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.

Examines of new approaches for the estimation of errors in approximate theories Represents methods of multiple scientific schools of various countries Enables the reader to better establish the basic equations

Autorentext
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. Holm Altenbach is Author/Co-author/Editor of 80 books, 580 scientific papers (310 of which were peer-reviewed), and 550 scientific lectures. He was Managing Editor (2004 to 2014) and has been Editor-in-Chief (since 2006) of the Journal of Applied Mathematics and Mechanics (ZAMM). He was awarded by Dr.h.c. from the NTU "Kharkiv Polytechnic" (Ukraine), the University of Constanta (Romania) and the Vekua Institute (Georgia). He is a foreign member of the Russian and Ukrainian Academies of Sciences.

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. Prof. Dr. Alexander Ya. Grigorenko was born in Kyiv on June 17, 1955. He was graduated from the cybernetics department at the Kyiv State University in 1977 with a Diploma in Applied Mathematics, has worked at the Institute of Mechanics since 1981, and has headed the department of numerical methods since 2005. He defended Ph.D. thesis in 1980 and (Dr. Sci. thesis Phys.-Math.) and in 1993 and was awarded the title of Professor in 2001. His main achievements are in the field of solid mechanics: wave and vibration processes in elastic and electroelastic bodies, numerical analysis of stationary deformation of anisotropic inhomogeneous shells and elastic bodies, and dentistry biomechanics.

Professor Roman M. Kushnir is Chief of Department of Thermomechanics and Director of the Pidstryhach Institute for Applied Problems of Mechanics and Mathematics of Ukrainian National Academyof

Inhalt
Stages of Yaroslav M. Grigorenko's Life Path and the Main Results of his Scientific Research.- Finite Element Modeling of Partially Conductive Interfacial Crack in Piezoelectric Bimaterial.- Asymptotic Behavior of Forced Vibrations of Layered Plates.- Methods of Numerical Solution of Problems of Thermo-Plasticity Taking Into Account the Stress Mode.- Analysis of the Beam Approximation Applicability in Problems on Compression of Bodies Along Closely Spaced Cracks.- Analysis of Fracture of an Orthotropic Plate with a Crack Under Biaxial Loading .- Two-Parametric Analysis of a Semi-Infinite Three-Layered High-Contrast Elastic Strip under Antiplane Shear Deformation.- Optimization of Thermal Treatment Modes of Bodies Made of Functionally Graded Materials.- Numerical Analysis of Contact between Elastic Bodies in the Presence of Thin Coating and Nonlinear Winkler Surface Layers.- Weight Optimization of Non-Homogeneous Rotation Shells by Methods of Optimal Processes Theory.- On M-integral in Linear Micropolar Elasticity with Symmetric Stress Tensor.- Nonlinear Dynamic Analysis of the Progressive Collapse on Multi-Core Computers.- Fatigue Endurance of Thin-Walled Cylindrical Shells Under Biaxial Combined Loading.- Stress State of Corrugated Shells with Oblique Cuts.- Numerical Analysis of Free Vibration Frequencies of Hexagonal Plate.- Selected Aspects of Thermomechanics of Ferrite Bodies under Electromagnetic Actions.- The Influence of the Temperature Dependence of Thermomechanical Characteristics of FGM on the Thermostressed State of a Hollow Sphere.- Stress Concentration Around a Circular Hole in Thin Plates and Cylindrical Shells with a Radially Inhomogeneous Inclusion.- Solving Incorrect Problems of the Elasticity Theory.- Influence of Boundary Conditions and Dissipative Heating onto Resonance Vibration of Shear Compliant Viscoelastic Cylindrical Shell with Piezoelectric Sensors.- Topology Optimization of Adhesively Bonded Double Lap Joint.- Research of Vibration Behavior of Porous FGM Panels by the Ritz Method.- Longitudinal Shear of Bimaterials with Interphase Thin Physically Nonlinear Layered.- Dynamics of Three-Layer Spherical Shells With Heterogeneous Filler Under Nonstationary Loads Functional-Gradient Inhomogeneities.- New Structural Approach for Determination of Effective Thermoelastic Modules of Discrete Composite Layers.- Modeling of the Thermally Stressed State of Functionally Graded Shallow Shells in a Three-Dimensional Formulation.- Longitudinal Shear of Bimaterials with Interphase Thin Physically Nonlinear Layered Functional-Gradient Inhomogeneities.- Solving of Stress State Problems of Anisotropic Thick Noncircular Cylindrical Shells with Different Nonhomogeneous Structures Based on Discrete Continual Approach.- Transition from the Classical Biot Problem on Cylindrical Wave to the Case of Transversely Isotropic Medium.- Stress State of the Solid Fuel of a Rocket Engine Supported by the Shell Under Pulse Loading.- Dynamics of Shell with Structural Features.- Stationary Temperature Fields in Radially-Inhomogeneous Hollow Cylinders.- Influence of Delamination Defects on the Dynamic Stress-Strain State of Composite Elements of Launch Vehicles.