Robust geometry and topology optimization of plane frames using order statistics and force density method with global stability constraint

This paper presents a worst case approach for robust geometry and topology optimization of plane frames with global stability constraint. Uncertainty is assumed to exist in the nodal locations cross-sectional areas, values objective constraint functions are relaxed quantile structural responses represented by order statistics given robustness confidence levels. In alleviate difficulty caused melting nodes some extent, force density method applied an auxiliary truss model frame, closely spaced merged. A presented generating correlated imperfections along each member, penalization proposed geometrical stiffness matrix exclude superficial local buckling. It demonstrated numerical examples that result obtained less sensitive uncertainty, also satisfied under uncertainty specified