)00117-9.

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Tian, Feifei, Siyuan Li, Bingliang Hu, Pengchong Wang, Xiongbo Hao, and Wanli Zhao. "A Structure Load Performance Integrated Model Method for the Bridge-Type Displacement Amplification Mechanism." Machines 10, no. 9 (2022): 792. http://dx.doi.org/10.3390/machines10090792.

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The modeling of compliant bridge-type displacement amplification mechanisms has challenges due to the intrinsic coupling of kinematic and mechanical behaviors. A structure load performance integrated model method for the bridge-type displacement amplification mechanism is presented. The established modeling based on Castigliano’s second theorem considers the deformations of all members, the effect of external load and the nonlinear shear effect. Compared to the finite element model (FEM) and existing models, the established modeling precisely predicts significant nonlinearity of the displaceme

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Hu, Jun Feng, Pei Li, and Xiang Fu Cui. "Performance of a Parabolic Flexible Joint Using Compliance Closed-Form Equation." Advanced Materials Research 490-495 (March 2012): 2484–88. http://dx.doi.org/10.4028/www.scientific.net/amr.490-495.2484.

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Considering the effects of structural sizes of a parabolic flexible joint on its performance, compliance, sensitivity and accuracy analysis are performed in this paper. The closed-form equations are formulated for compliances to characterize both the active rotation and all other in- and out-of-plane parasitic motions, and accuracy equations are also obtained by using the Castigliano’s second theorem. According to the closed-form compliance equations, the effects of the structural parameters, such as thickness, notch depth, length and width, on the compliance of flexible joint are analyzed, re

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Bounab, Belkacem. "Multi-objective optimal design based kineto-elastostatic performance for thedeltaparallel mechanism." Robotica 34, no. 2 (2014): 258–73. http://dx.doi.org/10.1017/s0263574714001416.

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SUMMARYThis paper addresses the dimensional-synthesis-based kineto-elastostatic performance optimization of thedeltaparallel mechanism. For the manipulator studied here, the main consideration for the optimization criteria is to find the maximum regular workspace where the robotdeltamust posses high stiffness and dexterity. The dexterity is a kinetostatic quality measure that is related to joint's stiffness and control accuracy. In this study, we use the Castigliano's energetic theorem for modeling the elastostatic behavior of thedeltaparallel robot, which can be evaluated by the mechanism's r

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Meng, Qiaoling, Zhongzhe Chen, Haolun Kang, Zhijia Shen, and Hongliu Yu. "Analytical Modeling and Application for Semi-Circular Notch Flexure Hinges." Applied Sciences 13, no. 16 (2023): 9248. http://dx.doi.org/10.3390/app13169248.

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Flexure-based compliant mechanisms can be used to achieve bio-imitability and adaptability in the applications of biomedical engineering. However, a nonlinear load-displacement profile increases the design complexity of this type of compliant mechanism, especially when the cross-section of the flexure hinge is not constant. This paper proposes two general analytical models by analyzing the compliance and stress characteristics of the semi-circular notch flexure hinge undergoing large deflections, which is a typical variable cross-section of a flexure hinge, based on the Castigliano’s second th

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Graça, Nuno, and Paulo M. S. T. de Castro. "Fatigue behaviour of a spring: a case study." MATEC Web of Conferences 349 (2021): 04009. http://dx.doi.org/10.1051/matecconf/202134904009.

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A durability design case study concerning a U spring is presented. For a given geometry of the component, the question was to predict the maximum permissible displacement per cycle whilst ensuring a service life of at least 260 kcycles. The stiffness of the spring was evaluated using the finite elements software SolidWorks. As an approximation a linear model was used in the finite elements analysis, which was also compared with an analytical treatment based on Castigliano’s theorem. Using a given safety factor, a high cycle fatigue analysis was performed assuming the use of a steel with 650 MP

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Zhou, Rui, Weicheng Gao, Wei Liu, and Jianxun Xu. "An Analytical Model for the Uniaxial Tensile Modulus of Plain-Woven Fabric Composites and Its Application and Experimental Validation." Aerospace 9, no. 1 (2022): 26. http://dx.doi.org/10.3390/aerospace9010026.

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With advantages in efficiency and convenience, analytical models using experimental inputs to predict the mechanical properties of plain-woven fabric (PWF) composites are reliable in guaranteeing the composites’ engineering applications. Considering the importance of the aspect above, a new analytical model for predicting the uniaxial tensile modulus of PWF is proposed in this article. The composite yarns are first simplified as the lenticular-shaped cross-sections undulate along arc-composed paths. Force analyses of the yarn segments are then carried out with the internal interactions simplif

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Huaxian, Wei, Li Wei, Liu Yufei, Wang Yuqiao, and Yang Xuefeng. "Quasi-static analysis of a compliant tripod stage with plane compliant lever mechanism." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 231, no. 9 (2015): 1639–50. http://dx.doi.org/10.1177/0954406215619193.

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In nanopositioning system, the compliant tripod stages have proved to have enormous advantages for out-of-plane (z/tip/tilt) positioning in turns of compactness, simplicity in structure, and economic cost. However, most of the present-day compliant tripod stage undergo manufacturing problems due to a complicate structure, and little study has been carried out to formulate the tri-inputs and tri-outputs relationship, which is essential for precise positioning. Accordingly, this paper presents the quasi-static analysis of a novel compliant tripod stage with an equivalent plane model to achieve p

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Wang, Mingze, Cheng Zhang, Shutian Liu, and Xiaoli Wang. "Modeling and Analysis of a Conical Bridge-Type Displacement Amplification Mechanism Using the Non-Uniform Rational B-Spline Curve." Materials 16, no. 18 (2023): 6162. http://dx.doi.org/10.3390/ma16186162.

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This paper presents a new analytical model of a conical bridge-type displacement amplification mechanism (DAM) considering the effect of external loads and a piezostack actuator (PSA). With the merits of simple implementation and better fitting, the non-uniform rational B-spline (NURBS) is employed to parameterize conical connecting beams of the DAM, and an analytical model of the displacement amplification ratio and input stiffness is established based on Castigliano’s second theorem. After that, considering the interactions with elastic loads and PSA, the actual displacement amplification ra

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