Optimization of Structures With Control Forces and Displacements

Optimization problems are formulated for structural engineering problems using control forces and displacements applied to different beam systems. These external control forces are employed to reduce the internal forces and required cross-section dimensions for given loading conditions. A formulation is presented for an actively controlled system, a passively controlled system, a passive system with prestress forces and a passive system without control forces. For purposes of illustration, in the control, bending moments and shear forces are introduced by support displacements in an indeterminate beam structure. The latter displacements can be controlled with an external energy supply (active system), elastic supports (passive system) or they can be predetermined (prestressed system). Numerical examples demonstrate the structural weight advantages for the different systems. Comparison of results also show the magnitude of the increased allowable loading capacities in each system for fixed cross-sectional dimensions. The methods developed can be extended to a variety of different structural applications and problems.