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

The feasibility of harvesting energy using polyvinylidene fluoride patches mounted on a vibrating prestressed membrane, itself attached to a tensegrity structure, was investigated. Kinematics of the tensegrity structure and the attached membrane is described and conditions for stable equilibrium for the structure are derived. Nonlinear partial differential equations describing the dynamics of the membrane attached to the tensegrity structure and under the action of a time-dependent transverse pressure are derived using the principle of virtual work. These equations are linearized and the modes of the structure are obtained using the finite element method. These modes are used as basis functions in developing a reduced-order model to obtain the response of the complete structure under the applied transverse dynamic pressure. The polyvinylidene fluoride patch on the structure is connected to an electrical load resistance. The electrical current passing through the load resistance is calculated using Gauss’s...

Cornel Sultan

Papers

Optimal Energy Harvesting From A Membrane Attached To A Tensegrity Structure