Isogeometric shape optimization for quasi-static processes.

*(English)*Zbl 1352.74257Summary: A framework to solve shape optimization problems for quasi-static processes is developed and implemented numerically within the context of isogeometric analysis (IGA). Recent contributions in shape optimization within IGA have been limited to static or steady-state loading conditions. In the present contribution, the formulation of shape optimization is extended to include time-dependent loads and responses. A general objective functional is used to accommodate both structural shape optimization and passive control for mechanical problems. An adjoint sensitivity analysis is performed at the continuous level and subsequently discretized within the context of IGA. The methodology and its numerical implementation are tested using benchmark static problems of optimal shapes of orifices in plates under remote bi-axial tension and pure shear. Under quasi-static loading conditions, the method is validated using a passive control approach with an a priori known solution. Several applications of time-dependent mechanical problems are shown to illustrate the capabilities of this approach. In particular, a problem is considered where an external load is allowed to move along the surface of a structure. The shape of the structure is modified in order to control the time-dependent displacement of the point where the load is applied according to a pre-specified target.

##### MSC:

74P20 | Geometrical methods for optimization problems in solid mechanics |

74S30 | Other numerical methods in solid mechanics (MSC2010) |

65D17 | Computer-aided design (modeling of curves and surfaces) |

##### Keywords:

isogeometric analysis; shape optimization; quasi-static process; passive optimal control; adjoint method
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\textit{Z.-P. Wang} and \textit{S. Turteltaub}, Int. J. Numer. Methods Eng. 104, No. 5, 347--371 (2015; Zbl 1352.74257)

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