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

Isogeometric FEM-BEM coupled structural-acoustic analysis of shells using subdivision surfaces

We introduce a coupled finite and boundary element formulation for acoustic scattering analysis over thin shell structures. A triangular Loop subdivision surface discretisation is used for both geometry and analysis fields. The Kirchhoff-Love shell equation is discretised with the finite element method and the Helmholtz equation for the acoustic field with the boundary element method. The use of the boundary element formulation allows the elegant handling of infinite domains and precludes the need for volumetric meshing. In the present work the subdivision control meshes for the shell displacements and the acoustic pressures have the same resolution. The corresponding smooth subdivision basis functions have the $C^1$ continuity property required for the Kirchhoff-Love formulation and are highly efficient for the acoustic field computations. We validate the proposed isogeometric formulation through a closed-form solution of acoustic scattering over a thin shell sphere. Furthermore, we demonstrate the ability of the proposed approach to handle complex geometries with arbitrary topology that provides an integrated isogeometric design and analysis workflow for coupled structural-acoustic analysis of shells

The diffuse Nitsche method: Dirichlet constraints on phase-field boundaries

We explore diffuse formulations of Nitsche's method for consistently imposing Dirichlet boundary conditions on phase-field approximations of sharp domains. Leveraging the properties of the phase-field gradient, we derive the variational formulation of the diffuse Nitsche method by transferring all integrals associated with the Dirichlet boundary from a geometrically sharp surface format in the standard Nitsche method to a geometrically diffuse volumetric format. We also derive conditions for the stability of the discrete system and formulate a diffuse local eigenvalue problem, from which the stabilization parameter can be estimated automatically in each element. We advertise metastable phase-field solutions of the Allen-Cahn problem for transferring complex imaging data into diffuse geometric models. In particular, we discuss the use of mixed meshes, that is, an adaptively refined mesh for the phase-field in the diffuse boundary region and a uniform mesh for the representation of the physics-based solution fields. We illustrate accuracy and convergence properties of the diffuse Nitsche method and demonstrate its advantages over diffuse penalty-type methods. In the context of imaging based analysis, we show that the diffuse Nitsche method achieves the same accuracy as the standard Nitsche method with sharp surfaces, if the inherent length scales, i.e., the interface width of the phase-field, the voxel spacing and the mesh size, are properly related. We demonstrate the flexibility of the new method by analyzing stresses in a human vertebral body

Zero-gravity movement studies

The use of computer graphics to simulate the movement of articulated animals and mechanisms has a number of uses ranging over many fields. Human motion simulation systems can be useful in education, medicine, anatomy, physiology, and dance. In biomechanics, computer displays help to understand and analyze performance. Simulations can be used to help understand the effect of external or internal forces. Similarly, zero-gravity simulation systems should provide a means of designing and exploring the capabilities of hypothetical zero-gravity situations before actually carrying out such actions. The advantage of using a simulation of the motion is that one can experiment with variations of a maneuver before attempting to teach it to an individual. The zero-gravity motion simulation problem can be divided into two broad areas: human movement and behavior in zero-gravity, and simulation of articulated mechanisms

Optimal multi-block mesh generation for CFD

An assessment of various automatic block topology generation techniques for creating structured meshes has been performed in the first part of the paper. The objective is to find out optimal blocking methods for generating meshes suitable for flow simulations. The comparison has been carried out using an adjoint based error analysis of the meshes generated by these block topologies. Different objective functions and numerical schemes have been used for this assessment. It is found that, in general, the medial axis based approaches provide optimal blocking and yields better accuracy in computing the functional of interest. This is because the medial axis based methods produce meshes which have better flow alignment specially in case of internal flows. In the second part of the paper, the adjoint based error indicator has been used to adapt the block topology in the regions of large error.Rolls Royce, plc TSB SILOET II TS/L00691X/

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