Mary Frecker

Topological Synthesis of Compliant Mechanisms Using Multi-Criteria Optimization

Compliant mechanisms are mechanical devices that achieve motion via elastic deformation. A new method for topological synthesis of single-piece compliant mechanisms is presented, using a “design for required deflection” approach. A simple beam example is used to illustrate this concept and to provide the motivation for a new multi-criteria approach for compliant mechanism design. This new approach handles motion and loading requirements simultaneously for a given set of input force and output deflection specifications. Both a truss ground structure and a two-dimensional continuum are used in the implementation which is illustrated with design examples.

Topology optimization of compliant mechanisms using the homogenization method

A procedure to obtain a topology of an optimal structure considering flexibility is presented. The methodology is based on a mutual energy concept for formulation of flexibility and the homogenization method. A multi-objective optimization problem is formulated as an application of compliant mechanism design. Some examples of the design of compliant mechanisms for plane structures are presented. ( 1998 John Wiley & Sons, Ltd.

Recent Advances in Optimization of Smart Structures and Actuators

Much of the recent and past work in the area of smart materials and structures has focused on analysis of actuators and actively controlled systems. Although many sophisticated analysis models have been developed, they are often coupled with ad hoc design methods or informal optimization procedures. A subset of the work done by the smart structures community has focused on development of formal design methodologies and optimization methods specifically for smart actuators and structures. The objective of this paper is to review the current work in development of design methodologies and application of formal optimization methods to the design of smart structures and actuators. In a related paper, optimization strategies for sensor and actuator placement were reviewed by a researcher at NASA Langley in 1999. The current paper reviews the recent work done in this area since 1999, in addition to optimization strategies for topology design of actuators, actively controlled structures, and drive electronics design. The main focus is on piezoelectric ceramic actuators, but relevant work in shape memory alloys and magnetostrictive actuation are included as well. Future directions for research in optimization are also recommended.

A Nonlinear Model for Dielectric Elastomer Membranes

The material and geometrical nonlinearities of novel dielectric elastomer actuators make them more difficult to model than linear materials used in traditional actuators. To accurately model dielectric elastomers, a comprehensive mathematical formulation that incorporates large deformations, material nonlinearity, and electrical effects is derived using Maxwell-Faraday electrostatics and nonlinear elasticity. The analytical model is used to numerically solve for the resultant behavior of an inflatable dielectric elastomer membrane, subject to changes in various system parameters such as prestrain, external pressure, applied voltage, and the percentage electroded membrane area. The model can be used to predict acceptable ranges of motion for prescribed system specifications. The predicted trends are qualitatively supported by experimental work on fluid pumps [A. Tews, K. Pope, and A. Snyder, Proceedings SPIE, 2003)]. For a potential cardiac pump application, it is envisioned that the active dielectric elastomer membrane will function as the motive element of the device.

Efficient Pareto Frontier Exploration using Surrogate Approximations

In this paper we present an efficient and effective method of using surrogate approximations to explore the design space and capture the Pareto frontier during multiobjective optimization. The method employs design of experiments and metamodeling techniques (e.g., response surfaces and kriging models) to sample the design space, construct global approximations from the sample data, and quickly explore the design space to obtain the Pareto frontier without specifying weights for the objectives or using any optimization. To demonstrate the method, two mathematical example problems are presented. The results indicate that the proposed method is effective at capturing convex and concave Pareto frontiers even when discontinuities are present. After validating the method on the two mathematical examples, a design application involving the multiobjective optimization of a piezoelectric bimorph grasper is presented. The method facilitates multiobjective optimization by enabling us to efficiently and effectively obtain the Pareto frontier and identify candidate designs for the given design requirements.

