Isogeometric analysis (IGA) has been a particularly impactful development in the realm of Kirchhoff-Love thin-shell analysis because the high-order basis functions employed naturally satisfy the requirement of C 1 continuity. Still, engineering models of appreciable complexity, such as wind turbine blades, are typically modeled using multiple surface patches and, often, neither rotational continuity nor conforming discretization can be practically obtained at patch interfaces. A penalty approach for coupling adjacent patches is therefore presented. The proposed method imposes both displacement and rotational continuity and is applicable to either smooth or nonsmooth interfaces and either matching or non-matching discretization. The penalty formulations require only a single, dimensionless penalty coefficient for both displacement and rotation coupling terms, alleviating the problem-dependent nature of the penalty parameters. Using this coupling methodology, numerous benchmark problems encapsulating a variety of analysis types, geometrical and material properties, and matching and non-matching interfaces are addressed. The coupling methodology produces consistently accurate results throughout all tests. Furthermore, the suggested penalty coefficient of α = 10 3 is shown to be effective for the wide range of problem configurations addressed. Finally, a realistic wind turbine blade model, consisting of 27 patches and 51 coupling interfaces and having a chordwise-and spanwise-variant composite material definition, is subjected to buckling, vibration, and nonlinear deformation analysis using the proposed approach.

In this paper an interactive parametric design-through-analysis platform is proposed to help design engineers and analysts make more effective use of Isogeometric Analysis (IGA) to improve their product design and performance. We develop several Rhinoceros (Rhino) plug-ins to take input design parameters through a user-friendly interface, generate appropriate surface and/or volumetric models, perform mechanical analysis, and visualize the solution fields, all within the same Computer-Aided Design (CAD) program. As part of this effort we propose and implement graphical generative algorithms for IGA model creation and visualization based on Grasshopper, a visual programming interface to Rhino. The developed platform is demonstrated on two structural mechanics examples-an actual wind turbine blade and a model of an integrally bladed rotor (IBR). In the latter example we demonstrate how the Rhino functionality may be utilized to create conforming volumetric models for IGA. KeywordsIsogeometric analysis, NURBS and T-splines, Parametric design, Rhino and Grasshopper, Visual programming, Graphical generative algorithms RightsWorks produced by employees of the U.S. Government as part of their official duties are not copyrighted within the U.S. The content of this document is not copyrighted. In this paper an interactive parametric design-through-analysis platform is proposed to help design engineers and analysts make more effective use of Isogeometric Analysis (IGA) to improve their product design and performance. We develop several Rhinoceros (Rhino) plug-ins to take input design parameters through a user-friendly interface, generate appropriate surface and/or volumetric models, perform mechanical analysis, and visualize the solution fields, all within the same Computer-Aided Design (CAD) program. As part of this effort we propose and implement graphical generative algorithms for IGA model creation and visualization based on Grasshopper, a visual programming interface to Rhino. The developed platform is demonstrated on two structural mechanics examples-an actual wind turbine blade and a model of an integrally bladed rotor (IBR). In the latter example we demonstrate how the Rhino functionality may be utilized to create conforming volumetric models for IGA. Authors Ming-Chen

This work describes a fluid-structure interaction (FSI) design optimization framework and applies it to improving the structural performance of a water brake used to stop aircraft landing on short runways. Inside the water brake, a dissipative torque is exerted on a rotor through interactions between rotor blades and a surrounding fluid. We seek to optimize blade shape over a parameterized design space, to prevent potentially-damaging stress concentrations without compromising performance. To avoid excessive numbers of costly simulations while exploring the design space, we use a surrogate management framework that combines derivative-free pattern search optimization with automated construction of a low-fidelity surrogate model, requiring only a handful of highfidelity FSI simulations. We avoid the difficult problem of generating fluid and structure meshes at new points in the design space by using immersogeometric FSI analysis. The structure is analyzed isogeometrically: its design geometry also serves as a computational mesh. This geometry is then immersed in an unfitted fluid mesh that does not depend on the structure's design parameters. We use this framework to make significant improvements to a baseline design found in the literature. Specifically, there is a 35% reduction of von Mises stress variance and a 25% reduction of maximum of stress, while the resisting torque and mass of the optimized blades remain uncompromised.

