Premium
Non‐existence of solutions in optimal structural design
Author(s) -
Stadler W.
Publication year - 1986
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.4660070303
Subject(s) - mathematical proof , context (archaeology) , optimal design , contradiction , axial symmetry , mathematical optimization , boundary (topology) , mathematics , space (punctuation) , computer science , function (biology) , mathematical analysis , geometry , geology , philosophy , paleontology , statistics , epistemology , operating system , evolutionary biology , biology
Recently, much effort has been expended in establishing the well‐posedness of optimal structural design problems. Experience indicates, however, that awareness of the non‐existence of a solution may also be beneficial and can eliminate time wasted in searching for non‐existing numerical or analytical optima. Two standard approaches to non‐existence proofs are presented: the construction of suitable sequences and the use of necessary conditions — both within the context of contradiction proofs. The methods are illustrated with examples from optimal structural design ranging from the minimum weight design of an axially loaded rod to that of axisymmetrically loaded shells of revolution. It is shown that the causes of non‐existence can be the choice of function space, boundary conditions, and a discontinuous dependence on parameters, among others. Some possible guidelines for a successful formulation of well‐posedness in structural design are included.