Alternative statements of optimal load-bearing structure design problems

We analyze the well-known statements of optimal design problems for load-bearing maximum rigidity structures in which a principle of the minimum of total potential energy of structure deformation is used. A version of the generalized statement of optimization problems for processes described by linear equations with a symmetric operator is proposed. On the basis of the version outlined, we present a mathematical algorithm for obtaining beam structures of maximum rigidity, in which the finite element method is used to solve an analytical problem. We give the numerical results of solving two problems of optimal design of maximum rigidity structures that are simulated by cantilever and statically indeterminate beams.