Optimization in Trusses Using Optimal Control Theory

A method is given for the optimum design of linearly elastic trusses which can be partitioned into a series of statically determinate substructures. In the case of such structures the design problem is formulated as a problem in optimal control theory. The member areas of substructures are treated as control variables and the interacting forces between substructures are taken as the state variables. Transformation equations for state variables are derived using equilibrium and displacement compatibility conditions. The design problem is envisaged as a problem of determining optimal controls to minimize the weight of the truss. This necessitates the solution of a number of smaller problems in sequence, instead of a single problem of larger dimension. Solution of the resulting optimal control problem can be obtained using the method of local variations.