Feasible Form Parameter Design of Complex Ship Hull Form Geometry

This thesis introduces a new methodology for robust form parameter design of complex hull form geometry via constraint programming, automatic differentiation, interval arithmetic, and truncated hierarchical B- splines. To date, there has been no clearly stated methodology for assuring consistency of general (equality and inequality) constraints across an entire geometric form parameter ship hull design space. In contrast, the method to be given here can be used to produce guaranteed narrowing of the design space, such that infeasible portions are eliminated. Furthermore, we can guarantee that any set of form parameters generated by our method will be self consistent. It is for this reason that we use the title feasible form parameter design. In form parameter design, a design space is represented by a tuple of design parameters which are extended in each design space dimension. In this representation, a single feasible design is a consistent set of real valued parameters, one for every component of the design space tuple. Using the methodology to be given here, we pick out designs which consist of consistent parameters, narrowed to any desired precision up to that of the machine, even for equality constraints. Furthermore, the method is developed to enable the generation of complex hull forms using an extension of the basic rules idea to allow for automated generation of rules networks, plus the use of the truncated hierarchical B-splines, a wavelet-adaptive extension of standard B-splines and hierarchical B-splines. The adaptive resolution methods are employed in order to allow an automated program the freedom to generate complex B-spline representations of the geometry in a robust manner across multiple levels of detail. Thus two complementary objectives are pursued: ensuring feasible starting sets of form parameters, and enabling the generation of complex hull form geometry

Sketch-based path design

We first present a novel approach to sketching 2D curves with minimally varying curvature as piecewise clothoids. A stable and efficient algorithm fits a sketched piecewise linear curve using a number of clothoid segments with G2 continuity based on a specified error tolerance. We then present a system for conceptually sketching 3D layouts for road and other path networks. Our system makes four key contributions. First, we generate paths with piecewise linear curvature by fitting 2D clothoid curves to strokes sketched on a terrain. Second, the height of paths above the terrain is automatically determined using a new constraint optimization formulation of the occlusion relationships between sketched strokes. Third, we present the break-out lens, a novel widget inspired by break-out views used in engineering visualization, to facilitate the in-context and interactive manipulation of paths from alternate view points. Finally, our path construction is terrain sensitive. ii Acknowledgements I would like to acknowledge the efforts of my supervisor, Karan Singh, and thank him for his guidance over the duration of the Masters program. I learned much from him a

Component-based Geometry Manipulation for Aerodynamic Shape Optimization with Overset Meshes

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/143082/1/6.2017-3327.pd

Optimal shape design with automatically differentiated CAD parametrisations

PhD ThesisTypical engineering workflow for aerodynamic design could be considered as a three-stage process: modelling of a new component in a CAD system, its detailed aerodynamic analysis on the computational grid using flow simulations (CFD) and manufacturing of the CAD component. Numerical shape optimisation is becoming an essential industrial method to improve the aerodynamic performance of shapes immersed in fluids. High-fidelity optimisation requires fine design spaces with many design variables, which can only be tackled with gradient-based optimisation methods. Adjoint CFD can efficiently calculate the necessary flow sensitivities on computational grids and ideally, also CAD parametrisation should be kept inside the loop to maintain a consistent CAD model during the optimisation and streamline the design process. However, (i) typical commercial CAD systems do not offer derivative computation and (ii) standard CAD parametrisations may not define a suitable design space for the optimisation. This thesis presents an automatically differentiated (AD) version of the open-source CAD kernel OpenCascade Technology (OCCT), which robustly provides shape derivatives with respect to CAD parameters. Developed block-vector AD mode outperforms commonly used finite difference approaches in both efficiency and accuracy. Coupling of OCCT with an adjoint CFD solver provides for the first time a fully differentiated design chain. Extension of OCCT to perform shape optimisation is demonstrated by using CAD parametrisations based on (a) user-defined parametric CAD models and (b) BRep (NURBS) models. The imposition of geometric constraints, a salient part of the industrial design, is shown for both approaches. Novel parametrisation techniques that can handle components with surface-surface intersections or simultaneously incorporate approaches (a) and (b) for the optimisation of a single component are demonstrated. The CAD-based methodology is successfully applied for aerodynamic shape optimisation of three industrial test cases. Additionally, advantages of the differentiated CAD is showcased for the commonly occurring CAD re-parametrisation and mesh-to-CAD fitting problems

ShapeWright--finite element based free-form shape design

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 1990.Includes bibliographical references (p. 179-192).by George Celniker.Ph.D

