Shinnosuke Fujita

Shape Optimization of Free-form Shells Using Invariants of Parametric Surface

A new approach is proposed for shape optimization of shells, where the requirements on geometrical properties, constructability, and mechanical performance are simultaneously considered in the problem formulation. The surface shape is modeled using a triangular Bézier patch to reduce the number of design variables, while the ability of generating moderately complex shape is maintained. The strain energy under specified loading condition is used to represent the mechanical performance, and the geometrical properties are quantitatively defined using algebraic invariants of the parametric surface. The developable surface that has high constructability is generated by assigning an appropriate constraint on an algebraic invariant. The effectiveness of the proposed approach is demonstrated through several numerical examples, and the characteristics of the optimal shapes under various constraints are discussed.

Alternating direction method of multipliers for truss topology optimization with limited number of nodes: a cardinality-constrained second-order cone programming approach

Abstract This paper addresses the compliance minimization of a truss, where the number of available nodes is limited. It is shown that this optimization problem can be recast as a second-order cone programming with a cardinality constraint. We propose a simple heuristic based on the alternative direction method of multipliers. The efficiency of the proposed method is compared with a global optimization approach based on mixed-integer second-order cone programming. Numerical experiments demonstrate that the proposed method often finds a solution having a good objective value with small computational cost.