An integrated design-analysis framework for three dimensional composite panels

We present an integrated design-analysis framework for three dimensional composite panels. The main components of the proposed framework consist of (1) a new curve/surface offset algorithm and (2) the isogeometric concept recently emerged in the computational mechanics community. Using the presented approach, finite element analysis of composite panels can be performed with the only input is the geometry representation of the composite surface. In this paper, non-uniform rational B-splines (NURBS) are used to represent the panel surfaces. A stress analysis of curved composite panel with stiffeners is provided to demonstrate the proposed framework

Constructing IGA-suitable planar parameterization from complex CAD boundary by domain partition and global/local optimization

In this paper, we propose a general framework for constructing IGA-suitable planar B-spline parameterizations from given complex CAD boundaries consisting of a set of B-spline curves. Instead of forming the computational domain by a simple boundary, planar domains with high genus and more complex boundary curves are considered. Firstly, some pre-processing operations including B\'ezier extraction and subdivision are performed on each boundary curve in order to generate a high-quality planar parameterization; then a robust planar domain partition framework is proposed to construct high-quality patch-meshing results with few singularities from the discrete boundary formed by connecting the end points of the resulting boundary segments. After the topology information generation of quadrilateral decomposition, the optimal placement of interior B\'ezier curves corresponding to the interior edges of the quadrangulation is constructed by a global optimization method to achieve a patch-partition with high quality. Finally, after the imposition of C1=G1-continuity constraints on the interface of neighboring B\'ezier patches with respect to each quad in the quadrangulation, the high-quality B\'ezier patch parameterization is obtained by a C1-constrained local optimization method to achieve uniform and orthogonal iso-parametric structures while keeping the continuity conditions between patches. The efficiency and robustness of the proposed method are demonstrated by several examples which are compared to results obtained by the skeleton-based parameterization approach

Exact conversion from Bézier tetrahedra to Bézier hexahedra

International audienceModeling and computing of trivariate parametric volumes is an important research topic in the field of three-dimensional isogeo-metric analysis. In this paper, we propose two kinds of exact conversion approaches from Bézier tetrahedra to Bézier hexahedra with the same degree by reparametrization technique. In the first method, a Bézier tetrahedron is converted into a degenerate Bézier hexahedron, and in the second approach, a non-degenerate Bézier tetrahedron is converted into four non-degenerate Bézier hexahedra. For the proposed methods, explicit formulas are given to compute the control points of the resulting tensor-product Bézier hexahedra. Furthermore, in the second method, we prove that tetrahedral spline solids with C k-continuity can be converted into a set of tensor-product Bézier volumes with G k-continuity. The proposed methods can be used for the volumetric data exchange problems between different trivariate spline representations in CAD/CAE. Several experimental results are presented to show the effectiveness of the proposed methods

Doctor of Philosophy

dissertationWhile boundary representations, such as nonuniform rational B-spline (NURBS) surfaces, have traditionally well served the needs of the modeling community, they have not seen widespread adoption among the wider engineering discipline. There is a common perception that NURBS are slow to evaluate and complex to implement. Whereas computer-aided design commonly deals with surfaces, the engineering community must deal with materials that have thickness. Traditional visualization techniques have avoided NURBS, and there has been little cross-talk between the rich spline approximation community and the larger engineering field. Recently there has been a strong desire to marry the modeling and analysis phases of the iterative design cycle, be it in car design, turbulent flow simulation around an airfoil, or lighting design. Research has demonstrated that employing a single representation throughout the cycle has key advantages. Furthermore, novel manufacturing techniques employing heterogeneous materials require the introduction of volumetric modeling representations. There is little question that fields such as scientific visualization and mechanical engineering could benefit from the powerful approximation properties of splines. In this dissertation, we remove several hurdles to the application of NURBS to problems in engineering and demonstrate how their unique properties can be leveraged to solve problems of interest

Mesh Morphing Methods for Virtual Prototyping and Mechanical Component Optimization

In this thesis, the coupling of mathematical geometry and its discretization (mesh) is performed using a method that fills the gap between simulation and design. Different modelling strategies are studied, tested and developed to bridge commercial CAD with a new methodology able to perform more accurate simulations without loosing the connection with the geometrical features. The aim of the thesis is to enhance the capabilities of Finite Element Methods (FEM) with the properties of Non-Uniform Radial Basis Functions (NURBS) inherited from CAD models in the design phase leading to a perfect representation of the model's boundary. The parametric space definition of the basis functions is borrowed from standard IGA (Isogeometric Analysis) and the possibility of process CAD models without the need for trivariate NURBS from NEFEM (NURBS Enhanced Finite Element Method). This particular combination yields to a bilinear Lagrangian basis and a new mapping between Cartesian and Parametric spaces for quadrilaterals. Using this new formulation it is possible to track the changes of the geometry and reduce the simulation's error up to 25-50% because of the perfect shape representation when compared to an equivalent FEM system. The problems presented are defined in a 2D space and solved using Matlab. NURBS are the key point to perform parametric morphing and simple optimizations while FEM remains the best way to perform simulations. This new method prevents to remodel B-Rep (Boundary Representation) parts after some simple modification due to the analysis and improves the geometry accuracy of the discretization. The geometrical file is directly imported from commercial software and processed by the method. Accuracy, convergence and seamless integration with commercial CAD packages are demonstrated applied to problems of arbitrary 2D geometry. The main problems treated are thermal analysis and solid mechanics where the better results are achieved

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

Methods for kinematic analysis of the right ventricle

Despite playing a large role in many cardiovascular diseases (such as pulmonary hypertension), the heart's right ventricle (RV) is still poorly understood in regards to its complex shape and motion over the cardiac cycle. In this report, we examine the kinematics of the right ventricle and our ongoing progress towards developing a computational pipeline to extract functional measurements of deformation from cardiac computed tomography (CT) images. While other techniques in [2], [9], and [31] have been used to model the RV shape and motion, they lack a clear physical interpretation of their results. By using a central axis governed by blood ow direction, left ventricle based coordinate system, and deformable NURBS shape representation, we aim to identify kinematic modes that have a more direct physiological meaning. In doing so, the proposed methods could be eventually developed into an image-based tool for both diagnostic and prognostic purposes.Computational Science, Engineering, and Mathematic

The Construction of Conforming-to-shape Truss Lattice Structures via 3D Sphere Packing

Truss lattices are common in a wide variety of engineering applications, due to their high ratio of strength versus relative density. They are used both as the interior support for other structures, and as structures on their own. Using 3D sphere packing, we propose a set of methods for generating truss lattices that fill the interior of B-rep models, polygonal or (trimmed) NURBS based, of arbitrary shape. Once the packing of the spheres has been established, beams between the centers of adjacent spheres are constructed, as spline based B-rep geometry. We also demonstrate additional capabilities of our methods, including connecting the truss lattice to (a shell of) the B-rep model, as well as constructing a tensor-product trivariate volumetric representation of the truss lattice - an important step towards direct compatibility for analysis.RYC-2017-2264