Elastic Parallelepiped. Elastic Strip. Elastic Layer. Thick Plate
In what follows we make a study of the elastic parallelepiped subjected to the action of a normal load; the result thus obtained will be then particularized for the elastic strip and for the elastic layer.
- PDF / 2,163,914 Bytes
- 35 Pages / 439.37 x 666.142 pts Page_size
- 83 Downloads / 206 Views
Elastic Parallelepiped. Elastic Strip. Elastic Layer. Thick Plate
In what follows we make a study of the elastic parallelepiped subjected to the action of a normal load; the result thus obtained will be then particularized for the elastic strip and for the elastic layer. One makes then various considerations concerning the finite thick plate. To solve the above mentioned problems, we shall use representations with the stress functions introduced in Sect. 5.3.2.5.
11.1 Elastic Parallelepiped The first fundamental problem for an elastic parallelepiped has been formulated, in 1852, by G. Lamé [4], who considered it to be very important both from the theoretical and the practical point of view, emphasizing—at the same time—the difficulties which appear in its solving. In his book, G. Lamé stimulates the young researchers to deal with this problem, for which he only sketches some results. At the same time, twice (in 1846 and 1858), the Academy of Sciences in Paris proposed this problem, endowing it with a prize; it became a classical problem of the theory of elasticity. This problem has not been sufficiently studied. There have been various considerations: theoretical, as well experimental; from the last point of view, the researchers dealt with the problem of compression of the concrete cubes. We mention thus the classical treatise of A. Föppl and L. Föppl [2]. The Russian school of elasticity tackled this problem by various approximate methods of computation. We mention thus the papers of M. M. Filonenko-Borodich [14–18], based on a variational method of Castigliano and on a choice of a system of functions which have been previous considered by the same author [1]; one used triple Fourier series, obtaining results in the first or in the second approximation for some cases of loading. A. I. Meshkov [28, 29] takes again this methods of computation for the oblique parallelepiped, considering loads which lead to torsion too.
P. P. Teodorescu, Treatise on Classical Elasticity, Mathematical and Analytical Techniques with Applications to Engineering, DOI: 10.1007/978-94-007-2616-1_11, Ó Springer Science+Business Media Dordrecht 2013
481
482
11
Elastic Parallelepiped. Elastic Strip. Elastic Layer. Thick Plate
The same method of computation has been applied by E. S. Kononenko [24, 25] to study the state of stress of concrete cubes subjected to compression. V. P. Netrebko [32, 33] deals with the torsion of the elastic parallelepiped acted upon by tangential loads. E¯. N. Baı˘da [9–11], using a method of computation analogous to that indicated by Boussinesq and Galerkin, makes some considerations concerning the isotropic and the anisotropic elastic parallelepiped. M. Mishonov [31] deals with the elastic parallelepiped acted upon by arbitrary volume forces, using triple Fourier series; by a certain procedure, one also obtains results for superficial loads as a limit case. In what follows, we will use the results given by us [38] and presented at the 1960 IUTAM Congress.
11.1.1 Stress Functions. Boundary Conditions Let b
Data Loading...
