Volumetric Untrimming: Precise decomposition of trimmed trivariates into tensor products

3D objects, modeled using Computer Aided Geometric Design tools, are traditionally represented using a boundary representation (B-rep), and typically use spline functions to parameterize these boundary surfaces. However, recent development in physical analysis, in isogeometric analysis (IGA) in specific, necessitates a volumetric parametrization of the interior of the object. IGA is performed directly by integrating over the spline spaces of the volumetric spline representation of the object. Typically, tensor-product B-spline trivariates are used to parameterize the volumetric domain. A general 3D object, that can be modeled in contemporary B-rep CAD tools, is typically represented using trimmed B-spline surfaces. In order to capture the generality of the contemporary B-rep modeling space, while supporting IGA needs, Massarwi and Elber (2016) proposed the use of trimmed trivariates volumetric elements. However, the use of trimmed geometry makes the integration process more difficult since integration over trimmed B-spline basis functions is a highly challenging task. In this work, we propose an algorithm that precisely decomposes a trimmed B-spline trivariate into a set of (singular only on the boundary) tensor-product B-spline trivariates, that can be utilized to simplify the integration process in IGA. The trimmed B-spline trivariate is first subdivided into a set of trimmed B\'ezier trivariates, at all its internal knots. Then, each trimmed B\'ezier trivariate, is decomposed into a set of mutually exclusive tensor-product B-spline trivariates, that precisely cover the entire trimmed domain. This process, denoted untrimming, can be performed in either the Euclidean space or the parametric space of the trivariate. We present examples on complex trimmed trivariates' based geometry, and we demonstrate the effectiveness of the method by applying IGA over the (untrimmed) results.Comment: 18 pages, 32 figures. Contribution accepted in International Conference on Geometric Modeling and Processing (GMP 2019

JIGSAW-GEO (1.0): locally orthogonal staggered unstructured grid generation for general circulation modelling on the sphere

An algorithm for the generation of non-uniform, locally-orthogonal staggered unstructured spheroidal grids is described. This technique is designed to generate very high-quality staggered Voronoi/Delaunay meshes appropriate for general circulation modelling on the sphere, including applications to atmospheric simulation, ocean-modelling and numerical weather prediction. Using a recently developed Frontal-Delaunay refinement technique, a method for the construction of high-quality unstructured spheroidal Delaunay triangulations is introduced. A locally-orthogonal polygonal grid, derived from the associated Voronoi diagram, is computed as the staggered dual. It is shown that use of the Frontal-Delaunay refinement technique allows for the generation of very high-quality unstructured triangulations, satisfying a-priori bounds on element size and shape. Grid-quality is further improved through the application of hill-climbing type optimisation techniques. Overall, the algorithm is shown to produce grids with very high element quality and smooth grading characteristics, while imposing relatively low computational expense. A selection of uniform and non-uniform spheroidal grids appropriate for high-resolution, multi-scale general circulation modelling are presented. These grids are shown to satisfy the geometric constraints associated with contemporary unstructured C-grid type finite-volume models, including the Model for Prediction Across Scales (MPAS-O). The use of user-defined mesh-spacing functions to generate smoothly graded, non-uniform grids for multi-resolution type studies is discussed in detail.Comment: Final revisions, as per: Engwirda, D.: JIGSAW-GEO (1.0): locally orthogonal staggered unstructured grid generation for general circulation modelling on the sphere, Geosci. Model Dev., 10, 2117-2140, https://doi.org/10.5194/gmd-10-2117-2017, 201

Integrated modeling and analysis methodologies for architecture-level vehicle design.

