Michell trusses in the presence of microscale material randomness: limitation of optimality
Martin Ostoja‐Starzewski · Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences · 2001
The classical problem of a Michell (optimal) truss concerns a minimum-weight design of a planar truss that transmits a given load to a given rigid foundation with the requirement that the axial stresses in the bars of the truss stay within an allowable range σ0 ≤ σ ≤ σ0. The present study considers this problem when the truss is made of a material with random microstructure, that is, when σ0 is a random field. The trusses tending to the optimal state can be determined through a net of characteristics generalized to a stochastic setting. While in the classical case of a homogeneous material this net gives the minimum weight as its spacing tends to zero, the presence of a random microstructure prevents the attainment of this state. Basically, the finer the net, the stronger the scatter of characteristics, which forces one to use more structural material to compensate for these fluctuations. In effect, there is a limitation to the attainment of the optimality of the Michell truss made of a hypothetical perfectly homogeneous material.