On the Masur paradox

摘要: It was shown by Barnett, Shield, and Prager in the sixties that optimal elastic beam design for a deflection constraint, continuously variable stiffness is proportional to square root of product real virtual moments. In case constraint at single point, moments equilibrate unit load point. As Masur pointed out early seventies, above optimality condition implies must everywhere have same sign. Tn view fact corresponding adjoint displacement fields be kinematically admissible, justifiably concluded solution satisfying all requirements may not exist some problems. An explanation this apparent paradox, involving an unusual type singularity solution, given paper. also mathematical programming (MP) methods do yield close approximation exact class problems considered, while iterative criteria (OC) fully confirm findings.