Abstract
This paper presents a shape optimization method for a linear buckling load maximization problem of plate and shell structures. The structures are assumed to be movable in the tangent and/or normal direction to the surface. The buckling load factor is set as the objective function, and is maximized under a volume and side constraints conditions, and also multiple root limitation condition. The shape gradient function for this problem is derived using the Lagrange multiplier method and the formula of the material derivative. The shape gradient function is then applied to a velocity analysis. The free-form optimization method, a H^1 gradient method for shells is used to determine the optimal surface variation. This method is applied to an open cylindrical roof and a two dimensional column. The results show the validity of this method to determine the optimal free-forms of plate and shell structures in linear buckling design problems.
