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Home > Science, Technology & Agriculture > Technology: general issues > Engineering: general > Influence Function Approach: Selected Topics of Structural Mechanics
Influence Function Approach: Selected Topics of Structural Mechanics

Influence Function Approach: Selected Topics of Structural Mechanics


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About the Book

Structural mechanics is the study of the effects that forces of different physical origin (mechanical, thermal, magnetic and so on) produce on elements of structures such as cables, pillars, beams, plates and shells. This text represents the first ever attempt to include in a book format a number of standard problems from structural mechanics, which are treated by means of a single mathematical approach that is novel in the field. The influence (Green's) function method constitutes the basis for this approach. The material in this volume is based on the implementation of two important notions taken from different sciences. One of them (the influence function of a point concentrated force) is brought from structural mechanics, while the other (the Green's function of a boundary-value problem) is taken from mathematics. They are closely related to each other, and their relation represents the keystone in this text. Bringing these notions together allows us to create a single methodological approach to a variety of problems in structural mechanics, makes their analysis easier and builds up a solid foundation for some further developments in the field.In presenting the material in this text, it was presumed that the reader's background is equally solid in undergraduate mathematics and mechanics. The reader is assumed to be relatively fluent in differential and integral calculus and to possess, at the same time, a workable knowledge of the fundamental principles of statics and dynamics. Each chapter contains extensive 'end chapter exercises' specifically developed for each chapter, with answers and comments available in the Appendix.

Table of Contents:
Introduction 1 - Mathematics Behind Influence Function Elements of Ordinary Differential Equations; Cramer's Rule; Introduction to Fourier Series; Some Series Summation Formulae; Numerical Solution of ODE; Introduction to Integral Equations; End Chapter Exercises 2 - Green's Functions Construction Based on Defining Properties; Symmetry of Green's Functions; Alternative Construction of Green's Functions; Boundary-contact Value Problems; Matrix of Green's Type Formalism Extended; End Chapter Exercises 3 - Kirchhoff Beam Problems Single-span Beams; Bending of Beams of Uniform Rigidity; Beams on Elastic Foundation; End Chapter Exercises; Compendium of Influence Functions for Beams 4 - Other Beam Problems Beams of Variable Flexural Rigidity; Transverse Natural Vibrations; Euler Buckling Problems; Bending of Multi-span Beams; End Chapter Exercises 5 - Bending of Plates and Shells Influence Matrices for Plates and Shells; Poisson-Kirchhoff Plates; Plates on Elastic Foundation; Reissner Plates; Thin Shells of Revolution; End Chapter Exercises Answers to End Chapter Exercises

About the Author :
Dr. Yuri A. Melnikov earned a Dr.Sc. degree in Computational Mechanics at the Moscow Civil Engineering Institute, Moscow, Russia and a Ph.D. in Differential Equations) at Dnipropetrovsk State University, Dnipropetrovsk, Ukraine. He joined the Department of Mathematical Sciences of Middle Tennessee State University (Murfreesboro, Tennessee) in August 1992. He previously served as a Visiting Professor at the Department of Mechanical Engineering at Vanderbilt University (Nashville, Tennessee)and Chair of the Applied Mathematics Department at the Dnipropetrovsk State University (Ukraine). His field of expertise is applied mathematics and computational mechanics.


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Product Details
  • ISBN-13: 9781845643010
  • Publisher: WIT Press
  • Publisher Imprint: WIT Press
  • Language: English
  • Sub Title: Selected Topics of Structural Mechanics
  • ISBN-10: 1845643011
  • Publisher Date: 07 Feb 2008
  • Binding: Digital (delivered electronically)
  • No of Pages: 388


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