Force fields within Michell-like cantilevers transmitting a point load to a straight support

Abstract

The paper concerns distribution of the force fields within Michell cantilevers supported on a segment of a straight line. The allowable yield stresses for tension and compression are not necessarily equal. The paper puts emphasis on checking the final results for the optimal weight by computing the weight in two manners: as a virtual work or, alternatively, by finding the force fields, the density of fibres and then by summing up the weights of all the parts of the optimal cantilever, i.e. the weights of the reinforcing bars and the weights of all the fibrous domains. If this duality gap vanishes, the solution is correct. © 2006 Springer.