Linear and Non-Linear Deformations of Elastic Solids  book cover
1st Edition

Linear and Non-Linear Deformations of Elastic Solids

ISBN 9780367333652
Published December 9, 2019 by CRC Press
596 Pages 87 B/W Illustrations

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Book Description

Linear and Non-Linear Deformations of Elastic Solids aims to compile the advances in the field of linear and non-linear elasticity through discussion of advanced topics. Broadly classified into two parts, it includes crack, contact, scattering and wave propagation in linear elastic solids and bending vibration, stability in non-linear elastic solids supported by MATLAB examples. This book is aimed at graduate students and researchers in applied mathematics, solid mechanics, applied mechanics, structural mechanics and includes comprehensive discussion of related analytical/numerical methods.

Table of Contents

Section I Linear Elasticity

1. Basic Fundamentals and an Overview

2. One or Two-Dimensional Singular Integral Equation in Contact

and Crack and Method of Solution

3. Two-Dimensional Contact and Crack Problems in Isotropic

Elastic Media: Complex Variable Technique

4. Two-Dimensional Contact and Crack Problems in Anisotropic Media

5. Complete Solution to Three-Dimensional Indentation

and Crack Problems in Isotropic Elastic Media

6. Three-Dimensional Interface Crack in Isotropic and Anisotropic

Elastic Media

7. Three-Dimensional Elliptic Indentation and Crack Problem

in Piezoelectric Media

8. Crack-Microcrack Interaction and Crack and Punch in Plate

and Layered Media

9. Weight Function Theory

10. Surface Displacement in an Elastic Half Space Due to an Earthquake

Source on an Inclined Fault Plane

11. Earth Response to Uniform Self Similar Crack Motion

12. Growth of a Semi-infinite Crack at a Varying Velocity

13. Dynamic Response of Elliptical Footings

14. Two-Dimensional Low Frequency Scattering of Acoustic Wave

by a Rough Surface

15. Scattering and Impact Response of Half Plane Crack in Transversely

Isotropic and Isotropic Media

16. Scattering from an Elliptic Crack

17. Two-Dimensional Crack and Contact Problems – Transform Method

18. Effective Moduli of Elastic Inclusion and Inhomogeneity

19. Numerical Method in Elasto-Static and Elasto-Dynamic Crack


Section II Nonlinear Elasticity

20. Large Amplitude Free Vibration of Rotating Nonhomogeneous

Beams with Nonlinear Spring and Mass System

21. Stability of an Anisotropic Right-Angled Isosceles Triangular

Plate Under Large Deflection

22. Large Amplitude Free Vibrations of Irregular Plates Using Complex

Variable Technique

23. Large Amplitude Vibrations of Thin Elastic Plates Using

Conformal Transformation

24. Large Deflection of a Circular Plate on an Elastic Foundation

25. A Modified Approach to the Nonlinear Analysis of Thin Elastic Plates

26. Large Amplitude Free Vibration of Parabolic Plates

27. Large Amplitude Free Vibration of Sandwich Parabolic Plates

28. Large Amplitude Vibration of Orthotropic Sandwich Elliptic Plates

29. Large Amplitude Vibration of Heated Orthotropic Sandwich

Elliptic Plates

30. Stability Analysis of Thermal Bending and Buckling of Plates

Due to Large Deflection

31. Stability of Thin Plates Due to Edge Thrust Under Large Deflections,

Buckling Being Resisted by a Force Proportional to the Displacement

32. Large Deflection of Clamped Cylindrical Shell

33. Large Deflection of Heated Orthotropic Thin Cylindrical Shell

34. Nonlinear Vibration and Stability of an Orthotropic Sandwich

Shell of Double Curvature with Orthotropic Core

35. Nonlinear Vibrations of a Heated Orthotropic Sandwich Shell

of Double Curvature with Orthotropic Core

36. Nonlinear Vibration of Spherical Shells of Variable Thickness

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Prof. Arabinda Roy graduated from Presidency College, followed by from the University of Calcutta .He has two Doctoral degrees to his credit, one from Calcutta University (1969) and the other from the University of Cambridge (U.K) in 1972 under Dr. E.R. Lapwood. He was awarded Commonwealth Research Fellowship to work at Emmanuel College, Cambridge (1969-72).He started his professional career in 1974 at Geological Survey of India as Senior Geophysicist. He later joined his alma mater the Department of Applied Mathematics, University of Calcutta from where he retired as a Professor in 2007 after serving for more than three decades. He was a visiting Professor at I.I.M.A.S., UNAM for a year in 1981. He worked as Principal investigator in a UGC research project. Four students worked under him for Ph.D. degree. Roy’s research interests primarily include theoretical Seismology, wave propagation, vibration and scattering problems, contact and crack theory and associated fields. He has oft-quoted publications in journals of international repute.

Rasajit Kumar Bera

Prof. Rasajit Kumar Bera is a Gold Medalist in Applied Mathematics from University of Calcutta. He received his Ph.D. from Jadavpur University in 1968. Previously, he was a faculty in Presidency College, Kolkata, Bengal Engineering College, Shibpur and joined as Professor & Head of the Department of Science in NITTTR, Kolkata in 1993 from where he retired. He was then invited to act as Professor& Head of the Department of Mathematics in Heritage Institute of Technology, Kolkata where he taught for more than ten years. He guided ten students for Ph.D. Degrees in different topics of Applied Mathematics including Fractional Calculus. 130 Research Papers of him have been published in National and International Journals. He has also contributed in more than ten books. Mathematical Physics for Engineers published by New Age International Publishers and Encyclopaedia of Thermal Stresses edited by Prof. R.B. Hetnarski, published by Springer are among them. Prof. Bera is an associate editor of International Journal of Applied and Computational Mathematics – A Springer Scopus indexed journal. His research interest includes Mathematical Theory of Linear and Non-Linear Elasticity, Generalized Thermo-Elasticity, Thermo-Elasticity in Random Media, Numerical Methods and Computation, Fractional Calculus. Among many Research Projects completed by him, a Major Project from Bhaba Atomic Research Centre(BARC) on Fractional Calculus applied to describe Reactor Kinetics & Flux Matching is worth mentioning.