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Project

Efficient vibro-acoustic simulations using isogeometric analysis and its hybrid coupling with the wave based method.

This dissertation presents research contributions to the development of flexible NURBS-based isogeometric frameworks for performing vibro-acoustic simulations in the low- to mid-frequency range. The research is set in the light of the increasing importance of being able to numerically predict the noise and vibration characteristics of products, driven by growing market expectations and tightening regulations. The main aim of isogeometric methods in that context is to provide a natural transition from Computer-Aided Design (CAD) to Computer-Aided Engineering (CAE) by introducing CAD descriptions in a CAE environment, in order to avoid costly and time-consuming meshing steps.

A first part of the research investigates the potential of using Non-Uniform Rational B-Splines (NURBS) shape functions for steady-state dynamic analysis in general and for Helmholtz problems in 2D in particular. The main findings include the higher efficiency of NURBS-based IsoGeometric Analysis (IGA) on a per-degree-of-freedom basis as compared to the conventional Finite Element Method (FEM) with Lagrange polynomials, both for eigenvalue and for boundary value problems. The practical considerations imposed by the NURBS tensor product, however, can compromise this enhanced performance, indicating the importance of flexible multipatch coupling techniques and of using efficient isogeometric discretisations when it comes to computational performance.

A second part of the research develops a NURBS-based isogeometric indirect Boundary Element Method (BEM) for solving 3D acoustic problems. The intrinsically surface-based character of CAD descriptions makes an IGA-BEM combination a powerful approach. The employed indirect boundary integral formulation allows the modelling of open-boundary surfaces and combined interior/exterior problems. Moreover, the variational scheme yields complex-symmetric system matrices which lead to a more efficient solving as compared to collocation schemes. The method is verified against analytical solutions and benchmarked against the conventional polynomial-based indirect BEM. Improvements in accuracy by a factor of half an order up to several orders of magnitude are observed for a given model size. Considering the drastic scaling of BEM solving times, this offers huge potential reductions in computation time.

The third and final part of the research introduces a flexible method for coupling non-conforming NURBS multipatch surfaces in both a C0- and a C1-sense, for use in solving acoustic and thin shell vibration problems with NURBS-based isogeometric approaches. The C0-coupling consists of imposing constraints in a weak sense, globally along the entire interface, whereas the C1-coupling explicitly matches first-order derivatives of the discretisation in a set of well-chosen collocation points. For non-conforming patches, a well-chosen master-slave formulation is used to obtain a set of dependent variables that can be eliminated from the system of equations. The interface constraints only depend on the mesh, allowing them to be generated in an inexpensive pre-processing step. The resulting coupling relationships are linear equations that can be enforced by means of a simple matrix condensation, thereby reducing the model size. This can be done without any user interaction: no stabilisation or penalty parameters are involved. Numerical examples confirm the accuracy of the coupling method. The C0-coupling approach is successfully applied in acoustic problems using isogeometric FEM and BEM approaches, with non-conforming meshes performing nearly identically to conforming or even single patch meshes. The C1-coupling technique is validated using several numerical case studies of static as well as dynamic thin shell analysis. The geometries under study include curved patches as well as kink connections without G1-continuity.

Date:4 Jun 2012 →  20 Jun 2017
Keywords:Vibro-acoustic simulations, Isogeometric analysis
Disciplines:Mechanics
Project type:PhD project