Aircraft structural morphing using tendon-actuated compliant cellular trusses

Recently, smoothly-deforming aircraft structures have been investigated for their ability to adapt to varying flight conditions. Researchers aim to achieve large changes in the shape of the wings: area changes of up to 50% and aspect-ratio changes of up to 200% are being pursued. The research described in this paper aims to develop a structural concept capable of achieving continuous stable deformations over a large range of aircraft shapes. The basic concept underlying the approach is a compliant cellular truss, with tendons used as active elements. The truss members of the unit cell are connected through compliant joints such that only modest bending moments may be transmitted from one member to another. Actuation is achieved by pulling on one set of cables while releasing another set. The tendonactuated compliant truss can be made to behave locally, and temporarily, as a nearmechanism, by releasing appropriate cables. As a result, in the absence of aerodynamic forces, the structure can be morphed using relatively low forces. The cables are reeled in or released in a controlled manner while the structure is loaded, hence, the stability of the structure can be maintained in any intermediate position. Highly-distributed actuation also enables the simultaneous achievement of global shape changes as the accumulation of local ones, while the use of compliant joints rather than true rotating joints eliminates binding as a significant concern. A six-noded octahedral cell with diagonal tendon actuation is developed for a bending type deformation in the wing. Initial cell geometry is determined by “strain matching” to the local morphing deformation required by the application. A finite element analysis is performed on a wing made of these unit cells and sized for a representative UAV weighing 3000 lbs. The areas of the individual truss members are sized so that they don’t fail or buckle under the air loads, while deflection at the wing tip is reduced. The octahedral unit cell is capable of achieving smooth deformations of the truss structure. The cell size is dictated by the available space and the morphing strain. The cell sizes are reasonable for strains on the order of 10% to 15% and get smaller for larger strains. Additional cell shapes are being investigated for larger area changes through a process of topology optimization using genetic algorithms. Numerous other technical challenges remain, including the details of actuation and a robust skin.

Modeling of a dielectric elastomer diaphragm for a prosthetic blood pump

The electromechanical behavior of dielectric elastomers is to be exploited for medical application in artificial blood pumps. It is required that the pump diaphragm achieves a swept volume increase of 70 cc into a systolic pressure of 120 mmHg with the main design objective being volumetric efficiency. As such, a model that accommodates large deformation behavior is used. In order to design prosthetic blood pumps that closely mimic the natural pumping chambers of the heart, a dielectric elastomer diaphragm design is proposed. The elastomers change in shape in response to the applied electric field will permit it to be the active element of the pump just as the ventricular walls are in the natural heart. A comprehensive analytical model that accounts for the combined elastic and dielectric behavior of the membrane is used to compute the stresses and deformations of the inflated membrane. Dielectric elastomers are often pre-strained in order to obtain optimal electromechanical performance. The resulting model incorporates pre-strain and shows how system parameters such as pre-strain, pressure, electric field, and edge constraints affect membrane deformation. The model predicts more than adequate volume displacement for moderate pre-strain of the elastomer.

Topology optimization of compliant mechanisms with multiple outputs

A procedure for the topology design of compliant mechanisms with multiple output requirements is presented. Two methods for handling the multiple output requirements are developed, a combined virtual load method and a weighted sum of objectives method. The problem formulations and numerical solution procedures are discussed and illustrated by design examples. The examples illustrate the capabilities of the design procedure, the effect of the direction of the output deflection requirements on the solution, as well as computational issues such as the effect of the starting point and effect of the material resource constraint.

Sequence and task analysis of instrument use in common laparoscopic procedures

Background: In the area of instrument evaluation, one aspect that still requires objective assessment is the dynamics of instrument maneuver and exchange. If we could gain a better understanding of these phenomena, we could improve the design of the instruments themselves. Methods: A total of 29 laparoscopic procedures were videotaped and reviewed using time motion analysis. Instrument multifunctionality was determined using a standardized list of laparoscopic maneuvers. State transition diagrams were utilized to document the sequence of instrument exchanges. Results: The curved dissector, atraumatic grasper, and cautery scissors were identified as the most multifunctional instruments; each was able to perform five distinct maneuvers. Instrument sequences were found to consist of a three-part dissect ? clip ? cut cycle and a two-part dissect ? suction cycle of instrument exchange. Conclusion: This study demonstrated that laparoscopic instruments are often used to perform a variety of maneuvers in addition to their primary function. Furthermore, there are common patterns in instrument exchange that provide a potential source of design parameters for improved surgical efficiency.

Design of a PZT Bimorph Actuator Using a Metamodel-Based Approach

The design of a variable thickness piezoelectric bimorph actuator for application to minimally invasive surgery is proposed. The actuator is discretized into five segments along its length, where the thicknesses of the segments are used as design variables in the problem of optimizing both the force and deflection at the tip. Metamodeling techniques are used to construct computationally inexpensive approximations of finite element simulations and to rapidly explore the design space and the Pareto frontier. A prototype device and experimental verification of the analytical results are also discussed.