Static deflection modeling of combined flexible beams using elliptic integral solution

Xu, Ke; Liu, Haitao; Xiao, Juliang

doi:10.1016/j.ijnonlinmec.2020.103637

Cited by 18 publications

(9 citation statements)

References 48 publications

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“…Before designing and fabricating the structures in detail, a performance prediction should be performed and analyzed. Scholars has developed several methods to evaluate the performance of inclined fixed-guided beams [22], such as pseudo-rigid-body models [23][24][25], elliptic integral models [26][27][28] and finite element models [29]. In all the above mentioned methods, the elliptic integral solution is generally considered to be the most accurate method for analyzing large deflections of thin beams in compliant mechanisms [26].…”

Section: Design Simulation and Modelingmentioning

confidence: 99%

Design and Analysis of a Novel Compliant Tensile Testing Module Based on Buckled Fixed-Guided Beam

et al. 2021

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The need to accurately measure the mechanical properties of freestanding thin films such as carbon nanotube reinforced nanocomposite thin films and various buckypaper is increasingly urgent. This paper presents the design and control of a novel compliant tensile testing module based on buckled fixedguided beams aimed at accurately measuring the mechanical properties of free-standing thin films. The piezoelectric stack actuator that can provide high resolution for the output displacement is chosen to actuate the tensile testing module. The advantages of the module are its compactness, no friction, no wear, low cost and good repeatability. The performance is further evaluated by the established analytical model using the elliptic integral approach and the nonlinear finite-element analysis (FEA). A metal prototype of the tensile testing design has been fabricated and the performance of the fabricated prototype is investigated through open-loop displacement response experiments. Experimental results demonstrate the effectiveness of the proposed ideas for the mechanism. The design holds great potential applications in measuring mechanical properties of free-standing thin-film materials such as carbon nanotube reinforced nanocomposite thin films and various buckypaper as well as other freestanding thin-film materials.

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Section: Design Simulation and Modelingmentioning

confidence: 99%

Design and Analysis of a Novel Compliant Tensile Testing Module Based on Buckled Fixed-Guided Beam

et al. 2021

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“…Zhang and Chen (2013) proposed a complete elliptic integral solution method for a complex bending problem of plane beams with multiple inflection points, thus expanding the solution ability of the elliptic integral method. Xu et al (2021) studied the accurate solution of large deflection of composite elastic beams based on the elliptic integral. Inspired by the previous studies, this method in the design of the cryogenic wind tunnel is explored in this paper.…”

Section: Introductionmentioning

confidence: 99%

Design and validation of a single-jack variable Mach number nozzle in a cryogenic transonic wind tunnel

Yu¹,

Wang²,

Nie³

et al. 2022

Journal of Theoretical and Applied Mechanics

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The wind tunnel with variable Mach numbers controlled by a single jack is highly desired in the aerospace, automobile and building industry due to its superior controllability and working range. Decreasing the temperature of a test gas is an efficient and economical approach to achieving higher Reynolds numbers that accommodate all working statuses of test subjects, which however, brings new challenges to the wind tunnel design nowadays. This paper proposes a new design concept of a single-jack variable Mach number nozzle based on its particular cryogenic characteristics, as the nozzle is the core structure to achieve variable Mach numbers. The contours of the nozzle under different Reynolds numbers and Mach numbers are modeled and solved by an incomplete elliptic integral, followed by modification with cryogenic characteristics. A 0.3-m cryogenic wind tunnel is utilized as a validation platform for the nozzle design, resulting in designed contours being in line with the measured contours. Moreover, the root means square (RMS) deviations of Mach number 1.3 at the core position are controlled within 0.011 in low and high temperatures, which surpasses the other existing wind tunnels.

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“…[14,15], but a single beam element is only accurate for small deformation. An analytical solution for large bending of beams exist which is based on elliptic integrals [16][17][18][19]. However, the application of this solution in 3D leads to an infinite series of elliptic integrals [20,21].…”

Section: Introductionmentioning

confidence: 99%

Efficient Computation of Large Deformation of Spatial Flexure-Based Mechanisms in Design Optimizations

Dwarshuis

Aarts

Ellenbroek

et al. 2022

Journal of Mechanisms and Robotics

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Design optimizations of flexure-based mechanisms take a lot of computation time, in particular when large deformations are involved. In an optimization procedure statically deformed configurations of many designs have to be obtained, while finding the statically deformed configuration itself requires tens to hundreds of load step iterations. The kinematically started deformation method (KSD-method) [1] computes deformed configurations fast by starting the computation from an approximation. This approximation is obtained by allowing the mechanism only to move in the motion-direction, based on kinematic equations, using data of the flexure joints in the mechanism. This is possible as flexure based mechanisms are typically designed to be kinematically determined in the motion directions. In this paper the KSD-method is extended such that it can also be applied without joint-data, such that it is not necessary to maintain a database with joint-data. This paper also shows that the method can be used for mechanisms containing joints that allow full spatial motion. Several variants of the KSD method are presented and evaluated for accuracy and required computation time. One variant, which uses joint-data, is 21 times faster and shows errors in stress and stiffness below 1%, compared to a conventional multibody analysis on the same model. Another variant, which does not use joint-data, reduces the computation time by a factor of 14, keeping errors below 1%. The KSD-method is shown to be helpful in design optimizations of complex flexure mechanisms for large range of motion.

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Static deflection modeling of combined flexible beams using elliptic integral solution

Cited by 18 publications

References 48 publications

Design and Analysis of a Novel Compliant Tensile Testing Module Based on Buckled Fixed-Guided Beam

Design and Analysis of a Novel Compliant Tensile Testing Module Based on Buckled Fixed-Guided Beam

Design and validation of a single-jack variable Mach number nozzle in a cryogenic transonic wind tunnel

Efficient Computation of Large Deformation of Spatial Flexure-Based Mechanisms in Design Optimizations

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