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This book provides an overview of the current of the state of the
art in the multiscale mechanics of solids and structures. It
comprehensively discusses new materials, including theoretical and
experimental investigations their durability and strength, as well
as fractures and damage
This book marks the 60th birthday of Prof. Vladimir Erofeev - a
well-known specialist in the field of wave processes in solids,
fluids, and structures. Featuring a collection of papers related to
Prof. Erofeev's contributions in the field, it presents articles on
the current problems concerning the theory of nonlinear wave
processes in generalized continua and structures. It also discusses
a number of applications as well as various discrete and continuous
dynamic models of structures and media and problems of nonlinear
acoustic diagnostics.
This book provides an overview of the current of the state of the
art in the multiscale mechanics of solids and structures. It
comprehensively discusses new materials, including theoretical and
experimental investigations their durability and strength, as well
as fractures and damage
This book marks the 60th birthday of Prof. Vladimir Erofeev - a
well-known specialist in the field of wave processes in solids,
fluids, and structures. Featuring a collection of papers related to
Prof. Erofeev's contributions in the field, it presents articles on
the current problems concerning the theory of nonlinear wave
processes in generalized continua and structures. It also discusses
a number of applications as well as various discrete and continuous
dynamic models of structures and media and problems of nonlinear
acoustic diagnostics.
This book commemorates the 80th birthday of Prof. W.
Pietraszkiewicz, a prominent specialist in the field of general
shell theory. Reflecting Prof. Pietraszkiewicz's focus, the
respective papers address a range of current problems in the theory
of shells. In addition, they present other structural mechanics
problems involving dimension-reduced models. Lastly, several
applications are discussed, including material models for such
dimension-reduced structures.
This book presents a liber amicorum dedicated to Wolfgang H.
Muller, and highlights recent advances in Prof. Muller's major
fields of research: continuum mechanics, generalized mechanics,
thermodynamics, mechanochemistry, and geomechanics. Over 50 of
Prof. Muller's friends and colleagues contributed to this book,
which commemorates his 60th birthday and was published in
recognition of his outstanding contributions.
This book is an homage to the pioneering works of E. Aero and G.
Maugin in the area of analytical description of generalized
continua. It presents a collection of contributions on micropolar,
micromorphic and strain gradient media, media with internal
variables, metamaterials, beam lattices, liquid crystals, and
others. The main focus is on wave propagation, stability problems,
homogenization, and relations between discrete and continuous
models.
This book is an homage to the pioneering works of E. Aero and G.
Maugin in the area of analytical description of generalized
continua. It presents a collection of contributions on micropolar,
micromorphic and strain gradient media, media with internal
variables, metamaterials, beam lattices, liquid crystals, and
others. The main focus is on wave propagation, stability problems,
homogenization, and relations between discrete and continuous
models.
On the roots of continuum mechanics in differential geometry -- a
review.- Cosserat media.- Cosserat-type shells.- Cosserat-type
rods.- Micromorphic media.- Electromagnetism and generalized
continua.- Computational methods for generalized continua. The need
of generalized continua models is coming from practice. Complex
material behavior sometimes cannot be presented by the classical
Cauchy continua. At present the attention of the scientists in this
field is focused on the most recent research items * new models, *
application of well-known models to new problems, * micro-macro
aspects, * computational effort, and * possibilities to identify
the constitutive equations The new research directions are
discussed in this volume - from the point of view of modeling and
simulation, identification, and numerical methods.
In this volume scientists and researchers from industry discuss
the new trends in simulation and computing shell-like structures.
The focus is put on the following problems: new theories (based on
two-dimensional field equations but describing non-classical
effects), new constitutive equations (for materials like
sandwiches, foams, etc. and which can be combined with the
two-dimensional shell equations), complex structures (folded,
branching and/or self intersecting shell structures, etc.) and
shell-like structures on different scales (for example: nano-tubes)
or very thin structures (similar to membranes, but having a
compression stiffness). In addition, phase transitions in shells
and refined shell thermodynamics are discussed. The chapters of
this book are the most exciting contributions presented at the
EUROMECH 527 Colloquium "Shell-like structures: Non-classical
Theories and Applications" held in Wittenberg, Germany.
The book presents foundations of the micropolar continuum mechanics
including a short but comprehensive introduction of stress and
strain measures, derivation of motion equations and discussion of
the difference between Cosserat and classical (Cauchy) continua,
and the discussion of more specific problems related to the
constitutive modeling, i.e. constitutive inequalities, symmetry
groups, acceleration waves, etc.
This book presents the theoretical and experimental foundations of
quasi-static deformation of elastoplastic and viscoplastic
materials and structural elements made of them. Experimental
studies of deformation and fracture of materials under complex
loading under impulse influences are described and discussed. A
short introduction of theoretical and numerical methods for
studying the stress-strain state of elastoplastic structural
elements under dynamic, impulse loading and their interaction with
other media is given.
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.
The book is devoted to the 70th birthday of Prof. Sergey M.
