In this paper, we present a method to create draw-beads for improving the strength of sheet metal structures. We define a mechanically natural creation law such that local curvatures are created in proportion to the amount of local stresses in the perpendicular direction of the principal stress direction for resisting distributed bending moments. The local curvature is created by self-equilibrium bending moment. Owing to the law, the draw-beads are created without any artificial operations such as basis vectors. The thickness is assumed to be constant and the volume is constrained to a specified value. By repeating the stress analysis and the bead creation analysis alternately, the maximum stress is reduced, while creating the draw-beads. Orthogonal material property is defined only in the bead creation analysis. A threshold value is introduced to avoid a meaningless disturbance of the shape, and its effect is investigated. The validity of this numerical method to create the draw-beads for improving the strength of sheet metal structures is verified through some examples.

In this paper, we present a numerical analysis method for shape ontimization in the rigidity design of plate and shell structures. It is assumed that the design damain is varied in the in-plane direction to maintain the curvatures of the initial shape. An external work, or a compliance is used as an index of the rigidity. The weight minimization problem subjected to the rigidity constraint is formulated as a non-parametric shape optimization problem using the Lagrangian approach and the material derivative method. The shape gradient function and the optimality conditions are theoretically derived for this problem. The traction method is applied to determine the smooth in-plane domain variation that minimizes the objective functional. This method is applied to a simple shell example and a practical automotive chassis component to verify the effectiveness and practical utility for weight reduction of plate and shell structures subjected to the rigidity constraint.

In this paper, we present a numerical analysis method for in-plane shape optimization of plate and shell structures subjected to a von Mises strength criterion. The weight minimization problem is formulated as a non-parametric shape optimization problem using the Lagrangian approach and the material derivative method. The shape gradient function and the optimality conditions are theoretically derived for this problem. The traction method is applied to determine the smooth in-plane domain variation that minimizes the objective functional. This method is applied to simple shell examples and practical automotive chassis components to verify the effectiveness and practical utility for weight reduction of plate and shell structures subjected to the strength criterion.

In this paper, we present a solution to shape optimization of plate and shell structures for a natural frequency problem. The weight is minimized under a natural frequency constraint. The designed boundaries are assumed to be movable only to in-plane directions. Optimized structures are discretized by the plane elements based on the Mindlin-Reissner's plate theory. A non-parametric, or a distributed shape optimization problem is formulated and the shape gradient function is theoretically derived using the material derivative method and the Lagrange multiplier method. The traction method, or the shape optimization method developed by authors is applied to obtain the optimal shape in this problem. The validity of this numerical solution to minimize the weight of plate and shell structures is verified through simple and practical examples.