Advanced Mechanics of Solids

Abstract

3R5. Advanced Mechanics of Solids. - OT Bruhns (Institut fur Mechanik, Ruhr-Univ Bochum, Universitatsstr 150, Bochum, D-44780, Germany). Springer-Verlag, New York. 2003. 206 pp. ISBN 3-540-43797-5. $49.95.Reviewed by P Puri (Dept of Math, Univ of New Orleans, 2000 Lakeshore Dr, New Orleans LA 70148).The author of this book is a well-known researcher in solid mechanics and has made some important contributions to the theory of elasticity and plasticity. In general, the material in this book is presented quite well and can be used as an introductory one-semester course in solid mechanics. Readers are expected to have the basic knowledge of ordinary and partial differential equations, mechanics, and some elementary knowledge of the theory of beams. The solved examples are well chosen and help the student understand the theory and procedure for solving problems given in the exercises. Useful exercises are given in the last section of every chapter, except Chapter 10. The reviewer likes the fact that answers to all exercises are given. The figures in the book are neat and clearly drawn. The book is not intended to be a comprehensive book on mechanics of solids like a recent book on elasticity by Hetnarski and Ignaczak. Chapter 1 presents the fundamental concepts, principles of linear continuum mechanics, and the derivation of the basic equations. A minor comment: Eq (1.84) is more similar to Eq (1.76) than to Eq (1.75). Chapter 2 contains the development of constitutive equations based on Hooke’s law. The expressions for strain and complementary energy are derived in Section 2. The three equilibrium equations in terms of displacements and the equivalent six Beltrami equations in terms of stresses are stated in Section 3. Section 4 discusses the influence of temperature. The rest of the sections are devoted to Hooke’s law in two dimensions, the strength criteria, and the principle of complementary virtual work. It appears to the reviewer that for the derivation of Eq (2.18) a reference to Eq (2.9) is more appropriate than Eq (2.6) and that it would be helpful to refer to Eq (1.53) for the derivation Eq (2.19). The theory of simple beams is developed in Chapter 3. Topics covered in this chapter are normal stresses, shearing stresses, shear center of thin-walled open sections, influence of distributed loads, and stresses in non-prismatic bars, and deflections of beams. In Chapter 4, the torsion of prismatic bars is explored. Various types of cross sections are considered in the first three sections, and the influence of restrained warping is discussed in Section 4. The next chapter is on curved beams. The four sections in this chapter analyze general static’s, beams with large curvature, beams with small curvature, and the deflection of curved beams. Reciprocity theorems, energy principles, theorems of Engesser and Castigliano, statically indeterminate systems, complementary and strain energy of the beams are explained in Chapter 6. Chapter 7 is concerned with two-dimensional problems of plane stress and plane strain, which are discussed in the first section. In the second section, the special case in which the body forces have potential is discussed. In the next section the equations of plane strain and plane stress are given in polar form. The theory of elastic plates and shells is presented in Chapter 8. General remarks are given in Section 1. Section 2 consists of the solved examples for discs. Discussions on thin plates, Kirchhoff’s theory, boundary conditions, axially symmetric bending of circular plates, and the elastic energy of plates are contained in Section 3. Membrane theory of shells of revolution is given in Section 4. The notion of stability, bifurcation with finite degrees of freedom, snap through buckling, and column buckling are the topics covered in Chapter 9. The principle of virtual work, Hamilton’s principle, Euler-Lagrange equations, and the Legrange multiplier method are given in Chapter 10. This is the only chapter, which has no solved examples or exercises. The next two chapters are concerned with vibration. The first two sections in Chapter 11 are on undamped and damped free vibrations. This material is generally covered in introductory differential equations. The third section consists of forced vibration with harmonic excitation, and the last section in this chapter is on isolators, which tend to dampen the vibrations. The last chapter covers the material on free and forced vibrations with several degrees of freedom. This chapter also includes answers to the exercises. Advanced Mechanics of Solids is recommended to people interested in learning the basics of solid mechanics and understanding the interaction of forces on solids. The book is particularly suitable for structural engineers.