A study on symmetry properties in structural optimization

1. Abstract In the present paper, some symmetry results for optimal solutions in structural optimization have been proposed and proven. It is found that under some invariant assumptions, for many structural optimization problems that can be formulated as quasi-convex programs, there exists at least one symmetric global optimal solution if the prescribed loading and support conditions are symmetric. Meanwhile, for some specific non-convex cases, a weaker result is also presented. Furthermore, some new results about the symmetry properties of robust optimization, which has seldom been toughed in the literature, are also presented. Numerous concrete examples illustrate the claims made in the present work explicitly.