A geometrically exact isogeometric Kirchhoff plate: Feature‐preserving automatic meshing and C1 rational triangular Bézier spline discretizations

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/144603/1/nme5809.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/144603/2/nme5809_am.pd

Optimization of a Centrifugal Compressor Using the Design of Experiment Technique

Centrifugal compressor performance is affected by many parameters, optimization of which can lead to superior designs. Recognizing the most important parameters affecting performance helps to reduce the optimization process cost. Of the compressor components, the impeller plays the most important role in compressor performance, hence the design parameters affecting this component were considered. A turbocharger centrifugal compressor with vaneless diffuser was studied and the parameters investigated included meridional geometry, rotor blade angle distribution and start location of the main blades and splitters. The diffuser shape was captured as part of the meridional geometry. Applying a novel approach to the problem, full factorial analysis was used to investigate the most effective parameters. The Response Surface Method was then implemented to construct the surrogate models and to recognize the best points over a design space created as based on the Box-Behnken methodology. The results highlighted the factors that affected impeller performance the most. Using the Design of Experiment technique, the model which optimized both efficiency and pressure ratio simultaneously delivered a design with 3% and 11% improvement in each respectively in comparison to the initial impeller at the design point. Importantly, this was not at the expense of sacrificing range, of critical concern in compressor design

Terrain Surface Modeling Using Triangular Spline Patches

Algorithms and software for digital terrain modeling using TIN based surface model are presented in the paper. Processing of all types of terrain surface data are supported: mass points, local extrema, contours, breaklines, structure lines, fault lines, etc. TIN topology and Bézier triangular surface patches are used for terrain surface reconstruction. Special attention is dedicated to the problem of respecting all implicit information about terrain surface that are contained within the input data. This is especially important in cases when terrain surface has to be reconstructed by using mostly contour data, since there are a lot of additional information that are implicitly contained within the data of this type. The software also contains functions for efficient verification of collected terrain data and DTM. Special consideration is given to the numerical procedures and algorithms aiming at providing contours and other outputs of DTM analysis of cartographic quality as required by many surveyors and their clients. The results of experiments demonstrated that the quality of terrain surface reconstruction from contours and/or other data using developed procedures and software is better, or at least as good as the quality achieved by using procedures and methods implemented within standard GIS/DTM software

Non-Uniform Rational B-Splines and Rational Bezier Triangles for Isogeometric Analysis of Structural Applications

Isogeometric Analysis (IGA) is a major advancement in computational analysis that bridges the gap between a computer-aided design (CAD) model, which is typically constructed using Non-Uniform Rational B-splines (NURBS), and a computational model that traditionally uses Lagrange polynomials to represent the geometry and solution variables. In IGA, the same shape functions that are used in CAD are employed for analysis. The direct manipulation of CAD data eliminates approximation errors that emanate from the process of converting the geometry from CAD to Finite Element Analysis (FEA). As a result, IGA allows the exact geometry to be represented at the coarsest level and maintained throughout the analysis process. While IGA was initially introduced to streamline the design and analysis process, this dissertation shows that IGA can also provide improved computational results for complex and highly nonlinear problems in structural mechanics. This dissertation addresses various problems in structural mechanics in the context of IGA, with the use of NURBS and rational Bézier triangles for the description of the parametric and physical spaces. The approaches considered here show that a number of important properties (e.g., high-order smoothness, geometric exactness, reduced number of degrees of freedom, and increased flexibility in discretization) can be achieved, leading to improved numerical solutions. Specifically, using B-splines and a layer-based discretization, a distributed plasticity isogeometric frame model is formulated to capture the spread of plasticity in large-deformation frames. The modeling approach includes an adaptive analysis where the structure of interest is initially modeled with coarse mesh and knots are inserted based on the yielding information at the quadrature points. It is demonstrated that improvement on efficiency and convergence rates is attained. With NURBS, an isogeometric rotation-free multi-layered plate formulation is developed based on a layerwise deformation theory. The derivation assumes a separate displacement field expansion within each layer, and considers transverse displacement component as C0-continuous at dissimilar material interfaces, which is enforced via knot repetition. The separate integration of the in-plane and through-thickness directions allows to capture the complete 3D stresses in a 2D setting. The proposed method is used to predict the behavior of advanced materials such as laminated composites, and the results show advantages in efficiency and accuracy. To increase the flexibility in discretizing complex geometries, rational Bézier triangles for domain triangulation is studied. They are further coupled with a Delaunay-based feature-preserving discretization algorithm for static bending and free vibration analysis of Kirchhoff plates. Lagrange multipliers are employed to explicitly impose high-order continuity constraints and the augmented system is solved iteratively without increasing the matrix size. The resulting discretization is geometrically exact, admits small geometric features, and constitutes C1-continuity. The feature-preserving rational Bézier triangles are further applied to smeared damage modeling of quasi-brittle materials. Due to the ability of Lagrange multipliers to raise global continuity to any desired order, the implicit fourth- and sixth-order gradient damage models are analyzed. The inclusion of higher-order terms in the nonlocal Taylor expansion improves solution accuracy. A local refinement algorithm that resolves marked regions with high resolution while keeping the resulting mesh conforming and well-conditioned is also utilized to improve efficiency. The outcome is a unified modeling framework where the feature-preserving discretization is able to capture the damage initiation and early-stage propagation, and the local refinement technique can then be applied to adaptively refine the mesh in the direction of damage propagation.PHDCivil EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/147668/1/ningliu_1.pd

