Engineering Commons^™

Symmetric Equations For Evaluating Maximum Torsion Stress Of Rectangular Beams In Compliant Mechanisms, Guimin Chen, Larry L. Howell

Faculty Publications

There are several design equations available for calculating the torsional compliance and the maximum torsion stress of a rectangular cross-section beam, but most depend on the relative magnitude of the two dimensions of the cross-section (i.e.,the thickness and the width). After reviewing the available equations, two thickness-to-width ratio independent equations that are symmetric with respect to the two dimensions are obtained for evaluating the maximum torsion stress

of rectangular cross-section beams. Based on the resulting equations, outside lamina emergent torsional joints are analyzed and some useful design insights are obtained. These equations, together with the previous work on symmetric equations …

Kinematic/Static Model Of Complex Compliant Mechanisms With Serial-Parallel Substructures: A General Approach, Mingxiang Ling, Junyi Cao, Larry L. Howell

Faculty Publications

Kinematic and static analyses of compliant mechanisms are crucial at the early stage of design, and it can be difficult and laborsome for complex configurations with distributed compliance. In this paper, a general and concise kinematic/static modeling method of flexure-hinge-based compliant mechanisms with arbitrary serial-parallel substructures is presented to provide accurate and efficient solutions by combining the matrix displacement method with the transfer matrix method. The transition between the elemental stiffness matrix and the transfer matrix of the flexure hinge and the flexible beam is straightforward, enabling the condensation of a hybrid serial-parallel substructure into one equivalent element simple. Then, …

Origami-Inspired Sacrificial Joints For Folding Compliant Mechanisms, Todd G. Nelson, Alex Avila, Larry L. Howell, Just L. Herder, Davood Farhadi Machekposhtic

Faculty Publications

Folding is a manufacturing method which can create complex 3D geometries from flat materi- als and can be particularly useful in cost-sensitive or planar-limited fabrication applications.

This paper introduces compliant mechanisms that employ folding techniques from origami to evolve from a flat material to deployed state. We present origami-inspired sacrificial joints, joints which have mobility during assembly of the mechanism but are rigid in their final position, to create regions of high and low stiffness and the proper alignment of compliant flexures in folded mechanisms. To demonstrate the method we fold steel sheet to create some well-known and complex compliant …

Normalized Coordinate Equations And Energy Method For Predicting Natural Curved-Fold Configurations, Jacob Badger, Todd G. Nelson, Rober J. Lang, Denise M. Halverson, Larry L. Howell

Faculty Publications

Of the many valid configurations that a curved fold may assume, it is of particular interest to identify natural—or lowest energy—configurations that physical models will preferentially assume. We present normalized coordinate equations—equations that relate fold surface properties

to their edge of regression—to simplify curved-fold rela- tionships. An energy method based on these normalized

coordinate equations is developed to identify natural con- figurations of general curved folds. While it has been noted

that natural configurations have nearly planar creases for curved folds, we show that non-planar behavior near the crease ends substantially reduces the energy of a fold.

Regional Stiffness Reduction Using Lamina Emergent Torsional Joints For Flexible Printed Circuit Board Design, Bryce P. Defigueiredo, Brian Dale Russell, Trent K. Zimmerman, Larry L. Howell

Faculty Publications

Flexible printed circuit boards (PCBs) make it possi- ble for engineers to design devices that use space efficiently

and can undergo changes in shape and configuration. How- ever, they also suffer from trade-offs due to non-ideal mate- rial properties. Here, a method is presented that allows en- gineers 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 fi- nite element models are presented to calculate the maximum

stresses caused by deflection. An example device is produced …

Origami-Based Design Of Conceal-And-Reveal Systems, Bryce P. Defigueiredo, Kyler A. Tolman, Spencer P. Magleby, Nathan A. Pehrson, Erica Crampton, Larry L. Howell

