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This book examines new approaches for the estimation of errors in approximate theories. Numerical and analytical methods in mechanics often require the establishment of a set of basic equations, and various approaches exist to create approximate theories from them. The problem is that nobody knows the boundaries of the estimation of errors in approximate theories.
This book presents new approaches to overcome this problem and to provide the reader with suitable methods for the relevant field, including a representation of different scientific schools and different countries. These new methods are helping to solve many problems not only in analytical Mechanics but also in Physics, Mathematics, and Civil Engineering.
Prof. Dr.-Ing.habil. Dr.h.c.mult. Holm Altenbach is a member of the International Association of Applied Mathematics and Mechanics and the International Research Center on Mathematics and Mechanics of Complex Systems (M&MoCS), Italy. He has held positions at the Otto-von-Guericke-Universität, Magdeburg, and Martin Luther-Universität Halle-Wittenberg, both in Germany. Holm Altenbach received his doctorate in 1983 with a thesis on elastic shells with inhomogeneous properties in the thickness direction on the basis of a Timoshenko theory, and in 1987 he habilitated as a doctor of technical sciences with a thesis on viscoelastic shells.
He is currently Full Professor of Engineering Mechanics (retired) at the Otto-von-Guericke-Universität Magdeburg, Faculty of Mechanical Engineering, Institute of Mechanics (since 2022).
His areas of scientific interest include
General theory of elasticand inelastic plates and shells
Creep and damage mechanics
Strength theories and nano- and micromechanics.
Professor Viacheslav L. Bogdanov was born on November 25, 1965, in Kyiv Region of Ukraine and graduated from the Faculty of Mechanics and Mathematics of Kyiv State University in1989. He is working at the S. P. Timoshenko Institute of Mechanics of the National Academy of Sciences of Ukraine (NASU) since 1989, receiving an appointment as Principal Researcher (2009). He is serving as Vice-President of the NASU and Head of Section of Physical, Technical and Mathematical Sciences of the NASU (from 2020 until present).
He received the Candidate of Sciences degree (Ph.D.) (1992) and the Doctor of Sciences degree (2009) in Physics & Mathematics. He is Academician of the NASU (since 2015).
His principal scientific results have been obtained in the mechanics of deformable solids: fracture mechanics, the three-dimensional theory of stability of deformable bodies, and mechanics of composite materials. He developed a combined approach to investigating non-classical problems of fracture mechanics (problems of fracture of pre-stressed bodies with cracks and fracture of solids under compressive loading along parallel cracks). He is Author or Co-author of 18 monographs, textbooks, reference publications, and more than 150 scientific papers.
He is Technical Authority in Applied Mathematics and Mechanics of Solids. His experience includes Education, Teaching, and Programming.
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