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Element (natuurfilosofie) --- Natuurfilosofie

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Elasticity --- Finite element method --- Mathematical models

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This definitive introduction to finite element methods was thoroughly updated for this 2007 third edition, which features important material for both research and application of the finite element method. The discussion of saddle-point problems is a highlight of the book and has been elaborated to include many more nonstandard applications. The chapter on applications in elasticity now contains a complete discussion of locking phenomena. The numerical solution of elliptic partial differential equations is an important application of finite elements and the author discusses this subject comprehensively. These equations are treated as variational problems for which the Sobolev spaces are the right framework. Graduate students who do not necessarily have any particular background in differential equations, but require an introduction to finite element methods will find this text invaluable. Specifically, the chapter on finite elements in solid mechanics provides a bridge between mathematics and engineering.

Finite element method. --- Elasticity --- Mathematical models.

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Finite element method. --- Oceans and Seas. --- Éléments finis, Méthode des.

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Ferromagnetic models of ships and submarines that predict or reproduce their magnetic signatures have found applications in the development of both offensive and defensive military systems from World War II to the present. The mathematical basis of generalized coordinate systems will be presented and demonstrated with example applications to analytic spherical and prolate spheroidal magnetic ship models. In addition, the advantages and pitfalls of using complex finite-element- and boundary-element numerical techniques to predict high-order near-field ship signatures will be discussed, followed by a short description of the design and testing of complementary physical scale models. Extrapolation of measured magnetic signatures from testing environments to threat areas using semi-empirical math models will be presented, along with an explanation of their inherent instabilities and methods for regularizing them. These magnetic ship signature modeling techniques are used today in designing optimized signature reduction systems that have a minimum impact on ships and their systems. The discussion will be closed with an important discussion of the verification and validation of magnetic models of surface ships and submarines.

Boundary element methods. --- Ferromagnetism --- Finite element method. --- Magnetism of ships --- Mathematical models. --- Ships, Magnetism of --- FEA (Numerical analysis) --- FEM (Numerical analysis) --- Finite element analysis --- BEM (Engineering analysis) --- BIE analysis --- BIE methods --- Boundary element analysis --- Boundary elements methods --- Boundary integral equation analysis --- Boundary integral equation methods --- Boundary integral methods --- Magnetic boundary-element models. --- Magnetic finite-element models. --- Magnetic scale models. --- Magnetic ship models. --- Model verification and validation. --- Multi-pole expansion. --- Naval vessel empirical models. --- Prolate spheroidal coordinates. --- Spherical coordinates. --- Magnetic ranges --- Numerical analysis --- Isogeometric analysis --- Magnetism