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＜電子ブック＞
Random Fields of Piezoelectricity and Piezomagnetism : Correlation Structures / by Anatoliy Malyarenko, Martin Ostoja-Starzewski, Amirhossein Amiri-Hezaveh
(SpringerBriefs in Mathematical Methods. ISSN:23650834)

版	1st ed. 2020.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2020
本文言語	英語
大きさ	XI, 97 p. 2 illus., 1 illus. in color : online resource
著者標目	*Malyarenko, Anatoliy author Ostoja-Starzewski, Martin author Amiri-Hezaveh, Amirhossein author SpringerLink (Online service)
件　名	LCSH:Probabilities LCSH:Continuum mechanics LCSH:Magnetism LCSH:Condensed matter FREE:Applied Probability FREE:Continuum Mechanics FREE:Magnetism FREE:Condensed Matter Physics
一般注記	Preface -- 1. Continuum Theory of Piezoelectricity and Piezomagnetism -- 2. Mathematical preliminaries -- 3. The Choice of a Basis in the Space VG -- 4. Correlation Structures -- References -- Index Random fields are a necessity when formulating stochastic continuum theories. In this book, a theory of random piezoelectric and piezomagnetic materials is developed. First, elements of the continuum mechanics of electromagnetic solids are presented. Then the relevant linear governing equations are introduced, written in terms of either a displacement approach or a stress approach, along with linear variational principles. On this basis, a statistical description of second-order (statistically) homogeneous and isotropic rank-3 tensor-valued random fields is given. With a group-theoretic foundation, correlation functions and their spectral counterparts are obtained in terms of stochastic integrals with respect to certain random measures for the fields that belong to orthotropic, tetragonal, and cubic crystal systems. The target audience will primarily comprise researchers and graduate students in theoretical mechanics, statistical physics, and probability HTTP:URL=https://doi.org/10.1007/978-3-030-60064-8

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