We present a new method for immersogeometric fluid flow analysis that directly uses the CAD boundary representation (B-rep) of a complex object and immerses it into a locally refined, non-boundary-fitted discretization of the fluid domain. The motivating applications include analyzing the flow over complex geometries, such as moving vehicles, where the detailed geometric features usually require time-consuming, labor-intensive geometry cleanup or mesh manipulation for generating the surrounding boundary-fitted fluid mesh. The proposed method avoids the challenges associated with such procedures. A new method to perform point membership classification of the background mesh quadrature points is also proposed. To faithfully capture the geometry in intersected elements, we implement an adaptive quadrature rule based on the recursive splitting of elements. Dirichlet boundary conditions in intersected elements are enforced weakly in the sense of Nitsche's method. To assess the accuracy of the proposed method, we perform computations of the benchmark problem of flow over a sphere represented using B-rep. Quantities of interest such as drag coefficient are in good agreement with reference values reported in the literature. The results show that the density and distribution of the surface quadrature points are crucial for the weak enforcement of Dirichlet boundary conditions and for obtaining accurate flow solutions. Also, with sufficient levels of surface quadrature element refinement, the quadrature error near the trim curves becomes insignificant. Finally, we demonstrate the effectiveness of our immersogeometric method for high-fidelity industrial scale simulations by performing an aerodynamic analysis of an agricultural tractor directly represented using B-rep. AbstractWe present a new method for immersogeometric fluid flow analysis that directly uses the CAD boundary representation (B-rep) of a complex object and immerses it into a locally refined, non-boundary-fitted discretization of the fluid domain. The motivating applications include analyzing the flow over complex geometries, such as moving vehicles, where the detailed geometric features usually require time-consuming, labor-intensive geometry cleanup or mesh manipulation for generating the surrounding boundary-fitted fluid mesh. The proposed method avoids the challenges associated with such procedures. A new method to perform point membership classification of the background mesh quadrature points is also proposed. To faithfully capture the geometry in intersected elements, we implement an adaptive quadrature rule based on the recursive splitting of elements. Dirichlet boundary conditions in intersected elements are enforced weakly in the sense of Nitsche's method. To assess the accuracy of the proposed method, we perform computations of the benchmark problem of flow over a sphere represented using B-rep. Quantities of interest such as drag coefficient are in good agreement with reference values reported in the literature. The results show that the ...

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.

Valvular heart disease has recently become an increasing public health concern due to the high prevalence of valve degeneration in aging populations. For patients with severely impacted aortic valves that require replacement, catheter-based bioprosthetic valve deployment offers a minimally invasive treatment option that eliminates many of the risks associated with surgical valve replacement. Although recent percutaneous device advancements have incorporated thinner, more flexible biological tissues to streamline safer deployment through catheters, the impact of such tissues in the complex, mechanically demanding, and highly dynamic valvular system remains poorly understood. The present work utilized a validated computational fluid–structure interaction approach to isolate the behavior of thinner, more compliant aortic valve tissues in a physiologically realistic system. This computational study identified and quantified significant leaflet flutter induced by the use of thinner tissues that initiated blood flow disturbances and oscillatory leaflet strains. The aortic flow and valvular dynamics associated with these thinner valvular tissues have not been previously identified and provide essential information that can significantly advance fundamental knowledge about the cardiac system and support future medical device innovation. Considering the risks associated with such observed flutter phenomena, including blood damage and accelerated leaflet deterioration, this study demonstrates the potentially serious impact of introducing thinner, more flexible tissues into the cardiac system.

In this paper, we present an isogeometric analysis framework for design space exploration. While the methodology is presented in the setting of structural mechanics, it is applicable to any system of parametric partial differential equations. The design space exploration framework elucidates design parameter sensitivities used to inform initial and early-stage design. Moreover, this framework enables the visualization of a full system response, including the displacement and stress fields throughout the domain, by providing an approximation to the system solution vector. This is accomplished through a collocation-like approach where various geometries throughout the design space under consideration are sampled. The sampling scheme follows a quadrature rule while the physical solutions to these sampled geometries are obtained through an isogeometric method. A surrogate model to the design space solution manifold is constructed through either an interpolating polynomial or pseudospectral expansion. Examples of this framework are presented with applications to the Scordelis-Lo roof, a Flat L-Bracket, and an NREL 5MW wind turbine blade.

Early‐stage wind turbine blade design usually relies heavily on low‐fidelity structural models; high‐fidelity, finite‐element‐based structural analyses are reserved for later design stages because of their complex workflows and high computational expense. Yet, high‐fidelity structural analyses often provide design‐governing feedback such as buckling load factors. Mitigation of the issues of workflow complexity and computational expense would allow designers to utilize high‐fidelity feedback earlier, more easily, and more often in the design process. Thus, a blade analysis framework that employs isogeometric analysis (IGA), a simulation method that overcomes many of the aforementioned drawbacks associated with traditional finite element analysis (FEA), is presented. IGA directly utilizes the mathematical models generated by computer‐aided design (CAD) software, requiring less user interaction and no conversion of parametric geometries to finite element meshes. Furthermore, IGA tends to have superior per‐degree‐of‐freedom accuracy compared with traditional FEA. Issues unique to IGA in the context of wind turbine blade design, such as coupling of thin‐shell components, are addressed, and a design approach that combines reduced‐order aeroelastic analysis with IGA is outlined. Aeroelastic analysis is used to efficiently provide dynamic kinematic data for a wide range of wind load cases, while IGA is used to perform buckling analysis. The value of incorporating high‐fidelity analysis feedback into blade design is demonstrated through optimization of the NREL/SNL 5 MW wind turbine blade. A variety of potential designs are produced with reduced blade mass and material cost, and IGA‐based buckling analysis is shown to provide design‐governing constraint information.