A simple approach to the numerical simulation with trimmed CAD surfaces

In this work a novel method for the analysis with trimmed CAD surfaces is presented. The method involves an additional mapping step and the attraction stems from its sim- plicity and ease of implementation into existing Finite Element (FEM) or Boundary Element (BEM) software. The method is first verified with classical test examples in structural mechanics. Then two practical applications are presented one using the FEM, the other the BEM, that show the applicability of the method.Comment: 20 pages and 16 figure

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

Condition number analysis and preconditioning of the finite cell method

The (Isogeometric) Finite Cell Method - in which a domain is immersed in a structured background mesh - suffers from conditioning problems when cells with small volume fractions occur. In this contribution, we establish a rigorous scaling relation between the condition number of (I)FCM system matrices and the smallest cell volume fraction. Ill-conditioning stems either from basis functions being small on cells with small volume fractions, or from basis functions being nearly linearly dependent on such cells. Based on these two sources of ill-conditioning, an algebraic preconditioning technique is developed, which is referred to as Symmetric Incomplete Permuted Inverse Cholesky (SIPIC). A detailed numerical investigation of the effectivity of the SIPIC preconditioner in improving (I)FCM condition numbers and in improving the convergence speed and accuracy of iterative solvers is presented for the Poisson problem and for two- and three-dimensional problems in linear elasticity, in which Nitche's method is applied in either the normal or tangential direction. The accuracy of the preconditioned iterative solver enables mesh convergence studies of the finite cell method

Scaled boundary isogeometric analysis with C1 coupling for Kirchhoff plate theory

Although isogeometric analysis exploits smooth B-spline and NURBS basis functions for the definition of discrete function spaces as well as for the geometry representation, the global smoothness in so-called multipatch parametrizations is an issue. Especially, if strong C1 regularity is required, the introduction of function spaces with good convergence properties is not straightforward. However, in 2D there is the special class of analysis-suitable G1 (AS-G1) parametrizations that are suitable for patch coupling. In this contribution we show that the concept of scaled boundary isogeometric analysis fits to the AS-G1 idea and the former is appropriate to define C1-smooth basis functions. The proposed method is applied to Kirchhoff plates and its capability is demonstrated utilizing several numerical examples. Its applicability to non-trivial and trimmed shapes is demonstrated

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

Isogeometric Analysis on V-reps: first results

Inspired by the introduction of Volumetric Modeling via volumetric representations (V-reps) by Massarwi and Elber in 2016, in this paper we present a novel approach for the construction of isogeometric numerical methods for elliptic PDEs on trimmed geometries, seen as a special class of more general V-reps. We develop tools for approximation and local re-parametrization of trimmed elements for three dimensional problems, and we provide a theoretical framework that fully justify our algorithmic choices. We validate our approach both on two and three dimensional problems, for diffusion and linear elasticity.Comment: 36 pages, 44 figures. Reviewed versio

Parametric Design and Isogeometric Analysis of Tunnel Linings within the Building Information Modelling Framework

Both planning and design phase of large infrastructural project require analysis, modelling, visualization, and numerical analysis. To perform these tasks, different tools such as Building Information Modelling (BIM) and numerical analysis software are commonly employed. However, in current engineering practice, there are no systematic solutions for the exchange between design and analysis models, and these tasks usually involve manual and error-prone model generation, setup and update. In this paper, focussing on tunnelling engineering, we demonstrate a systematic and versatile approach to efficiently generate a tunnel design and analyse the lining in different practical scenarios. To this end, a BIM-based approach is developed, which connects a user-friendly industry-standard BIM software with effective simulation tools for high-performance computing. A fully automatized design-through-analysis workflow solution for segmented tunnel lining is developed based on a fully parametric design model and an isogeometric analysis software, connected through an interface implemented with a Revit plugin