A rapid and efficient isogeometric design space exploration framework with application to structural mechanics

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 5 MW wind turbine blade

An interactive geometry modeling and parametric design platform for isogeometric analysis

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

A framework for parametric design optimization using isogeometric analysis

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

Direct immersogeometric fluid flow analysis using B-rep CAD models

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\u27s 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

A rapid and efficient isogeometric design space exploration framework with application to structural mechanics

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 5 MW wind turbine blade.This is a manuscript of an article published as Benzaken, J., A. J. Herrema, M-C. Hsu, and J. A. Evans. "A rapid and efficient isogeometric design space exploration framework with application to structural mechanics." Computer Methods in Applied Mechanics and Engineering 316 (2017): 1215-1256. doi: 10.1016/j.cma.2016.12.026. Posted with permission.</p

A framework for parametric design optimization using isogeometric analysis

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.This is a manuscript of an article published as Herrema, Austin J., Nelson M. Wiese, Carolyn N. Darling, Baskar Ganapathysubramanian, Adarsh Krishnamurthy, and Ming-Chen Hsu. "A framework for parametric design optimization using isogeometric analysis." Computer Methods in Applied Mechanics and Engineering (2016). DOI:10.1016/j.cma.2016.10.048. Posted with permission.</p