The NURBS book
Isogeometric Analysis: Toward Integration of CAD and FEA
Isogeometric Analysis: Toward Integration of CAD and FEA
Isogeometric design of elastic arches for maximum fundamental frequency
Structural and Multidisciplinary Optimization
Isogeometric analysis and shape optimization via boundary integral
Computer-Aided Design
An isogeometrical approach to structural topology optimization by optimality criteria
Structural and Multidisciplinary Optimization
Shape optimization of continua using NURBS as basis functions
Structural and Multidisciplinary Optimization
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The subject of this work is numerical shape optimization in fluid mechanics, based on isogeometric analysis. The generic goal is to design the shape of a 2-dimensional flow domain to minimize some prescribed objective while satisfying given geometric constraints. As part of the design problem, the steady-state, incompressible Navier-Stokes equations, governing a laminar flow in the domain, must be solved. Based on isogeometric analysis, we use B-splines as the basis for both the design optimization and the flow analysis, thereby unifying the models for geometry and analysis, and, at the same time, facilitating a compact representation of complex geometries and smooth approximations of the flow fields. To drive the shape optimization, we use a gradient-based approach, and to avoid inappropriate parametrizations during optimization, we regularize the optimization problem by adding to the objective function a measure of the quality of the boundary parametrization. A detailed description of the methodology is given, and three different numerical examples are considered, through which we investigate the effects of the regularization, of the number of geometric design variables, and of variations in the analysis resolution, initial design and Reynolds number, and thereby demonstrate the robustness of the methodology.