Vol. 11, No. 3 (1955)
1955, 29 (3): 199-206. doi: 10.7498/aps.11.199
An investigation on the average number v of prompt neutrons emitted per thermal neutron induced fission of U235 has been made with the Fermi gas statistical model. Weizsacker-Fermi semi-empirical mass equation has been used in calculating the neutron binding energies of the fission fragments. Using Stern's value for the mass of U235, the total excitation energy Ee of the fission fragments has been estimated to be of the order of 10 to 20 Mev for different hypotheses regarding the primary fission products. The results of calculation (given in the third table) show that only the hypothesis of equal radioactive chain lengths together with the assumption (A) that the excitation energy Ee is shared by the two fragments in proportion to their masses yields values of v exceeding 2. The latter assumption is not in accord with the experimental finding of Fraser that the light fragment group emits on the average 30% more neutrons than does the heavy. However, a shift of mass of U235 towards larger values or of kinetic energy of fission fragments towards lower values so that 5 Mev more excitation energy is available would make v considerably larger than 2 even with the assumption (B) that the excitation energy is shared by the two fragments in inverse proportion to their masses, thus making possible conformity with Fraser's discovery. Even then, in no case has the value of v thus calculated exceeded 3 (as shown in the fourth table), which may then be taken as a theoretical upper bound for the value of ν for thermal neutron induced fission of U235. The results of this investigation are thus seen to be in harmony with the recently announced experimental value 2.5 ±0.1 for ν.
1955, 29 (3): 207-218. doi: 10.7498/aps.11.207
The classical Kirchhoff-Love theory of thin plates when applied to plates of variable thickness results in a fourth-order partial differential equation with variable coefficients which is difficult to solve. So far, only three cases are known with numerical certainty, namely, the symmetrical bending of circular plates, the unsymmetrical bending of a circular plate with quadratically varying stiffness, and a rectangular plate with linear stiffness in one direction and simply supported on two opposite edges. These solutions are analytic, generally involving special functions such as the exponential integrals and the confluent hypergeometric functions. The only difficulties involved are apparently in the nature of disagreeable computation.The problem of a clamped edge circular plate under uniform load with thickness represented by the expression .
1955, 29 (3): 239-258. doi: 10.7498/aps.11.239
The paper is an application of the author's general theory of sandwich plate (Ref. 1). Since the deformation is very small when buckling starts, the problem can be considered as a linear case. The theoretical critical stress found by this theory shows different types of buckling; symmetric and anti-symmetric, qausi-eulerian and wrinkling. The minimum symmetrical buckling stress found by the present theory, unlike most previous theoretical results (with isotropic core), is not always greater than the anti-symmetric buckling stress. In comparison with the existing theories, the theoretical results of the present work show better agreement with experiments for all types of buckling. The critical wrinkling stresses decrease when, other things remaining the same, the core to face thickness ratio decreases. This is verified by many wrinkling failures in the Forest Product Laboratory tests (Ref. 10, 11, 12). Previous theories with isotropic core theory have so far failed to indicate this fact. Comparison of the compression buckling of rectangular plates with two (the two loaded edges simply-supported, the other two being free) and four simply-supported edges has also been given in order to show the effect of the two additional supports.
Bending of sandwich beams has been treated as a non-linear problem. The non-linearity is called forth by the distributed thrust in the compression face. The non-linear differential equations for cantilevered sandwich beams with concentrated load at end are solved by using load parameter power series. On account of the labour involved in this method, the solution has been calculated up only to terms containing the square of the load. This will be an approximation going a little beyond the usual small load range which can be covered by a linear theory. Its value is not so much that it gives a correction to linear theory, but rather that it shows the latter's range of validity. The results of the present theory show that if the fixed faces are stressed to their elastic limit, they almost always have appreciable non-linear stresses. The theoretical expressions give good experimental checks. The existence of such non-linearities clearly demonstrate that the proposed use of the experimentally determined "composite plate constants" from the linear theory will be of doubtful validity. In the face the linear bending stress of the outmost fibre at the fixed end is found always greater than the linear mean normal stress. Thus treatment of the faces as mere membrances, to simplify the bending problem of the sandwich plate, is likely to lead to large errors.