In order to satisfy customer expectations, a ground vehicle must be designed to meet a broad range of performance requirements. A satisfactory vehicle design process implements a set of requirements reflecting necessary, but perhaps not sufficient conditions for assuring success in a highly competitive market. An optimal architecture-level vehicle design configuration is one of the most important of these requirements. A basic layout that is efficient and flexible permits significant reductions in the time needed to complete the product development cycle, with commensurate reductions in cost. Unfortunately, architecture-level design is the most abstract phase of the design process. The high-level concepts that characterize these designs do not lend themselves to traditional analyses normally used to characterize, assess, and optimize designs later in the development cycle. This research addresses the need for architecture-level design abstractions that can be used to support ground vehicle development. The work begins with a rigorous description of hierarchical function-based abstractions representing not the physical configuration of the elements of a vehicle, but their function within the design space. The hierarchical nature of the abstractions lends itself to object orientation - convenient for software implementation purposes - as well as description of components, assemblies, feature groupings based on non-structural interactions, and eventually, full vehicles. Unlike the traditional early-design abstractions, the completeness of our function-based hierarchical abstractions, including their interactions, allows their use as a starting point for the derivation of analysis models. The scope of the research in this dissertation includes development of meshing algorithms for abstract structural models, a rigid-body analysis engine, and a fatigue analysis module. It is expected that the results obtained in this study will move systematic design and analysis to the earliest phases of the vehicle development process, leading to more highly optimized architectures, and eventually, better ground vehicles. This work shows that architecture level abstractions in many cases are better suited for life cycle support than geometric CAD models. Finally, substituting modeling, simulation, and optimization for intuition and guesswork will do much to mitigate the risk inherent in large projects by minimizing the possibility of incorporating irrevocably compromised architecture elements into a vehicle design that no amount of detail-level reengineering can undo

A geometric framework for immersogeometric analysis

The purpose of this dissertation is to develop a geometric framework for immersogeometric analysis that directly uses the boundary representations (B-reps) of a complex computer-aided design (CAD) model and immerses it into a locally refined, non-boundary-fitted discretization of the fluid domain. Using the non-boundary-fitted mesh which does not need to conform to the shape of the object can alleviate the challenge of mesh generation for complex geometries. This also reduces the labor-intensive and time-consuming work of geometry cleanup for the purpose of obtaining watertight CAD models in order to perform boundary-fitted mesh generation. The Dirichlet boundary conditions in the fluid domain are enforced weakly over the immersed object surface in the intersected elements. The surface quadrature points for the immersed object are generated on the parametric and analytic surfaces of the B-rep models. In the case of trimmed surfaces, adaptive quadrature rule is considered to improve the accuracy of the surface integral. For the non-boundary-fitted mesh, a sub-cell-based adaptive quadrature rule based on the recursive splitting of quadrature elements is used to faithfully capture the geometry in intersected elements. The point membership classification for identifying quadrature points in the fluid domain is based on a voxel-based approach implemented on GPUs. A variety of computational fluid dynamics (CFD) simulations are performed using the proposed method to assess its accuracy and efficiency. Finally, a fluid--structure interaction (FSI) simulation of a deforming left ventricle coupled with the heart valves shows the potential advantages of the developed geometric framework for the immersogeomtric analysis with complex moving domains

Curvilinear Interface Methodology for Finite-Element Applications

Recent trends in design and manufacturing suggest a tendency toward multiple centers of specialty which results in a need for improved integration methodology for dissimilar finite element or CFD meshes. Since a typical finite element or CFD analysis requires about 50% of an engineers effort to be devoted to modeling and input, there is a need to advance the state-of-the-art in modeling, methodology. These two trends indicate a need to for the capability to combine independently-modeled configurations in an automated and robust way without the need for global remodeling. One approach to addressing this need is the development of interfacing methodology which will automatically integrate independently modeled subdomains. The present research included the following objectives: (i) to develop and implement computational methods for automatically remodeling non-coincident finite element models having a pre-defined interface, (ii) to formulate and implement a parametric representation of general space curves and surfaces with a well-defined orientation, and (iii) to demonstrate the computational methodology with representative two- and three-dimensional finite element models. Methodology for automatically remodeling non-coincident subdomains was developed and tested for two- and three-dimensional, independently modeled subdomains. Representative classes of applications have been solved which gave good agreement with reference solutions obtained with conventional methods. The two-dimensional classes of problems solved included flat and curved membranes multiple subdomains having large gaps between the subdomains and general space curves representing an interface for re-modeling the portions of subdomains adjacent to the interface. The three-dimensional classes of problems solved includes multiple three-dimensional subdomains having large three-dimensional gap between previously modeled subdomains. The interface was represented by general surfaces with a well-defined orientation and having curvature in possibly more than one direction. The results demonstrated the re-modeling methodology to be general, flexible in use, highly automated, and robust for a diverse class of problems. The research reported represents an important advancement in the area of automated re-modeling for computational mechanics applications

