A history of the theory of elasticity and of the strength of materials Volume 2, no. 2 ; from Galilei to the present time

by Isaac Todhunter

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1893 ...un jour quelque ordre de phcnomenes auquel l'hypothese consideree sera plus applicable, et qui realisera ainsi cette curieuse analogie d'une distribution de pressions avec le mouvement de la chaleur dans une barre (173). The memoir concludes with two notes, the first of which deduces Hopkins' theorem for the value and direction of the maximum shear (see our Art. 1368), while the second deduces Saint-Venant's theorem for the direction and magnitude of the maximum see our Arts. 1570 and 4(8). 1G05. Various papers on the stability and thrust of loose earthwork by Boussinesq, briefly resuming, generalising or simpli fying the results of the above memoir, will be found in volumes of the Comptes rendus. (a) T. Lxxvii., pp. 1521-5. Paris, 1873. An extract from the Brussels memoir under the same title as the see our Arts. 1571-99. (6) Sur les lois de la distribution plane des pressions a Finterieur des corps isolropes dans Fetal cFequilibre limite. T. Lxxviii., 757-9 and 786-9. Paris, 1874. In the first part of this paper Boussinesq supposes a conservative system of body-forces applied to a mass under uniplanar strain. The first two body-stress equations then dxx dig df _ Q dxy dyy df _.... dx dy dx ' dx dy dy f being the potential of the body-forces. Hence we find, as in our Arts. 1576-7, for an elastic d?Tx d?n „ d'Ti A (d? d dx + dy3 and for a pulverulent or plastic (-dy1) xx + »nj dxdy The remainder of the first part of the memoir is devoted to the condition of limiting equilibrium discussed in our Art. 1585. (c) The second part of the memoir is devoted to discussing the integration of equations (i) for the case of limiting equilibrium. Boussinesq, as in our Art. 1568, takes 7", and T for the principal traction...

200 pages, Paperback

First published June 2, 2011

About the author

English mathematician known for his writings on the history of mathematics.