Optimum Stiffness and Strength of Elastic Structures

Previously established principles of optimizing the stiffness of elastic structures are confined mainly to cases (such as bars and trusses) in which the strain energy density is linearly related to the design variable. This coverage is extended to broader classes of elastic structures as well as to the problem of maximum strength. For fixed value of the objective function, the design criterion of constant weighted strain energy in the design fibers is a necessary condition to make the stiffness stationary. Several classes of structures are exhibited for which this criterion is also sufficient for either a global maximum or minimum. Moreover, under certain (nontrivial) circumstances, the same criterion may also be sufficient for maximum resistance against stress failure. The effect of design constraints, either from above or below, is also described. In addition, explicit methods of investigating local stiffness optimality are established and demonstrated, including the effect of local singularities at point of vanishing stress.