Symmetric Equations for Evaluating Maximum Torsion Stress of Rectangular Beams in Compliant Mechanisms

Chen, Guimin; Howell, Larry L.

doi:10.1186/s10033-018-0214-9

Cited by 10 publications

(8 citation statements)

References 27 publications

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“…When finalizing a design, consideration of the elastic limits is required. Equations of maximum stress of LET joints [13,39] can be applied to determine the stresses of LET arrays.…”

Section: Finite Element Analysis Comparisonmentioning

confidence: 99%

Load–Displacement Characterization in Three Degrees-of-Freedom for General Lamina Emergent Torsion Arrays

Pehrson

Bilancia

Magleby

et al. 2020

Journal of Mechanical Design

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Lamina emergent torsion (LET) joints for use in origami-based applications enables folding of panels. Placing LET joints in series and parallel (formulating LET arrays) opens the design space to provide for tunable stiffness characteristics in other directions while maintaining the ability to fold. Analytical equations characterizing the elastic load–displacement for general serial–parallel formulations of LET arrays for three degrees-of-freedom are presented: rotation about the desired axis, in-plane rotation, and extension/compression. These equations enable the design of LET arrays for a variety of applications, including origami-based mechanisms. These general equations are verified using finite element analysis, and to show variability of the LET array design space, several verification plots over a range of parameters are provided.

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“…When finalizing a design, consideration of the elastic limits is required. Equations of maximum stress of LET joints [13,39] can be applied to determine the stresses of LET arrays.…”

Section: Finite Element Analysis Comparisonmentioning

confidence: 99%

Load–Displacement Characterization in Three Degrees-of-Freedom for General Lamina Emergent Torsion Arrays

Pehrson

Bilancia

Magleby

et al. 2020

Journal of Mechanical Design

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“…where k t is the stiffness of the torsion beams and k b is the stiffness of the bending member. The torsional stiffness k t is found from [28] k t ¼…”

Section: Single Lamina Emergent Torsionalmentioning

confidence: 99%

“…Numerous approximations for the shear stress in a rectangular beam are available, and a particularly accurate approximation is provided by Chen and Howell [28] as…”

Section: Single Lamina Emergent Torsionalmentioning

confidence: 99%

Regional Stiffness Reduction Using Lamina Emergent Torsional Joints for Flexible Printed Circuit Board Design

DeFigueiredo

Zimmerman

Russell

et al. 2018

Journal of Electronic Packaging

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Flexible printed circuit boards (PCBs) make it possible for engineers to design devices that use space efficiently and can undergo changes in shape and configuration. However, they also suffer from tradeoffs due to nonideal material properties. Here, a method is presented that allows engineers to introduce regions of flexibility in otherwise rigid PCB substrates. This method employs geometric features to reduce local stiffness in the PCB, rather than reducing the global stiffness by material selection. Analytical and finite element models are presented to calculate the maximum stresses caused by deflection. An example device is produced and tested to verify the models.

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“…The methods of designing compliant mechanisms generally include two types. The first is the pseudo-rigid-body model-based method [6], which has been successfully adopted to design lumped compliant mechanisms with flexure hinges. The second is the topology optimization approach [7], which is mainly applied to design fully compliant mechanisms.…”

Section: Introductionmentioning

confidence: 99%

Topological Design of Multi-Material Compliant Mechanisms with Global Stress Constraints

Zhan

Luo

et al. 2021

Micromachines

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This paper presents an approach for the topological design of multi-material compliant mechanisms with global stress constraints. The element stacking method and the separable stress interpolation scheme are applied to calculate the element stiffness and element stress of multi-material structures. The output displacement of multi-material compliant mechanisms is maximized under the constraints of the maximum stress and the structural volume of each material. The modified P-norm method is applied to aggregate the local von Mises stress constraints for all the finite elements to a global stress constraint. The sensitivities are calculated by the adjoint method, and the method of moving asymptotes is utilized to update the optimization problem. Several numerical examples are presented to demonstrate the effectiveness of the proposed method. The appearance of the de facto hinges in the optimal mechanisms can be suppressed effectively by using the topology optimization model with global stress constraints, and the stress constraints for each material can be met.

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Symmetric Equations for Evaluating Maximum Torsion Stress of Rectangular Beams in Compliant Mechanisms

Cited by 10 publications

References 27 publications

Load–Displacement Characterization in Three Degrees-of-Freedom for General Lamina Emergent Torsion Arrays

Load–Displacement Characterization in Three Degrees-of-Freedom for General Lamina Emergent Torsion Arrays

Regional Stiffness Reduction Using Lamina Emergent Torsional Joints for Flexible Printed Circuit Board Design

Topological Design of Multi-Material Compliant Mechanisms with Global Stress Constraints

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