The Mathematics of Finite Elements and Applications
The Mathematics of Finite Elements and Applications

Author: J. R. Whiteman

Publisher: Academic Press

Published: 2014-05-10

Total Pages: 535

ISBN-13: 1483268845

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The Mathematics of Finite Elements and Applications provides information pertinent to the mathematics of finite elements, applications, algorithms, and computational techniques. This book discusses the developments in the mathematics of finite elements. Organized into 32 chapters, this book begins with an overview of the basis of the finite element process as a general approximation tool. This text then examines the methods for obtaining bounds on the errors in finite element solutions to two-dimensional elliptic boundary value problems defined on simply connected polygonal regions. Other chapters consider the practical implementation of the Galerkin and the Rayleigh–Ritz methods to equations of importance to physics and engineering. This book discusses as well a fundamental investigation into the problem of convergence in the finite element method. The final chapter deals with an algorithm that is applicable to the analysis of arbitrary plane stress or plane strain configurations. This book is a valuable resource for numerical analysts, mathematical physicist, applied mathematicians, computer scientists, and engineers.

Stochastic Structural Dynamics
Stochastic Structural Dynamics

Author: T. Ariaratnam

Publisher: CRC Press

Published: 2020-12-18

Total Pages: 408

ISBN-13: 1000152979

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This book contains a series of original contributions in the area of Stochastic Dynamics, which demonstrates the impact of Mike Lin's research and teaching in the area of random vibration and structural dynamics.

Matrix Methods for Advanced Structural Analysis
Matrix Methods for Advanced Structural Analysis

Author: Manolis Papadrakakis

Publisher: Butterworth-Heinemann

Published: 2017-11-13

Total Pages: 468

ISBN-13: 0128118822

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Divided into 12 chapters, Matrix Methods for Advanced Structural Analysis begins with an introduction to the analysis of structures (fundamental concepts and basic steps of structural analysis, primary structural members and their modeling, brief historical overview of methods of static analysis, programming principles, and suggestions for the rational use of computer programs). This is followed by the principal steps of the Direct Stiffness Method including plane trusses, plane framed structures, space trusses, and space framed structures. The case of plane or space framed structure, including possible rigid elements at their beam ends (rigid joints) is discussed in detail. Other topics discussed in this reference include the procedure for analyzing beams with internal releases (partial connection of beam elements) and elastic hinges, as well as the alternative handling of internal releases by modifying the element stiffness matrix. Furthermore, the Method of Substructures is demonstrated for the solution of large-scale models in terms of the associated number of degrees of freedom. - The principal steps of the Direct Stiffness Method are presented for plane and space trusses, as well as plane and space framed structures - The handling of beams with internal releases and elastic hinges - The method of substructures for large-scale structures - A computer code (basic steps and source files) based on MATLAB® software for the analysis of beam-like structures