A History of the Theory of Elasticity and of the Strength of Materials, from Galilei to the Present Time

This chapter presents the concepts of strength of materials that are relevant to the analysis of frames. These are the modified Timoshenko theory of elastic beams (Sections 2.1-2.3) and the Euler-Bernoulli one (Section 2.4). These concepts are not presented as in the conventional textbooks of strength of materials. Instead, the formulations are described using the scheme that is customary in the theory of elasticity and that was described in Chapter 1 (Section 1.1.1) (i.e. in terms of kinematics, statics, and constitutive equations). Kinematics is the branch of mechanics that studies the movement of solids and structures without considering its causes. Statics studies the equilibrium of forces; the basic tool for this analysis is the principle of virtual work. The constitutive model that describes a one-to-one relationship between stresses and deformations completes the formulation of the elastic beam problem. Finally, in Section 2.5, some concepts of the elementary theory of torsion needed for the formulation of tridimensional frames are recalled.

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History of Strength of Materials. Stephen P. Timoshenko. McGraw-Hill, 1953. 452 pp. Diagrams and Photographs. 71s. 6d. net.

Journal of the Royal Aeronautical Society ◽

10.1017/s0368393100131578 ◽

1953 ◽

Vol 57 (516) ◽

pp. 826-826 ◽

Cited By ~ 1

Author(s):

P. L. Teed

Keyword(s):

Strength Of Materials ◽

History Of

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Lamb’s problem: a brief history

Mathematics and Mechanics of Solids ◽

10.1177/1081286519883674 ◽

2019 ◽

Vol 25 (3) ◽

pp. 501-514

Author(s):

Mohamad Emami ◽

Morteza Eskandari-Ghadi

Keyword(s):

Special Interest ◽

Mathematical Theory ◽

Three Dimensional ◽

Elastic Solid ◽

Theory Of Elasticity ◽

Scientific Investigation ◽

Lamb’S Problem ◽

Solution Methods ◽

Dimensional Version ◽

History Of

In this review note, a historical scientific investigation is presented for Lamb’s problem in the mathematical theory of elasticity. This problem first appeared in 1904 in the pioneering paper of Professor Sir Horace Lamb (Lamb, H. On the propagation of tremors over the surface of an elastic solid. Philos Trans R Soc Lon 1904; 203: 1–42). Of special interest here are the analytical studies of the three-dimensional version of Lamb’s problem, which consists of a semi-infinite, homogeneous, isotropic elastic solid that is set in motion by the exertion of a dynamical point force applied suddenly on the surface of the domain. The objective of this paper is to offer a comprehensive introduction to Lamb’s problem for the reader, along with discussing its mathematical complexities. An account is given of the history of this ever-significant problem from its earlier stages to the more recent investigations via outlining and discussing different rigorous approaches and methods of solution that have been hitherto suggested. The limitations of different methods, if they exist, are also discussed. Eventually, various solution methods are compared considering their nature, advantages, and restrictions.

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