OPTIMAL ELASTIC DESIGN OF BEAMS

According to the principle of minimum complementary energy a mathematicalstatement of optimal strength design problem for elastic beams is formulated in thisresearch, which is an extremum problem of functionals with equality and inequalityconstraints. Further the application of the Lagrangian multiplier method yields thenecessary conditions for extrema. A set of relations that must be satisfied the optimalsolution follows afterwarde. This set of relations can be used to verify the optimality of auniform strength design or any feasible elastic design. An iterative numerical method tofind the optimal solution when the uniform strength design is not optimal is also presented inthis paper.