Proper Orthogonal Decomposition for Surrogate Models in Aerodynamics

This study describes the design and implementation of surrogate models for aerodynamic optimization or database generations. Two different methods are presented: the first one follows the classical methodology: a parametric POD is applied to a set of initial solutions or snapshots obtained with an high fidelity CFD model. With respect to approaches presented in literature, in this research work no truncation of the POD modes is performed and they are all used to construct the surrogate model. Several applications are presented: a backward facing step case, the analysis of the flow around a NACA 0012 airfoil and a RAE 2822 supercritical airfoil, the optimization of an automotive external shape and a database generation of a three-dimensional aircraft

A survey of parametric modelling methods for designing the head of a high-speed train

With the continuous increase of the running speed, the head shape of the high-speed train (HST) turns out to be a critical factor for further speed boost. In order to cut down the time used in the HST head design and improve the modelling efficiency, various parametric modelling methods have been widely applied in the optimization design of the HST head to obtain an optimal head shape so that the aerodynamic effect acting on the head of HSTs can be reduced and more energy can be saved. This paper reviews these parametric modelling methods and classifies them into four categories: 2D, 3D, CATIA-based, and mesh deformation-based parametric modelling methods. Each of the methods is introduced, and the advantages and disadvantages of these methods are identified. The simulation results are presented to demonstrate that the aerodynamic performance of the optimal models constructed by these parametric modelling methods has been improved when compared with numerical calculation results of the original models or the prototype models of running trains. Since different parametric modelling methods used different original models and optimization methods, few publications could be found which compare the simulation results of the aerodynamic performance among different parametric modelling methods. In spite of this, these parametric modelling methods indicate more local shape details will lead to more accurate simulation results, and fewer design variables will result in higher computational efficiency. Therefore, the ability of describing more local shape details with fewer design variables could serve as a main specification to assess the performance of various parametric modelling methods. The future research directions may concentrate on how to improve such ability

Geometrically Consistent Aerodynamic Optimization using an Isogeometric Discontinuous Galerkin Method

International audienceThe objective of the current work is to define a design optimization methodology in aerodynamics, in which all numerical components are based on a unique geometrical representation, consistent with Computer-Aided Design (CAD) standards. In particular, the design is parameterized by Non-Uniform Rational B-Splines (NURBS), the computational domain is automatically constructed using rational Bézier elements extracted from NURBS boundaries without any approximation and the resolution of the flow equations relies on an adaptive Discontinuous Galerkin (DG) method based on rational representations. A Bayesian framework is used to optimize NURBS control points, in a single-or multi-objective, constrained, global optimization framework. The resulting methodology is therefore fully CAD-consistent, high-order in space and time, includes local adaption and shock capturing capabilities, and exhibits high parallelization performance. The proposed methods are described in details and their properties are established. Finally, two design optimization problems are provided as illustrations: the shape optimization of an airfoil in transonic regime, for drag reduction with lift constraint, and the multi-objective optimization of the control law of a morphing airfoil in subsonic regime, regarding the time-averaged lift, the minimum instantaneous lift and the energy consumption