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

Geometric Parameterisation and Aerodynamic Shape Optimisation

Aerodynamic optimisation plays an increasingly important role in the aircraft industry. In aerodynamic optimisation, shape parameterisation is the key technique, since it determines the design space. The ideal parameterisation method should be able to provide a high level of flexibility with a low number of design variables to reduce the complexity of the design space. In this work, the Class/Shape Function Transformation (CST) method is investigated for geometric representation of an entire transport aircraft for the purpose of aerodynamic optimisation. It is then further developed for an entire passenger transport aircraft, including such components as the wing, horizontal tail plane, vertical tail plane, fuselage, belly fairing, wingtip device, nacelle, flap tracking fairing and pylon. This work presents the parameterisation of these components in detail using the CST methods for the reference of future aerodynamic optimisation work. The intersection line calculation method between CST components is presented for future entire aircraft optimisation. The performance of the CST has been tested as well, and it found a few drawbacks of the CST methods; for example, it cannot provide some key intuitive design parameters and can lose the accuracy in the wing leading edge area. Therefore, two derivatives of the CST method are proposed: one is called the intuitive CST method (iCST), which is to transform the CST parameters to intuitive design parameters; the other is called the RCST method, which is able to increase the fitting accuracy of the original CST method with fewer design variables. Their performances are studied by comparing them regarding their accuracy in inversely fitting a wide range of aerofoils. Finally, the CST method is also developed to represent the shock control bump, which has better curvature continuity than cubic polynomials. The aerodynamic optimisation study based on adjoint approaches is carried out using the above parameterisation methods. Optimisation was performed on two-dimensional cases to make a preliminary investigation of the performances of the above parameterisation methods. The results showed that all of CST, iCST and RCST parameterisation methods are able to successfully reduce the drag. The results of the CST methods showed the lower order CST is able to provide fast convergence, and the high order CST is able to provide more flexibility and more local control of the shape to reach better optimal solution. The iCST providing intuitive parameters is improving the process of setup constraints, which is useful for aerofoil optimisation. The RCST showed good performance in aerodynamic optimisation in terms of convergence rate, number of design variables, low order of polynomials and smoothness of the shape. This work provides a reference to designer for choosing suitable parameterisation method in these three methods regarding specific requirement. The shock control bump optimisation on 2D aerofoil is performed to compare three shock control bump parameterisation methods. The results showed the CST parameterisation method is promising for shock control bump optimisation. Three-dimensional optimisation tests, including wing and winglet drag minimisation, were performed using the above parameterisation methods. The results showed that the CST methods are able to handle three-dimensional wing optimisation. It also investigated the effect of the order of CST method in optimisation. The results showed the lower order CST already performed well in optimisation in terms of optimal results and convergence rate. The optimisation also discussed the importance of using Cmx constraint in aerodynamic optimisation. In the winglet test cases, it showed the CST methods and adjoint approach are able to perform winglet optimisation. The drag of four winglets are successfully reduced. The downward winglet showed the potential benefits in terms of lower wing root bending momentum. At the end, the shock control bump optimisation using CST method on 3D wing has been performed. The results showed the mesh adjoint methods is able to identify the sensitive area for deploying shock control bumps and the CST shock control bump successfully reduced the wave drag

Automatic constraint-based synthesis of non-uniform rational B-spline surfaces

In this dissertation a technique for the synthesis of sculptured surface models subject to several constraints based on design and manufacturability requirements is presented. A design environment is specified as a collection of polyhedral models which represent components in the vicinity of the surface to be designed, or regions which the surface should avoid. Non-uniform rational B-splines (NURBS) are used for surface representation, and the control point locations are the design variables. For some problems the NURBS surface knots and/or weights are included as additional design variables. The primary functional constraint is a proximity metric which induces the surface to avoid a tolerance envelope around each component. Other functional constraints include: an area/arc-length constraint to counteract the expansion effect of the proximity constraint, orthogonality and parametric flow constraints (to maintain consistent surface topology and improve machinability of the surface), and local constraints on surface derivatives to exploit part symmetry. In addition, constraints based on surface curvatures may be incorporated to enhance machinability and induce the synthesis of developable surfaces;The surface synthesis problem is formulated as an optimization problem. Traditional optimization techniques such as quasi-Newton, Nelder-Mead simplex and conjugate gradient, yield only locally good surface models. Consequently, simulated annealing (SA), a global optimization technique is implemented. SA successfully synthesizes several highly multimodal surface models where the traditional optimization methods failed. Results indicate that this technique has potential applications as a conceptual design tool supporting concurrent product and process development methods