Vol. 9, No. 4 (1953)
1953, 22 (4): 215-220. doi: 10.7498/aps.9.215
In this paper, it is proved that Saint-Venant's solution for torsion can be obtained from the following simplified assumptions: (?τxz)/(?z)=(?τyz)/(?z)=0. These assumptions are much more simplified than those given by Saint-Venant in 1855, A. Clebsch in 1862, W. Voigt in 1887, and J. N. Goodier in 1937.
1953, 22 (4): 221-237. doi: 10.7498/aps.9.221
The problem of torsion of a prismatic body with multiply-connected, cross section is considered from the view-point of two basic variationa'l principles in the theory of elasticity, viz., the principle of minimum potential energy and the principle of complementary energy. According to the former, among all admissible states of strain, in the sense of being derived from sets of displacements chat satisify the specified displacement boundary conditions, the true state renders the potential energy of the system a minimum. In the latter, among all admissible states in the sense of satisfying the equilibrium conditions and the specified stress boundary conditions, the true state renders the complementary energy of the elastic body a minimum.
1953, 22 (4): 238-254. doi: 10.7498/aps.9.238
In this paper, the problem of torsion of prisms bounded by two intersecting circular cylinders is solved by means of Fourier's integrals. It is found that when the angle of intersection of these two circular cylinders is commensurable with π the stress function and the torsional rigidity of the prism can be expressed in closed form in terms of circular and hyperbolic sines and cosines.
1953, 22 (4): 255-274. doi: 10.7498/aps.9.255
The free torsion problem, solved by Saint-Venant with semi-inverse method, is well known in the theory of elasticity. "In this paper we discuss this problem systematically by considering a cylindrical bar whose cross section is a simply connected region under twist moment M, and assume that the stress function ψ is in the form of a third degree polynomial.
1953, 22 (4): 275-293. doi: 10.7498/aps.9.275
The theoretical conditions for brittle rupture were found with one single normal stress as the only mechanical variable. But, for the conditions of ductile rupture, experi-mental facts demand the specification of some stress states instead of a single stress and certain arbitrary stress functions were taken for this purpose. A theoretical formulation of the conditions for ductile rupture has not been made up to this date. Fundamentally, such problem would be approached from the dislocation theory, but quantitative treatment is difficult in the present state of this theory. Alternatively it may be possible to approach this problem from the view point of relaxation, should the basic phenomenon of strain hardening associated with ductile fracturing be well interrepted from this view point. It is believed that future studies along such lines will throw more light on the understanding of this problem. Yet, it was thought that if one considers the thermodynamic relation among various types of energy involved in ductile fracture instead of simply taking some arbitrary stress functions as criterion, the conclusions thus obtained would be helpful in understanding this problem, Thus this paper was written.
1953, 22 (4): 294-301. doi: 10.7498/aps.9.294
The analysis of a rotating circular plate is an easy problem because of circular symmetry. However, for the boundary other than circular, the problem will become much more complicated. For example, we may be theoretically interested in the stresses in a rectangular plate, which rotates with respect to its geometric center. If die thickness of he plate is small when compared with its length and width, the variation of stresses throughout the thickness can be neglected. Consequently, we shall have a two dimensional problem with body force acting. To solve a two dimensional problem with rectangular boundary is not always feasible. By using trigonometric series, we can only satisfy the conditions on the two sides of the plate. Accordingly the result can only be of value when the length of the plate is much larger than its width. If both dimensions of the plate are of the same order, the boundary conditions on the four sides must be considered. In the solution of the problem of this kind the principle of minimum strain energy may be successfully applied.
1953, 22 (4): 302-316. doi: 10.7498/aps.9.302
The purpose of this paper is to investigate to what extent the distribution of orbital angular momentum of nucleons in a nucleus implied by the (theory of shell structure limits the form of nuclear density. The effect of the latter has shown itself in a number of physical problems, such as the scattering of high, energy electrons by nuclei, the hyperfine structure, the absorption of negative μ-mesons by nuclei, internal conversion coefficient in heavy elements, etc.