A general optimality criterion for strength and stiffness of dual-material-property structures

An optimality criterion is established for combined strength and stiffness requirements per unit weight of structures utilizing materials which may have different strength, stiffness or density for the tension and compression members. In the extreme case this covers the use of different materials for tension and compression members; referred to here as dual-material structures. It is shown that additional considerations are required for statically determinate structures and proof of optimality is given for statically indeterminate and statically determinate cases. In all cases, the optimal structures are based on Michell structural layouts, in which the cross-sectional areas of the structural members are determined to give constant strain energy per unit mass. Material density may be replaced by material cost per unit volume to optimize combined strength and stiffness requirements for minimum material cost.