This chapter introduces the finite element method (FEM) as a tool for solution of classical electromagnetic problems. Although we discuss the main points in the application of the finite element method to electromagnetic design, including formulation and implementation, those who seek deeper understanding of the finite element method should consult some of the works listed in the bibliography section.

Introduction to the Finite Element Method

Analysis of cellular mechanotransduction, the mechanism by which cells convert mechanical signals into biochemical responses, has focused on identification of critical mechanosensitive molecules and cellular components. Stretch-activated ion channels, caveolae, integrins, cadherins, growth factor receptors, myosin motors, cytoskeletal filaments, nuclei, extracellular matrix, and numerous other structures and signaling molecules have all been shown to contribute to the mechanotransduction response. However, little is known about how these different molecules function within the structural context of living cells, tissues, and organs to produce the orchestrated cellular behaviors required for mechanosensation, embryogenesis, and physiological control. Recent work from a wide range of fields reveals that organ, tissue, and cell anatomy are as important for mechanotransduction as individual mechanosensitive proteins and that our bodies use structural hierarchies (systems within systems) composed of interconnected networks that span from the macroscale to the nanoscale in order to focus stresses on specific mechanotransducer molecules. The presence of isometric tension (prestress) at all levels of these multiscale networks ensures that various molecular scale mechanochemical transduction mechanisms proceed simultaneously and produce a concerted response. Future research in this area will therefore require analysis, understanding, and modeling of tensionally integrated (tensegrity) systems of mechanochemical control.

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Cellular mechanotransduction: putting all the pieces together again.

We consider distributed parameter systems where the underlying dynamics are spatially invariant, and where the controls and measurements are spatially distributed. These systems arise in many applications such as the control of vehicular platoons, flow control, microelectromechanical systems (MEMS), smart structures, and systems described by partial differential equations with constant coefficients and distributed controls and measurements. For fully actuated distributed control problems involving quadratic criteria such as linear quadratic regulator (LQR), H/sub 2/ and H/sub /spl infin//, optimal controllers can be obtained by solving a parameterized family of standard finite-dimensional problems. We show that optimal controllers have an inherent degree of decentralization, and this provides a practical distributed controller architecture. We also prove a general result that applies to partially distributed control and a variety of performance criteria, stating that optimal controllers inherit the spatial invariance structure of the plant. Connections of this work to that on systems over rings, and systems with dynamical symmetries are discussed.

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Distributed control of spatially invariant systems

The major challenge in biology today is biocomplexity: the need to explain how cell and tissue behaviors emerge from collective interactions within complex molecular networks. Part I of this two-part article, described a mechanical model of cell structure based on tensegrity architecture that explains how the mechanical behavior of the cell emerges from physical interactions among the different molecular filament systems that form the cytoskeleton. Recent work shows that the cytoskeleton also orients much of the cell's metabolic and signal transduction machinery and that mechanical distortion of cells and the cytoskeleton through cell surface integrin receptors can profoundly affect cell behavior. In particular, gradual variations in this single physical control parameter (cell shape distortion) can switch cells between distinct gene programs (e.g. growth, differentiation and apoptosis), and this process can be viewed as a biological phase transition. Part II of this article covers how combined use of tensegrity and solid-state mechanochemistry by cells may mediate mechanotransduction and facilitate integration of chemical and physical signals that are responsible for control of cell behavior. In addition, it examines how cell structural networks affect gene and protein signaling networks to produce characteristic phenotypes and cell fate transitions during tissue development.

Tensegrity II. How structural networks influence cellular information processing networks

https://digitalcommons.unl.edu/cgi/viewcontent.cgi?article=1065&context=usafresearch

A review of space robotics technologies for on-orbit servicing

Variance Constrained Control of Maneuvering Helicopters

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Modeling and Numerical Simulation of a Buoyancy Controlled Ocean Current Turbine

ThisNotepresentsamethodforthegenerationofenergysuboptimal,collision-free, reconﬁguration trajectories for formations ﬂying in deep space(gravity-free environment). The main idea is to introduce a set ofwaypoints through which these trajectories pass and to assume thatthe trajectories are piecewise cubic polynomials. The resulting op-timization problem has a quasi-quadratic structure in the waypointsparameters.Gradient-basedalgorithms,whichexploitthisstructure,are developed for the solution. Examples show that this methodol-ogy is very efﬁcient and fast.

Energy Suboptimal Collision-Free Reconfiguration for Spacecraft Formation Flying

A square membrane structure with clamped edges and four lead zirconate titanate bimorph actuators is modeled using Kirchhoff’s plate theory. Two systems are considered, defined by the relative location of the actuators on the membrane. The finite element method is used to generate linear time-invariant models in the second-order form. The number of elements used in the finite element method is determined via a systematic analysis based on the convergence of fundamental natural frequencies and mode shapes. Characteristics that are essential for system analysis and control design such as stability, controllability, and observability are investigated using methods based on the linear time-invariant first-order form of the linear equations of motion and methods based on the linear time-invariant second-order form directly generated via the finite element method. Comparisons between the accuracy and reliability of these methods are performed. Next, modern control problems aimed at minimizing vibrations and the...

System Analysis and Control Design for a Membrane with Bimorph Actuators

Increased interest in renewable energy production has created demand for novel methods of electricity production. With a high potential for low cost power generation in locations otherwise isolated from the grid, in-stream hydrokinetic turbines could serve to help meet this growing demand. Hydrokinetic turbines possess higher operations and maintenance (O&M) costs due to their isolated nature and harsh operating environment when compared with other sources of renewable energy. As such, techniques must be developed to mitigate these costs through the application of fault-tolerant control (FTC) and machine condition monitoring (MCM) for increased reliability and maintenance forecasting. Hence, the primary objective of this paper is to address a key limitation in hydrokinetic turbine research: the lack of widely available data for use in developing models by which to conduct FTC and MCM. To this end, a 20 kW research hydrokinetic turbine implemented in Fatigue Aerodynamics Structures and Turbulence (FAST) is presented and housed within the Matlab/Simulink environment. This paper details the high-fidelity simulation platform development together with the characteristics of generated data with a focus on future FTC and MCM implementation.

Cornel Sultan

Papers

Variance Constrained Control of Maneuvering Helicopters

Modeling and Numerical Simulation of a Buoyancy Controlled Ocean Current Turbine

Energy Suboptimal Collision-Free Reconfiguration for Spacecraft Formation Flying

System Analysis and Control Design for a Membrane with Bimorph Actuators

In-Stream Hydrokinetic Turbine Fault Detection and Fault Tolerant Control - A Benchmark Model