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Bonnans inria. Received: 24 July Revised: 2 May The paper deals with an optimal control problem with a scalar first-order state constraint and a scalar control. In presence of nonessential touch points, the arc structure of the trajectory is not stable.


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  6. Under some reasonable assumptions, we show that boundary arcs are structurally stable, and that touch point can either remain so, vanish or be transformed into a single boundary arc. Assuming a weak second-order optimality condition equivalent to uniform quadratic growth , stability and sensitivity results are given.

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    Close this notification. Smart Materials and Structures. Such solutions are, of course, impractical from structural engineering perspective.

    go Incorporating stress and stability metrics into the topology optimization formulation, however, involves significant mathematical challenges primarily due to the possibility of vanishing members, which ultimately leads to singularities and disjointed regions in the design space that gradient-based optimization struggles to navigate.

    This thesis reviews and discusses these challenges and explores a disaggregated formulation where design and state variables are treated as free optimization variables to enable consideration of stress, member buckling, and global system stability metrics in a mathematically consistent manner. The impact of various constraints and objectives on the optimized solutions is demonstrated for simple truss design problems.

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