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This book presents various dynamic processes in non-uniform
piezoceramic cylindrical and spherical bodies based on numerical
methods. It discusses different variants of nonhomogeneous
structural polarized piezoceramic materials in the shape of
cylinders and spheres, and highlights the validation of the
reliability of the results obtained by numerical calculations. The
content is based on an outlined theory and methods of
three-dimensional electroelasticity problems.
This book presents various dynamic processes in non-uniform
piezoceramic cylindrical and spherical bodies based on numerical
methods. It discusses different variants of nonhomogeneous
structural polarized piezoceramic materials in the shape of
cylinders and spheres, and highlights the validation of the
reliability of the results obtained by numerical calculations. The
content is based on an outlined theory and methods of
three-dimensional electroelasticity problems.
This brief book presents solutions of stress-strain problems for a
wide class of anisotropic inhomogeneous shells obtained by the
refined model. Studying these problems results in severe
computational difficulties due to partial differential equations
with variable coefficients resulting from the constitutive
relations of the original model. To solve this problem the book
uses spline-collocation and discrete-orthogonalization methods. It
analyses the influence of geometrical and mechanical parameters, of
various kinds of boundary conditions, and of the loading conditions
on the distributions of stress and displacement fields in shallow,
spherical, conical, and noncircular cylindrical shells. The
dependence of the stress-strain pattern on shell thickness
variations is studied. The authors solve the problem also for the
case of the thickness varying in two directions. They study how a
variation in shell thickness influences the stress-strain state and
consider noncircular cylindrical shells with elliptical and
corrugated sections are considered. The results obtained during
numerous calculations support the efficiency of the
discrete-orthogonalization approach proposed in the monograph for
solving static problems for anisotropic inhomogeneous shells when
using the refined model.
These two-partition books present essential approaches to
numerical-analytical solutions of problems in the mechanics of
shells with various structures and shapes based on refined and
spatial models. Further, it examines the mechanical behavior of
shallow, circular and noncircular, conical, spherical, and
functionally graded shells obtained by the refined model. The book
investigates the stress-strain state and free vibrations of
finite-length cylinders in spatial formulation (3D elasticity
theory). Further, it analyzes the influence of geometrical and
mechanical parameters, of boundary conditions, and of the loading
character on both the distributions of stress and displacement
fields, and on the dynamical characteristics in these shells and
cylinders. Lastly, it discusses in detail the validation of
reliability for the results obtained by numerical calculations. As
such, it complements the first part of the book, the volume Recent
Developments in Anisotropic Heterogeneous Shell Theory:
Applications of Refined and Three-dimensional Theory.
This volume focuses on the relevant general theory and presents
some first applications, namely those based on classical shell
theory. After a brief introduction, during which the history and
state-of-the-art are discussed, the first chapter presents the
mechanics of anisotropic heterogeneous shells, covering all
relevant assumptions and the basic relations of 3D elasticity,
classical and refined shell models. The second chapter examines the
numerical techniques that are used, namely discrete
orthogonalization, spline-collocation and Fourier series, while the
third highlights applications based on classical theory, in
particular, the stress-strain state of shallow shells, non-circular
shells, shells of revolution, and free vibrations of conical
shells. The book concludes with a summary and an outlook bridging
the gap to the second volume.
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