Bolza問題としてのはりの最大剛性解について

抄録

We establish a general theory of maximum stiffness design of elastic beams subject to a given volume. Determination of the maximum stiffness of a beam, with the height taken as an independent variable can be treated as the Bolza problem. The beam is taken to be symmetrical about its center line. The theory thus obtained can easily be extended to take account of variable width or section area of the beam, by defining a control vector u. An illustrative application is presented in cases of cantilever and simple beam designs subjected to a restriction of the lower bound under an arbitrary external load.