Relevant bibliographies by topics / Castigliano theorems

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Academic literature on the topic 'Castigliano theorems'

Author: Grafiati
Published: 2 June 2025
Last updated: 19 July 2025

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Journal articles on the topic "Castigliano theorems"

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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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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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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 by the dummy load distribution. Knowing the Airy stress function of an isotropic beam as a function of the bending moment, the normal force, the shear force and the axial and vertical load distributions, higher-order formulae for the deflection curves and the cross section rotation are obtained. The analytical results for statically determinate and indeterminate beams for various load cases are validated by analytical and finite element results. Furthermore, the results of the extended Castigliano theory (ECT) are compared to Bernoulli–Euler and Timoshenko results, which are special cases of ECT, if only the energies caused by the bending moment and the shear force are considered. It is shown that lower-order terms for the vertical deflection exist that yield more accurate results than the Timoshenko theory. Additionally, it is shown that a distributed load is responsible for shrinking or elongation in the axial direction.
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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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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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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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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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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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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-of-plane displacements and one described the accuracy of hinge, such that the optimization model can be established to meet performance requirements of flexure hinge. Based on the optimization model, the optimization designs of hyperbolic flexure hinge are performed to acquire its optimized structural parameters. And the optimization results have showed the optimization process can meet the design requirement.
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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 desenvolvimento dos modelos matemáticos. Utiliza-se da simulação numérica, através do programa de Elementos Finitos (FEA) Ansys onde, comparam se os resultados numéricos e analíticos que foram obtidos pelas equações do presente trabalho.
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Book chapters on the topic "Castigliano theorems"

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Anand, Lallit, and Sanjay Govindjee. "Principles of minimum potential energy and complementary energy." In Continuum Mechanics of Solids. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198864721.003.0012.

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With the displacement field taken as the only fundamental unknown field in a mixed-boundary-value problem for linear elastostatics, the principle of minimum potential energy asserts that a potential energy functional, which is defined as the difference between the free energy of the body and the work done by the prescribed surface tractions and the body forces --- assumes a smaller value for the actual solution of the mixed problem than for any other kinematically admissible displacement field which satisfies the displacement boundary condition. This principle provides a weak or variational method for solving mixed boundary-value-problems of elastostatics. In particular, instead of solving the governing Navier form of the partial differential equations of equilibrium, one can search for a displacement field such that the first variation of the potential energy functional vanishes. A similar principle of minimum complementary energy, which is phrased in terms of statically admissible stress fields which satisfy the equilibrium equation and the traction boundary condition, is also discussed. The principles of minimum potential energy and minimum complementary energy can also be applied to derive specialized principles which are particularly well-suited to solving structural problems; in this context the celebrated theorems of Castigliano are discussed.
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Conference papers on the topic "Castigliano theorems"

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Chen, Guimin, Fulei Ma, Ruiyu Bai, Spencer P. Magleby, and Larry L. Howell. "A Framework for Energy-Based Kinetostatic Modeling of Compliant Mechanisms." In ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/detc2017-68205.

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Although energy-based methods have advantages over the Newtonian methods for kinetostatic modeling, the geometric nonlinearities inherent in deflections of compliant mechanisms preclude most of the energy-based theorems. Castigliano’s first theorem and the Crotti-Engesser theorem, which don’t require the problem being solved to be linear, are selected to construct the energy-based kinetostatic modeling framework for compliant mechanisms in this work. Utilization of these two theorems requires explicitly formulating the strain energy in terms of deflections and the complementary strain energy in terms of loads, which are derived based on the beam constraint model. The kinetostatic modeling of two compliant mechanisms are provided to demonstrate the effectiveness of using Castigliano’s first theorem and the Crotti-Engesser theorem with the explicit formulations in this framework. Future work will be focused on incorporating use of the principle of minimum strain energy and the principle of minimum complementary strain energy.
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Aydın, Yasemin O¨, Kevin C. Galloway, Yigit Yazicioglu, and Daniel E. Koditschek. "Modeling the Compliance of a Variable Stiffness C-Shaped Leg Using Castigliano’s Theorem." In ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2010. http://dx.doi.org/10.1115/detc2010-29190.

