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A framework for parametric design optimization using isogeometric analysis. (English) Zbl 1439.74258

Summary: Isogeometric analysis (IGA) fundamentally seeks to bridge the gap between engineering design and high-fidelity computational analysis by using spline functions as finite element bases. However, additional computational design paradigms must be taken into consideration to ensure that designers can take full advantage of IGA, especially within the context of design optimization. In this work, we propose a novel approach that employs IGA methodologies while still rigorously abiding by the paradigms of advanced design parameterization, analysis model validity, and interactivity. The entire design lifecycle utilizes a consistent geometry description and is contained within a single platform. Because of this unified workflow, iterative design optimization can be naturally integrated. The proposed methodology is demonstrated through an IGA-based parametric design optimization framework implemented using the Grasshopper algorithmic modeling interface for Rhinoceros 3D. The framework is capable of performing IGA-based design optimization of realistic engineering structures that are practically constructed through the use of complex geometric operations. We demonstrate the framework’s effectiveness on both an internally pressurized tube and a wind turbine blade, highlighting its applicability across a spectrum of design complexity. In addition to inherently featuring the advantageous characteristics of IGA, the seamless nature of the workflow instantiated in this framework diminishes the obstacles traditionally encountered when performing finite-element-analysis-based design optimization.

MSC:

74P10 Optimization of other properties in solid mechanics
65D07 Numerical computation using splines
74S05 Finite element methods applied to problems in solid mechanics
65D17 Computer-aided design (modeling of curves and surfaces)
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)

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