This book presents the various approaches in establishment the basic equations of one- and two-dimensional structural elements. In addition, the boundaries of validity of the theories and the estimation of errors in approximate theories are given. Many contributions contain not only new theories, but also new applications, which makes the book interesting for researcher and graduate students.

Classical and improved plate theories with applications Cosserat and micropolar plates Asymptotic solution of layered problems

Autorentext
Prof. Dr.-Ing. habil. Dr. h.c. mult. Holm Altenbach is a member of the International Research Center on Mathematics and Mechanics of Complex Systems (M&MoCS), Italy, and International Association of Applied Mathematics and Mechanics (GAMM). In 1996, he was appointed as a full professor (Engineering Mechanics) at the Martin Luther University Halle-Wittenberg, and since 2011, he has been a full professor at the Otto von Guericke University Magdeburg. He graduated from Leningrad Polytechnic Institute in 1980 (diploma with a distinction), defended his Ph.D. and obtained his postgraduate degree (habilitation) from the same university in 1983 and 1987, respectively. His areas of scientific interest are theory of plates and shells with applications, continuum mechanics and material modeling, generalized media, sandwiches and laminates. He is an Editor-in-Chief of the Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik (the oldest journal in mechanics in Germany) and of Springer's Advanced Structured Materials series. He is a member of the editorial board of several journals: among them Continuum Mechanics and Thermodynamics, Technische Mechanik, Mechanics of Composite Materials, and Journal of Strain Analysis for Engineering Design. He was awarded the Polish Humboldt Prize in 2018. In November 2019, he was elected as a Foreign Member of the Russian Academy of Sciences and in May 2021 as a Foreign Member of the National Academy of Sciences of Ukraine. Professor Svetlana M. Bauer is professor at the Department of Theoretical and Applied Mechanics of the Faculty of Mathematics and Mechanics at Saint-Petersburg State University, Russia. She was graduated from Leningrad State University in 1975 and obtained the PhD (Physics & Mathematics, Mechanics of Solids) from Leningrad State University in 1980. In 2003, she got the D.Sc. degree (Physics & Mathematics, Mechanics of Solids) from Leningrad State University in 2003. She supervised of eight PhD theses and acted as author/co-author of 15 books and 200 journal and conference papers. Her research interests are asymptotic methods, theory of thin-walled structures, biomechanics, mechanics of solids, nano-mechanics, and models of plates and shells in ophthalmology.

Prof. Dr. hab. Victor A. Eremeyev is a member of American Mathematical Society; the International Research Center on Mathematics and Mechanics of Complex Systems (M&MoCS), Italy; and Polish Society of Theoretical and Applied Mechanics. Employment history includes positions at Rostov State University/South Federal University, Don State Technical University, and Southern Scientific Center of Russian Academy of Science, Rostov on Don, at Research Institute for Mechanics, National Research Lobachevsky State University of Nizhni Novgorod, Russia; at Martin Luther University Halle-Wittenberg and Otto von Guericke University Magdeburg, Germany; at Rzeszow University of Technology, Rzeszów; and Gdansk University of Technology, Gdansk, Poland. He is graduated from Rostov State University at 1985 (diploma in Mechanics with a distinction). He defended Ph.D. at Rostov State University in 1990 (title: The stability of two-phase nonlinear thermo-elastic bodies). Dr.hab was awarded Doctor of science in Physics & Mathematics in 2004 at Institute of Problems of Mechanical Engineering of Russian Academy of Science, Saint Petersburg, Russia (title: Mechanics of two-phase bodies with microstructure under finite deformations). His areas of interest are theory of plates and shells with applications, continuum mechanics, generalized media, nonlinear elasticity and nano- and micromechanics. He is the author/editor of 16 books written in Russian/English/Spanish, author/co-author of more than 230 scientific peer-reviewed papers indexed by Scopus/Web of Science. He is a member of editorial board of the following journals: Journal of Applied Mathematics and Mechanics (ZAMM); Mathematics and Mechanics of Solids; Archive of Applied Mechanics, Acta Mechanica; Mathematics and Mechanics of Complex Systems; Technische Mechanik; Nanoscience and Technology: An International Journal; PNRPU Mechanics Bulletin. He was awarded with International Prize "Tullio Levi-Civita" for the Mathematical and Mechanical Sciences - 2018 and the Royal Society Wolfson Visiting Fellowship - 2021.

Prof. Gennadi I. Mikhasev was born June 6, 1957 in Baran (Vitebsk region). He was educated at the Leningrad State University, Mathematics & Mechanics Faculty (1974-1981) and obtained his Candidate of Science (PhD) in Solid Mechanics from the Leningrad State University in 1984. He defended his second doctoral thesis (Doctor of Science in Solid Mechanics) at the Leningrad State University in 1998. His present position is professor and head of the department of Bio- and Nanomechanics of the Belarusian State University. He is the co-author/editor of 4 books in mechanics of thin shells, 2 handbooks in bio-mechanics , and of around 120 scientific peer-reviewed papers. His scientific focus is on the theory of thin shells, asymptotic methods, biomechanics, and nanomechanics. Academician Nikita F. Morozov was born July 28, 1932 in Leningrad. He was educated at the Leningrad State University, Mathematics & Mechanics Faculty (1949-1954) and obtained his Candidate of Science (PhD) in Physics and Mathematics from the Leningrad State University in 1958. He defended his second doctoral thesis (Doctor of Science in Physics and Mathematics) at the Leningrad State University in 1967. In 1994, he was elected as a Corresponding Member of the Russian Academy of Science and in 2000 as a Member of the Russian Academy of Science. His present position is professor and head of the department of theory of elasticity at St.-Petersburg State University. His scientific focus is on applications of mathematical methods to problems of fracture mechanics, singular integral equations, conformal mappings, bifurcations theory, integral transformations among other.

Inhalt

1. On one Class of Spatial Problems of Layered Plates and Applications in Seismology.- 2. Asymmetric Buckling of Heterogeneous Annular Plates.- 3. Bending Stiness of Multilayer Plates with Alternating Soft and Hard Layers.- 4. On the Bending of Multilayered Plates Considering Surface Viscoelasticity.- 5. Buckling of a Ring-stiened Cylindrical Shell Under the ExternalPressure.