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Full Description
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.
Contents
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.