Faculty Publications

This work introduces a type of motion termed “conceal-and-reveal” which is characterized by a state that protects a payload, a state that exposes the payload, and coupled motions between these two states. As techniques for thick, rigid origami-based engineering designs are being developed, origami is becoming increasingly more

attractive as inspiration for complex systems. This paper proposes a process for designing origami-based conceal- and-reveal systems, which can be generalized to design similar thick, rigid origami-based systems. The process

is demonstrated through the development of three conceal-and-reveal systems that present a luxury product to the consumer. The three designs also confirm …

A Pseudo-Static Model For Dynamic Analysis On Frequency Domain Of Distributed Compliant Mechanisms, Mingxiang Ling, Larry L. Howell, June Cao, Zhou Jiang

Faculty Publications

This paper presents a pseudo-static modeling methodology for dynamic analysis of distributed compliant mechanisms to provide accurate and efficient solutions. First, a dynamic stiffness matrix of the flexible beam is deduced, which has the same definition and a similar form as the traditional static compliance/stiffness matrix but is frequency-dependent. Second, the pseudo-static modeling procedure for the dynamic analysis is implemented in a statics-similar way. Then, all the kinematic, static and dynamic performances of compliant mechanisms can be analyzed based on the pseudo- static model. The superiority of the proposed method is that when it is used for the dynamic modeling …

Aerostructural Predictions Combining Fenics And A Viscous Vortex Particle Method, Ryan Anderson, Andrew Ning, Ru Xiang, Sebastiaan P. C. Van Schie, Mark Sperry, Darshan Sarojini, David Kamensky, John T. Hwang

Faculty Publications

Electric Vertical Takeoff and Landing (eVTOL) aircraft experience complex, unsteady aerodynamic interactions between rotors, wings, and fuselage that can make design difficult. We introduce a new framework for predicting aerostructural interactions. Specifically, we demonstrate the coupling of a finite element solver with Reissner-Mindlin shell theory for computing deflections and a viscous vortex particle for capturing wakes. We perform convergence studies of the aerodynamics and the coupled aerostructural model. Finally, we share some preliminary results of the dynamic aeroelastic response of Uber’s eCRM-002 main wing, and share some qualitative observations.

Low-Fidelity Design Optimization And Parameter Sensitivity Analysis Of Tilt-Rotor Evtol Electric Propulsion Systems, Tyler Critchfield, Andrew Ning

Faculty Publications

Urban air mobility requires a multidisciplinary approach to tackle the important chal- lenges facing the design of these aircraft. This work uses low-to-mid fidelity tools to model rotor aerodynamics, blade structures, vehicle aerodynamics, and electric propulsion for a tilt-rotor electric vertical takeoff and landing (eVTOL) aircraft. We use gradient-based design optimization and extensive parameter sensitivity analysis to explore the design space and complex tradeoffs of tilt-rotor distributed electric propulsion systems.

Sparsity For Gradient-Based Optimization Of Wind Farm Layouts, Benjamin T. Varela, Andrew Ning

Faculty Publications

Optimizing wind farm layouts is an important step in designing an efficient wind farm. Optimizing wind farm layouts is also a difficult task due to computation times increasing with the number of turbines present in the farm. The most computationally expensive part of gradient- based optimization is calculating the gradient. In order to reduce the expense of gradient calculation, we performed a study on the use of sparsity in wind farm layout optimization. This paper presents the findings of the sparsity study and provides a method to use sparsity in wind farm layout optimization. We tested this sparsity method by …

A Coupled Source Panel, Actuator Line, And Viscous Vortex Particle Method In An O(N) Scheme, Ryan Anderson, Andrew Ning

Faculty Publications

Wake interactions play a significant role in aerodynamics. However, common modeling approaches are either expensive or lack fidelity, making them unreliable or difficult to use in the design process. The vortex particle method can capture the relevant physics effectively, but imposing boundary conditions with solid surfaces in a computationally efficient way is challenging. We explore two possible methods of imposing solid surface boundary conditions of vortex particle simulations. The first, a novel variation on a pure particle approach, is easy to implement but is moderately expensive, and suffers from some numerical instability. The second, source panels accelerated with a fast …