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This paper discusses the application of Castigliano’s Theorem to a half circular beam intended for use as a shaped, tunable, passively compliant robot leg. We present closed-form equations characterizing the deflection behavior of the beam (whose compliance properties vary along the leg) under appropriate loads. We compare the accuracy of this analytical representation to that of a Pseudo Rigid Body (PRB) approximation in predicting the data obtained by measuring the deflection of a physical half-circular beam under the application of known static loads. We briefly discuss the further application of the new model for solving the dynamic equations of a hexapod robot with a C-shaped leg.
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Odom, E. M., and C. J. Egelhoff. "Teaching deflection of stepped shafts: Castigliano's theorem, dummy loads, heaviside step functions and numerical integration." In 2011 Frontiers in Education Conference (FIE). IEEE, 2011. http://dx.doi.org/10.1109/fie.2011.6143039.

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Meghdari, A. "A Variational Approach for Modeling Flexibility Effects in Manipulator Arms." In ASME 1990 Design Technical Conferences. American Society of Mechanical Engineers, 1990. http://dx.doi.org/10.1115/detc1990-0100.

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Abstract This paper presents a general technique to model flexible components (mainly links and joints flexibilities are considered) of manipulator arms based on the 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 Cartesian space. Once these deformations are computed, they may be used to correct for the positional errors arisen from the robotic structural deformations in the motion control algorithms.
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Esteki, H., and A. Hasannia. "Multi-Objective Optimization of Piezoelectric Microactuator Using Genetic Algorithms." In ASME 2008 International Mechanical Engineering Congress and Exposition. ASMEDC, 2008. http://dx.doi.org/10.1115/imece2008-66909.

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In flex-tensional piezoactuators, due to the low displacement of piezostacks, a compliant mechanism is used to amplify displacement of piezostack. In this paper, optimization of a compliant mechanism with corner-filleted flexure hinges is carried out using real-coded genetic algorithms (GAs) to avoid trapping in local optimums. The objective functions are displacement amplification and stiffness of mechanism and design variables are cross-sectional size and material used. The constraints which are applied on mechanism are based on piezostack dimensions and manufacturing limits. Displacement amplification and stiffness are calculated using strain energy and Castigliano’s displacement theorem.
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Antoine, J. F., G. Abba, and C. Sauvey. "Approximate Explicit Calculation of First Vibration Frequencies of an Unsymmetrical High Speed Rotor." In ASME 2003 International Mechanical Engineering Congress and Exposition. ASMEDC, 2003. http://dx.doi.org/10.1115/imece2003-55133.

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In order to easily predict and optimize the dynamic behavior of a high speed switched reluctance motor, a full analytic model, that gives directly and quickly the three first eigenfrequencies of the rotor, is proposed. The rotor is modelled as a 3 DOF Timoshenko’s beam model. The stiffness matrix is calculated with the Castigliano’s second theorem in structural analysis, which allows to obtain explicitly the eigenfrequencies expression and prevents to use classical finite element analysis. The influence of design and material modifications is studied and the dynamic behavior quickly predicted. The calculation time needed for testing a geometry is strongly smaller than with a finite element analysis.
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Liu, Pengbo, Songsong Lu, Peng Yan, and Zhen Zhang. "Kinetostatics Modeling and Decoupling Analysis of a Crosshair Flexures-Based Nanopositioner." In ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/detc2017-68097.