Aizikovich, which will celebrated on August 2nd 2021. His
scientific interests are related to the following topics: Mechanics
of contact interactions, Functionally graded materials, Mechanics
of fracture, Integral equations of mathematical physics, Inverse
problems of the theory of elasticity, and Applications of
elasticity to biological and medical problems of mechanics of
materials. The papers, collected in the book, are contributions of
authors from 10 countries.
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.
This book commemorates the 80th birthday of Prof. W.
Pietraszkiewicz, a prominent specialist in the field of general
shell theory. Reflecting Prof. Pietraszkiewicz's focus, the
respective papers address a range of current problems in the theory
of shells. In addition, they present other structural mechanics
problems involving dimension-reduced models. Lastly, several
applications are discussed, including material models for such
dimension-reduced structures.
This book presents a liber amicorum dedicated to Wolfgang H.
Muller, and highlights recent advances in Prof. Muller's major
fields of research: continuum mechanics, generalized mechanics,
thermodynamics, mechanochemistry, and geomechanics. Over 50 of
Prof. Muller's friends and colleagues contributed to this book,
which commemorates his 60th birthday and was published in
recognition of his outstanding contributions.
This book presents a collection of chapters on the current problems
of the theory of dynamical processes in generalized continua and
structures, and has been compiled to commemorate the 70th birthday
of Prof. Dmitry Indeitsev - a leading specialist in the field of
dynamical processes in solids, fluids and structures. It discusses
various applications related to Prof. Indeitsev's contributions,
including various discrete and continuous dynamic models of
structures and media, as well as a number of dynamical processes in
generalized media.
'A strong point of this book is its coverage of tensor theory,
which is herein deemed both more readable and more substantial than
many other historic continuum mechanics books. The book is
self-contained. It serves admirably as a reference resource on
fundamental principles and equations of tensor mathematics applied
to continuum mechanics. Exercises and problem sets are useful for
teaching ... The book is highly recommended as both a graduate
textbook and a reference work for students and more senior
researchers involved in theoretical and mathematical modelling of
continuum mechanics of materials. Key concepts are well described
in the text and are supplemented by informative exercises and
problem sets with solutions, and comprehensive Appendices provide
important equations for ease of reference.'Contemporary PhysicsA
tensor field is a tensor-valued function of position in space. The
use of tensor fields allows us to present physical laws in a clear,
compact form. A byproduct is a set of simple and clear rules for
the representation of vector differential operators such as
gradient, divergence, and Laplacian in curvilinear coordinate
systems. 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.This book provides a
clear, concise, and self-contained treatment of tensors and tensor
fields. It covers the foundations of linear elasticity, shell
theory, and generalized continuum media, offers hints, answers, and
full solutions for many of the problems and exercises, and Includes
a handbook-style summary of important tensor formulas.The book can
be useful for beginners who are interested in the basics of tensor
calculus. It also can be used by experienced readers who seek a
comprehensive review on applications of the tensor calculus 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.A tensor field is a
tensor-valued function of position in space. The use of tensor
fields allows us to present physical laws in a clear, compact form.
A byproduct is a set of simple and clear rules for the
representation of vector differential operators such as gradient,
divergence, and Laplacian in curvilinear coordinate systems.This
book is a clear, concise, and self-contained treatment of tensors,
tensor fields, and their applications. The book contains
practically all the material on tensors needed for applications. It
shows how this material is applied in mechanics, covering the
foundations of the linear theories of elasticity and elastic
shells.The main results are all presented in the first four
chapters. The remainder of the book shows how one can apply these
results to differential geometry and the study of various types of
objects in continuum mechanics such as elastic bodies, plates, and
shells. Each chapter of this new edition is supplied with exercises
and problems - most with solutions, hints, or answers to help the
reader progress. An extended appendix serves as a handbook-style
summary of all important formulas contained in the book.
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.A tensor field is a
tensor-valued function of position in space. The use of tensor
fields allows us to present physical laws in a clear, compact form.
A byproduct is a set of simple and clear rules for the
representation of vector differential operators such as gradient,
divergence, and Laplacian in curvilinear coordinate systems.This
book is a clear, concise, and self-contained treatment of tensors,
tensor fields, and their applications. The book contains
practically all the material on tensors needed for applications. It
shows how this material is applied in mechanics, covering the
foundations of the linear theories of elasticity and elastic
shells.The main results are all presented in the first four
chapters. The remainder of the book shows how one can apply these
results to differential geometry and the study of various types of
objects in continuum mechanics such as elastic bodies, plates, and
shells. Each chapter of this new edition is supplied with exercises
and problems - most with solutions, hints, or answers to help the
reader progress. An extended appendix serves as a handbook-style
summary of all important formulas contained in the book.
Advanced Engineering Analysis is a textbook on modern engineering
analysis, covering the calculus of variations, functional analysis,
and control theory, as well as applications of these disciplines to
mechanics. The book offers a brief and concise, yet complete
explanation of essential theory and applications. It contains
exercises with hints and solutions, ideal for self-study.
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