The high cantilevered beam of minimal compliance

The state of stress in a high (that is, blunt, tapering) trapezoidal cantilevered elastic beam loaded by a transverse force applied at the free end is determined by extending an approximate method proposed by Galerkin (Sbornik Len. Inst. 99 (1929)). The solution is used to solve the problem of finding, among the trapezoidal profiles of given area and width, that one which minimizes the compliance, or equivalently the displacement of the point of application of the load. The optimum profile is an isosceles trapezium, but certain additional conditions, for example those found in the bird kingdom, cause the optimum profile to become a non-symmetric trapezium two of whose adjacent sides contain a right angle.