A framework for isogeometric-analysis-based design and optimization of wind turbine blades

Typical wind turbine blade design procedures employ reduced-order models almost exclusively for early-stage design; high-fidelity, finite-element-based procedures are reserved for later design stages because they entail complex workflows, large volumes of data, and significant computational expense. Yet, high-fidelity structural analyses often provide design-governing feedback such as buckling load factors. Mitigation of the issues of workflow complexity, data volume, and computational expense would allow designers to utilize high-fidelity structural analysis feedback earlier, more easily, and more often in the design process. Thus, this work presents a blade analysis framework which employs isogeometric analysis (IGA), a simulation method that overcomes many of the aforementioned drawbacks associated with traditional finite element analysis (FEA). IGA directly utilizes the mathematical models generated by computer-aided design (CAD) software, requires less user interaction and no conversion of CAD geometries to finite element meshes, and tends to have superior per-degree-of-freedom accuracy compared to traditional FEA. The presented framework employs the parametric capabilities of the Grasshopper algorithmic modeling interface developed for the CAD software Rhinoceros 3D. This Grasshopper-based framework enables seamless, iterative design and IGA of CAD-based geometries and is demonstrated through the optimization of both a pressurized tube and a simplified wind turbine blade design. Further, because engineering models, such as wind turbine blades, are typically composed of numerous surface patches, a novel patch coupling technique is presented. For the sake of straightforward implementation and flexibility, the coupling technique is based on a penalty energy approach. Formulations for the penalty parameters are proposed to eliminate the problem-dependent nature of the penalty method. This coupling methodology is successfully demonstrated using a number of multi-patch benchmark examples with both matching and non-matching interface discretizations. Together, these technologies enable practical and efficient design and analysis of wind turbine blade shell structures. The presented IGA approach is employed to perform vibration, buckling, and nonlinear deformation analysis of the NREL/SNL 5 MW wind turbine blade, validating the effectiveness of the proposed approach for realistic, composite wind turbine blade designs. Further, a blade design framework that combines reduced-order aeroelastic analysis with the presented IGA methodologies 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 high-fidelity buckling analysis. Finally, the value and feasibility of incorporating high-fidelity IGA feedback into optimization is demonstrated through optimization of the NREL/SNL 5 MW wind turbine blade. Alternative structural designs that have improved blade mass and material cost characteristics are identified, and IGA-based buckling analysis is shown to provide design-governing constraint information

Finite element analysis based on a parametric model by approximating point clouds

Simplified models are widely applied in finite element computations regarding mechanical and structural problems. However, the simplified model sometimes causes many deviations in the finite element analysis (FEA) of structures, especially in the non-designed structures which have undergone unknowable deformation features. Hence, a novel FEA methodology based on the parametric model by approximating three-dimensional (3D) feature data is proposed to solve this problem in the present manuscript. Many significant anci effective technologies have been developeci to detect 3D feature information accurately, e.g., terrestrial laser scanning (TLS), digital photogrammetry, and radar technology. In this manuscript, the parametric FEA model combines 3D point clouds from TLS and the parametric surface approximation method to generate 3D surfaces and models accurately. TLS is a popular measurement method for reliable 3D point clouds acquisition and monitoring deformations of structures with high accuracy and precision. The B-spline method is applied to approximate the measured point clouds data automatically and generate a parametric description of the structure accurately. The final target is to reduce the effects of the model description and deviations of the FEA. Both static and dynamic computations regarding a composite structure are carried out by comparing the parametric and general simplified models. The comparison of the deformation and equivalent stress of future behaviors are reflected by different models. Results indicate that the parametric model based on the TLS data is superior in the finite element computation. Therefore, it is of great significance to apply the parametric model in the FEA to compute and predict the future behavior of the structures with unknowable deformations in engineering accurately