A closed-form model for nonlinear spatial deflections of rectangular beams in intermediate range

Bai, Ruiyu; Awtar, Shorya; Chen, Guimin

doi:10.1016/j.ijmecsci.2019.06.042

Cited by 30 publications

(4 citation statements)

References 23 publications

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“…When the deformation of the FLS is small, i.e., less than 0.1 L , the following approximate relationship can be satisfied [ 31 ]:

…”

Section: Six-dof Compliance Model Of the Fls Element Under Small Defo...mentioning

confidence: 99%

“…The relationship between the expansion/contraction deformation of the FLS and F X can be expressed as follows [ 31 ]:

…”

Section: Six-dof Compliance Model Of the Fls Element Under Small Defo...mentioning

confidence: 99%

“…Nijenhuis et al [ 30 ] presented a modeling approach for obtaining insight into the deformation and stiffness characteristics of general 3D flexure strips that undergo bending, shear, and torsion deformation. Bai et al [ 31 , 32 , 33 ] proposed load–displacement relationships for rectangular and large-aspect-ratio beams by solving their nonlinear governing differential equations using the power series method.…”

Section: Introductionmentioning

confidence: 99%

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A New Nonlinear Spatial Compliance Model Method for Flexure Leaf Springs with Large Width-to-Length Ratio under Large Deformation

Zhang

Pan

et al. 2022

Micromachines

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Flexure leaf spring (FLS) with large deformation is the basic unit of compliant mechanisms with large stroke. The stiffness along the non-working directions of FLSs with large width-to-length ratio (w/L) is high. The motion stability of the compliant mechanism based on this type of FLS is high. When this type of FLS is loaded along the width direction, the shear deformation needs to be characterized. Nevertheless, currently available compliance modeling methods for FLS are established based on Euler–Bernoulli beam model and cannot be used to characterize shear models. Therefore, these methods are not applicable in this case. In this paper, a new six-DOF compliance model for FLSs with large w/L is established under large deformation. The shear deformation along the width direction model is characterized based on the Timoshenko beam theory. The new constraint model and differential equations are established to obtain a high-precision compliance model expression for this type of FLS. The effects of structural parameters on the compliance of the FLS are analyzed. Finally, the accuracy of the model is verified both experimentally and by finite element simulation. The relative error between theoretical result and experiment result is less than 5%.

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“…When the deformation of the FLS is small, i.e., less than 0.1 L , the following approximate relationship can be satisfied [ 31 ]:

…”

Section: Six-dof Compliance Model Of the Fls Element Under Small Defo...mentioning

confidence: 99%

“…The relationship between the expansion/contraction deformation of the FLS and F X can be expressed as follows [ 31 ]:

…”

Section: Six-dof Compliance Model Of the Fls Element Under Small Defo...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A New Nonlinear Spatial Compliance Model Method for Flexure Leaf Springs with Large Width-to-Length Ratio under Large Deformation

Zhang

Pan

et al. 2022

Micromachines

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“…extended for different modeling scenarios of nonlinear deflections [3,[24][25][26], which makes the framework extensible.…”

Section: Crotti-engesser Theoremmentioning

confidence: 99%

An Energy-Based Framework for Nonlinear Kinetostatic Modeling of Compliant Mechanisms Utilizing Beam Flexures

Chen

Ma²,

Bai

et al. 2021

Journal of Computing and Information Science in Engineering

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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 the explicit formulations in this framework derived from Castigliano's first theorem and the Crotti-Engesser theorem.

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Nonlinear Strain Energy Formulation of Spatially Deflected Strip Flexures

Bai,

Yang,

et al. 2023

Mechanisms and Machine Science

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A closed-form model for nonlinear spatial deflections of rectangular beams in intermediate range

Cited by 30 publications

References 23 publications

A New Nonlinear Spatial Compliance Model Method for Flexure Leaf Springs with Large Width-to-Length Ratio under Large Deformation

A New Nonlinear Spatial Compliance Model Method for Flexure Leaf Springs with Large Width-to-Length Ratio under Large Deformation

An Energy-Based Framework for Nonlinear Kinetostatic Modeling of Compliant Mechanisms Utilizing Beam Flexures

Nonlinear Strain Energy Formulation of Spatially Deflected Strip Flexures

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