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"Lebedev, L. P"
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Tensor analysis with applications in mechanics
The tensorial nature of a quantity permits us to formulate transformation rules for its components under a change of basis. These rules are relatively simple and easily grasped by any engineering student familiar with matrix operators in linear algebra. More complex problems arise when one considers the tensor fields that describe continuum bodies. In this case general curvilinear coordinates become necessary. The principal basis of a curvilinear system is constructed as a set of vectors tangent to the coordinate lines. Another basis, called the dual basis, is also constructed in a special manner. The existence of these two bases is responsible for the mysterious covariant and contravariant terminology encountered in tensor discussions.
eBook
The calculus of variations and functional analysis
This is a book for those who want to understand the main ideas in the theory of optimal problems. It provides a good introduction to classical topics (under the heading of \"the calculus of variations\") and more modern topics (under the heading of \"optimal control\"). It employs the language and terminology of functional analysis to discuss and justify the setup of problems that are of great importance in applications. The book is concise and self-contained, and should be suitable for readers with a standard undergraduate background in engineering mathematics.
eBook
Introduction to Mathematical Elasticity
This book provides the general reader with an introduction to mathematical elasticity, by means of general concepts in classic mechanics, and models for elastic springs, strings, rods, beams and membranes. Functional analysis is also used to explore more general boundary value problems for three-dimensional elastic bodies, where the reader is provided, for each problem considered, a description of the deformation; the equilibrium in terms of stresses; the constitutive equation; the equilibrium equation in terms of displacements; formulation of boundary value problems; and variational principles, generalized solutions and conditions for solvability.
eBook
Tensor analysis
Tensor analysis is an essential tool in any science (e.g. engineering, physics, mathematical biology) that employs a continuum description. This concise text offers a straightforward treatment of the subject suitable for the student or practicing engineer. The final chapter introduces the reader to differential geometry, including the elementary theory of curves and surfaces. A well-organized formula list, provided in an appendix, makes the book a very useful reference. A second appendix contains full hints and solutions for the exercises.
eBook
Functional analysis : applications in mechanics and inverse problems
This book started its life as a series of lectures given by the second author from the 1970's onwards to students in their third and fourth years in the Department of Mechanics and Mathematics at Rostov State University.
eBook
THERMOELASTICITY AND THE DESIGN OF FORCE TRANSDUCERS
The transient process due to thermoelastic temperature change involves a body's going from an adiabatic (A) to an isothermal (I) regime. An effort is here made to alert designers of high-accuracy force transducers to the A-I passage as a major factor affecting the precision of the resulting instrument. The uncompensated part of the A-I passage can be reduced or eliminated through data processing. (AIAA)
Journal Article
Tensor analysis
Tensor analysis is an essential tool in any science (for example, engineering, physics, mathematical biology) that employs a continuum description. This concise text offers a straightforward treatment of the subject suitable for the student or practicing engineer. The final chapter introduces the reader to differential geometry, including the elementary theory of curves and surfaces. A well-organized formula list, provided in an appendix, aims to makes the text a very useful reference. A second appendix contains full hints and solutions for the exercises.
eBook
On Spatial Effects of Modelling in Linear Viscoelasticity
The parameters of a linear model of a viscoelastic material are determined by testing the material in homogeneous (i.e. spatially constant) states. Some of the qualitative properties of the behaviour of the material observed in the tests may be unexpectedly lost if the material is confined, so that the behaviour varies in space and is thus not homogeneous. One such property is the (Lyapunov) stability of the deformation. To ensure that the material possesses these properties it is necessary to impose some additional restrictions on the model parameters. These restrictions are found by analysing the boundary value problems for viscoelastic bodies of various shapes and subjected to various boundary conditions.[PUBLICATION ABSTRACT]
Journal Article
Some boundary value problems and models for coupled elastic bodies
A new class of boundary value problems is presented. These problems are described by related equations of different nature and possess such properties as the appearance of highest derivatives in boundary conditions. Such problems appear to model common engineering constructions composed of elements of different mechanical natures like plates, shells, membranes, or three-dimensional elastic bodies. Two problems are considered in detail, namely a three-dimensional elastic body with flat elements taken as a plate or a membrane, and a plate-membrane system. The existence-uniqueness theorems for the corresponding boundary value problems are established and an application of a conforming FEM is justified.
Journal Article