CONVEX SHAPES FOR GIVEN TORSION CONSTANT AND SECOND MOMENTS OF AREA

The paper presents approximate analytical solutions of the problem of finding the shape or a plane convex figure that encloses the least area but whose torsion constant and the least second moment of area about any centroidal axis are not less than certain prescribed values. It is shown that these solutions are in good agreement with the numerical solution of the corresponding-non-linear programming problem.