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1 Explores the foundation of continuum mechanics 2 Establishes the
tensorial nature of strain measures and influence of rotation of
frames on various measures 3 Illustrates the physical meaning of
the components of strains. 4 Provides the definitions and measures
of stress 5 Prepares graduate students for fundamental and basic
research work in engineering and sciences
Numerical Methods and Methods of Approximation in Science and
Engineering prepares students and other readers for advanced
studies involving applied numerical and computational analysis.
Focused on building a sound theoretical foundation, it uses a clear
and simple approach backed by numerous worked examples to
facilitate understanding of numerical methods and their
application. Readers will learn to structure a sequence of
operations into a program, using the programming language of their
choice; this approach leads to a deeper understanding of the
methods and their limitations. Features: Provides a strong
theoretical foundation for learning and applying numerical methods
Takes a generic approach to engineering analysis, rather than using
a specific programming language Built around a consistent,
understandable model for conducting engineering analysis Prepares
students for advanced coursework, and use of tools such as FEA and
CFD Presents numerous detailed examples and problems, and a
Solutions Manual for instructors
Written by two well-respected experts in the field, The Finite
Element Method for Boundary Value Problems: Mathematics and
Computations bridges the gap between applied mathematics and
application-oriented computational studies using FEM.
Mathematically rigorous, the FEM is presented as a method of
approximation for differential operators that are mathematically
classified as self-adjoint, non-self-adjoint, and non-linear, thus
addressing totality of all BVPs in various areas of engineering,
applied mathematics, and physical sciences. These classes of
operators are utilized in various methods of approximation:
Galerkin method, Petrov-Galerkin Method, weighted residual method,
Galerkin method with weak form, least squares method based on
residual functional, etc. to establish unconditionally stable
finite element computational processes using calculus of
variations. Readers are able to grasp the mathematical foundation
of finite element method as well as its versatility of
applications. h-, p-, and k-versions of finite element method,
hierarchical approximations, convergence, error estimation, error
computation, and adaptivity are additional significant aspects of
this book.
Unlike most finite element books that cover time dependent
processes (IVPs) in a cursory manner, The Finite Element Method for
Initial Value Problems: Mathematics and Computations focuses on the
mathematical details as well as applications of space-time coupled
and space-time decoupled finite element methods for IVPs.
Space-time operator classification, space-time methods of
approximation, and space-time calculus of variations are used to
establish unconditional stability of space-time methods during the
evolution. Space-time decoupled methods are also presented with the
same rigor. Stability of space-time decoupled methods, time
integration of ODEs including the finite element method in time are
presented in detail with applications. Modal basis, normal mode
synthesis techniques, error estimation, and a posteriori error
computations for space-time coupled as well as space-time decoupled
methods are presented. This book is aimed at a second-semester
graduate level course in FEM.
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