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

Tensegrity deployment using infinitesimal mechanisms

Purpose – The purpose of this paper is to show the feasibility of constrained model predictive control (MPC) for sophisticated helicopter models which are derived by physical considerations.Design/methodology/approach – Physics‐based modeling is used to create control‐oriented helicopter models. Advanced constrained controllers are designed and tested for these sophisticated models.Findings – The helicopter models are valid and constrained MPC shows considerable promise for robust tracking.Practical implications – MPCs can be implemented for highly constrained helicopter flights.Originality/value – A complete process of control‐oriented, physics‐based model development for helicopters followed by MPC design is developed. It is also proved that constrained MPC can be used and implemented online to robustly track discontinuous helicopter trajectories with heterogeneous constraints, even when the models are sophisticated and physics based.

Constrained predictive control of helicopters

This paper proposes a new space telescope design in which the classical truss structure of the telescope is replaced by a tensegrity structure. A tensegrity structure is a prestressed structure whose structural shape is guaranteed by the interaction between elastic members in tension (tendons) and a set of rigid members (bars). A nonlinear dynamical model of a two stage tensegrity telescope is derived. Static analysis is performed for tensegrity telescopes composed of two stages. The performance specifications for the control system are formulated in terms of the peak value (L ∞ norm) of the pointing and alignment errors. The control system is designed to minimize a certain upper bound on this peak value subject to a peak value constraint on the external disturbances. Evaluations of the design are performed through numerical simulations of the closed loop system.

Peak to peak control of an adaptive tensegrity space telescope

Efficient algorithms for collision-free energy sub-optimal path planning for formations of spacecraft flying in deep space are presented. The idea is to introduce a set of way-points through which the spacecraft are required to pass, combined with parameterizations of the trajectories which are energy-optimal for each spacecraft. The resulting constrained optimization problem is formulated as a quasi-quadratic parameter optimization problem in terms of the way-points parameters. The mathematical structure of the problem is further exploited to develop gradient-based algorithms in which the gradients are computed analytically. The collision avoidance constraints are approximated such that closed form solutions are generated. This combination results in fast and robust numerical algorithms which work very well for scenarios involving a large number of spacecraft (e.g. 20).

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Deep Space Formation Flying Spacecraft Path Planning

A modular multidisciplinary analysis and optimization framework tool has been built with the goal of optimally designing a supersonic aircraft. This paper addresses the specic challenge of designing an ecient long range supersonic bomber aircraft. This framework includes all the disciplines normally required for supersonic aircraft design and it also includes disciplines specically required by an advanced military aircraft that is tailless and has embedded engines. Results from running the analysis framework for a B-58 supersonic bomber test case are presented as a validation of the methods employed.

Cornel Sultan

Papers

Tensegrity deployment using infinitesimal mechanisms

Constrained predictive control of helicopters

Peak to peak control of an adaptive tensegrity space telescope

Deep Space Formation Flying Spacecraft Path Planning

A Multidisciplinary Design Optimization Framework for Design Studies of an Ecient Supersonic Air Vehicle