Flux penetration in slab shaped Type-I superconductors

We study the problem of flux penetration into type--I superconductors with high demagnetization factor (slab geometry).Assuming that the interface between the normal and superconducting regions is sharp, that flux diffuses rapidly in the normal regions, and that thermal effects are negligible, we analyze the process by which flux invades the sample as the applied field is increased slowly from zero.We find that flux does not penetrate gradually.Rather there is an instability in the process and the flux penetrates from the boundary in a series of bursts, accompanied by the formation of isolated droplets of the normal phase, leading to a multiply connected flux domain structure similar to that seen in experiments.Comment: 4 pages, 2 figures, Fig 2.(b) available upon request from the authors, email - [email protected]

Direct immersogeometric fluid flow analysis using B-rep CAD models

We present a new method for immersogeometric fluid flow analysis that directly uses the CAD boundary representation (B-rep) of a complex object and immerses it into a locally refined, non-boundary-fitted discretization of the fluid domain. The motivating applications include analyzing the flow over complex geometries, such as moving vehicles, where the detailed geometric features usually require time-consuming, labor-intensive geometry cleanup or mesh manipulation for generating the surrounding boundary-fitted fluid mesh. The proposed method avoids the challenges associated with such procedures. A new method to perform point membership classification of the background mesh quadrature points is also proposed. To faithfully capture the geometry in intersected elements, we implement an adaptive quadrature rule based on the recursive splitting of elements. Dirichlet boundary conditions in intersected elements are enforced weakly in the sense of Nitsche\u27s method. To assess the accuracy of the proposed method, we perform computations of the benchmark problem of flow over a sphere represented using B-rep. Quantities of interest such as drag coefficient are in good agreement with reference values reported in the literature. The results show that the density and distribution of the surface quadrature points are crucial for the weak enforcement of Dirichlet boundary conditions and for obtaining accurate flow solutions. Also, with sufficient levels of surface quadrature element refinement, the quadrature error near the trim curves becomes insignificant. Finally, we demonstrate the effectiveness of our immersogeometric method for high-fidelity industrial scale simulations by performing an aerodynamic analysis of an agricultural tractor directly represented using B-rep

Single-variable formulations and isogeometric discretizations for shear deformable beams

We present numerical formulations of Timoshenko beams with only one unknown, the bending displacement, and it is shown that all variables of the beam problem can be expressed in terms of it and its derivatives. We develop strong and weak forms of the problem. The strong form of the problem involves the fourth derivative of the bending displacement, whereas the symmetric weak form involves, somewhat surprisingly, third and second derivatives. Based on these, we develop isogeometric collocation and Galerkin formulations, that are completely locking-free and involve only half the degrees of freedom compared to standard Timoshenko beam formulations. Several numerical tests are presented to demonstrate the performance of the proposed formulations

Patch-wise quadrature of trimmed surfaces in Isogeometric Analysis

This work presents an efficient quadrature rule for shell analysis fully integrated in CAD by means of Isogeometric Analysis (IGA). General CAD-models may consist of trimmed parts such as holes, intersections, cut-offs etc. Therefore, IGA should be able to deal with these models in order to fulfil its promise of closing the gap between design and analysis. Trimming operations violate the tensor-product structure of the used Non-Uniform Rational B-spline (NURBS) basis functions and of typical quadrature rules. Existing efficient patch-wise quadrature rules consider actual knot vectors and are determined in 1D. They are extended to further dimensions by means of a tensor-product. Therefore, they are not directly applicable to trimmed structures. The herein proposed method extends patch-wise quadrature rules to trimmed surfaces. Thereby, the number of quadrature points can be significantly reduced. Geometrically linear and non-linear benchmarks of plane, plate and shell structures are investigated. The results are compared to a standard trimming procedure and a good performance is observed

An immersed-boundary/isogeometric method for fluid–structure interaction involving thin shells

A computational framework is designed to accurately predict the elastic response of thin shells undergoing large displacements induced by local hydrodynamic forces, as well as to resolve the complex fluid pattern arising from its interaction with an incompressible fluid. Within the context of partitioned algorithms, two different approaches are employed for the fluid and structural domain. The fluid motion is resolved with a pressure projection method on a Cartesian structured grid. The immersed shell is modeled by means of a NURBS surface, and the elastic response is obtained from a displacement-based isogeometric analysis relying on the Kirchhoff–Love theory. The two solvers exchange data through a direct-forcing immersed-boundary approach, where the interpolation/spreading of the variables between Lagrangian and Eulerian grids is implemented with a Moving Least Squares approximation, which has proven to be very effective for moving boundaries. In this scenario, the isoparametric paradigm is exploited to perform an adaptive collocation of the Lagrangian markers, decoupling the local grid density of fluid and shell domains and reducing the computational expense. The accuracy of the method is verified by refinement analyses, segregating the Eulerian/Lagrangian refinement, which confirm the expected scheme accuracy in space and time. The effectiveness of the method is then validated against different test-cases of engineering and biologic inspiration, involving fundamentally different physical and numerical conditions, namely: (i) a flapping flag, (ii) an inverted flag, (iii) a clamped plate, (iv) a buoyant seaweed in a free stream. Both strong and loose coupling approaches are implemented to handle different fluid-to-structure density ratios, providing accurate results

Isogeometric collocation methods for the Reissner-Mindlin plate problem

Within the general framework of isogeometric methods, collocation schemes have been recently proposed as a viable and promising low-cost alternative to standard isogeometric Galerkin approaches. In this paper, isogeometric collocation methods for the numerical approximation of Reissner-Mindlin plate problems are proposed for the first time. Locking-free primal and mixed formulations are herein considered, and the potential of isogeometric collocation as a geometrically flexible and computationally efficient simulation tool for shear deformable plates is shown through the solution of several numerical tests