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In the present paper, we take the input and output decoupling into account and propose a 2-DOF parallel nanopositioner, which is composed of lever amplification mechanisms, compound parallelogram mechanisms and novel crosshair flexures. In order to demonstrate the decoupling performance improvement of the crosshair flexures, the stiffness model of the crosshair flexures and the kinetostatics model of the nanopositioner are established based on Castigliano’s theorem and the compliance matrix method. Accordingly, the input and output decoupling compliance matrix models are derived to demonstrate the excellent decoupling property of the crosshair flexures based nanopositioner, which is further verified by finite-element analysis and experimental results. The open-loop experiments on the prototype stage demonstrate the maximum stroke of the nanopositioner is up to 65μm and the cross axis coupling errors are less than 1.6%.
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Bai, Shaoping, Lasse Køgs Andersen, and Carsten Rebbe Mølgaard. "Kinematics and Stiffness Modeling of a 4-DOF Parallel Robot for Schönflies Motion Generation." In ASME 2014 12th Biennial Conference on Engineering Systems Design and Analysis. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/esda2014-20094.

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This work deals with the design of parallel robots for the generation of pick-and-place operation, or Schönflies motion. The aim is to develop a robot with workspace optimized for fast pick-and-place operations, namely, a robot with a superellipsoidal reachable volume, which suits best for the pick-and-place operations on conveyers, where robots’ working areas are nearly rectangular. In this paper, the kinematics and stiffness modeling of the new robot are presented. A method of stiffness modeling by means of Castigliano’s Theorem is developed. Using the new method, the stiffness of the robot is analyzed. The results are compared with FEA simulation, which shows a good agreement between the results. The method is finally applied to the engineering design of the new robot for enhanced static and dynamic performance.
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Lindkvist, Lars. "Stiffness Model of Coiled Springs Including the Axial Asymmetry due to the Helical Geometry." In ASME 1994 Design Technical Conferences collocated with the ASME 1994 International Computers in Engineering Conference and Exhibition and the ASME 1994 8th Annual Database Symposium. American Society of Mechanical Engineers, 1994. http://dx.doi.org/10.1115/detc1994-0247.

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Abstract The stiffness of a short section of a coiled spring is derived by writing the elastic energy in the spring wire, considering its actual geometric form, and then applying the Castigliano theorem. The resulting linear stiffness model includes the effects of pitch, curvature of the wire and distortion due to normal and transverse forces in the wire. Further, the starting and ending points of the spring wire are taken into consideration. This stiffness model is used to derive the locally linearized stiffness matrix for a complete coiled spring that is laterally loaded. The stiffness matrix is evaluated by first calculating the non-linear deformation for a given external load and then linearizing the analysis about that equilibrium point. The deformation is calculated by summing the contributions from a number of small spring elements for which the deformations are considered to be linear. The natural frequencies of a mechanical system consisting of a rigid body and a laterally loaded spring are calculated and compared with experimental results. These experiments clearly verify the proposed theoretical stiffness matrix for the complete spring and detect the rotational asymmetry of the spring.
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Rezaei, Amir, Alireza Akbarzadeh, and Javad Enferadi. "Stiffness Analysis of a Spatial Parallel Mechanism With Flexible Moving Platform." In ASME 2010 10th Biennial Conference on Engineering Systems Design and Analysis. ASMEDC, 2010. http://dx.doi.org/10.1115/esda2010-24560.

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In this paper, stiffness analysis of a 3-DOF spatial, 3-PSP type, parallel manipulator is investigated. Most previous stiffness analysis studies of parallel manipulators are performed using lumped model as well as assuming a rigid moving platform. In this paper, unlike traditional stiffness analysis, the moving platform is assumed to be flexible. Additionally, a continuous method is used for obtaining mathematical model of the manipulator stiffness matrix. This method is based on strain energy and Castigliano’s theorem [1]. For this purpose, first we solve inverse kinematics problem then We must find relationship between the applied external torques on the moving platform and the resultant joints forces. Next, strain energy moving platform is calculated. Strain energy of this element is calculated using force analysis and inverse kinematics problem. Finally, a FEM model is generated and used to simulate the physical structure. Simulation results are compared with the analytical model.
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