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High-order shape functions used in isogeometric analysis allow the direct solution to the weighted residual formulation of the strong form, opening the door to new integration schemes (e.g. reduced Gauss–Lobatto quadrature, integration at superconvergent sites) but also to collocation approaches (e.g. using Greville or superconvergent collocation points). The goal of the present work is to compare these different methods through the application to the planar Kirchhoff rod, a fourth-order rotation-free formulation used to model slender beams under large deformations. Robustness of the geometrically-nonlinear solution is improved using the Mixed Integration Point (MIP) Newton, a method that combines the advantages of displacement and mixed formulations. Based on the observations of the convergence plots, convergence order estimates are provided for each discretization method. Advantages and weaknesses in terms of robustness and computation cost are also discussed for a set of benchmarks. ispartof: Computer Methods In Applied Mechanics And Engineering vol:340 pages:1023-1043 status: published

In this work, we explore new parametric models of a sphere with rational Bézier patches. The geometry is represented as a spherical tessellation with various topologies. The tiles are degeneracy-free rational Bézier surfaces, obtained using a general composite mapping method. Five novel, topologically distinct tilings are described, four of which have conforming parameterizations. The mesh of the fifth tiling is nonconforming despite having equal interface knot vectors (intrinsic nonconformity). We apply these novel geometries in three case studies that are proposed as benchmark problems for C0- and C1-multipatch IGA methods. ispartof: Computer Methods in Applied Mechanics and Engineering vol:332 pages:255-279 status: published

This paper presents a novel method that enables model order reduction of a fully-coupled, exterior vibro-acoustic finite element model for time domain simulations. The method preserves the stability of the full model and reduces the amount of degrees of freedom significantly, with only a moderate amount of calculation complexity. Infinite elements are used on the finite element boundary to satisfy the Sommerfeld radiation condition. Two different strategies to calculate the reduced order model are compared. The first strategy works with a split reduced basis and can be applied on any fully stable model. The second strategy starts from a modified Everstine formulation and directly builds a reduced basis from the full model, leading to more compact reduced order models. Furthermore, a method is derived to perform explicit time integration on the reduced system, while avoiding the inversion of the mass matrix, which might not be possible due to the presence of the infinite elements. Also this method is shown to preserve the stability of the model and a computationally efficient way for implementation of the method is discussed. The effectiveness of the novel methodology is demonstrated with two numerical models. ispartof: Computer Methods in Applied Mechanics and Engineering vol:325 pages:240-264 status: published

Wave propagation in complex periodic systems is often addressed with the Bloch theorem, and consists in applying periodic boundary conditions to a discretized unit cell. While this method has been developed for structures periodic by translation, in a recent work, for quasi-one-dimensional wave propagation, it has been shown that screw (translation plus rotation) and glide (translation plus reflection) periodicities can be accounted for as well, keeping the Cartesian coordinate system but revisiting the periodic boundary conditions. The goal of the present paper is to generalize this concept to quasi-two-dimensional wave propagation (two dimensional waves propagating in three dimensional structures). Dispersion relations for a set of reduced problems are then compared to results from the classical method, when available. By considering a smaller periodicity, the computational cost is decreased and the number of folding curves and non-interacting intersecting curves is reduced, improving their interpretability. While the size of a unit cell is divided by a factor two when glide symmetries are considered, this ratio is significantly increased for screw or rotational symmetries. Moreover, the proposed revisited Bloch method is applicable to screw symmetric structures that do not possess purely translational symmetries, and for which the classical method cannot be used (e.g. chiral nanotubes, longitudinally wrinkled helicoids). publisher: Elsevier articletitle: Bloch theorem with revised boundary conditions applied to glide, screw and rotational symmetric structures journaltitle: Computer Methods in Applied Mechanics and Engineering articlelink: http://dx.doi.org/10.1016/j.cma.2017.01.034 content_type: article copyright: © 2017 Elsevier B.V. All rights reserved. ispartof: Computer Methods in Applied Mechanics and Engineering vol:318 pages:497-513 status: published

This paper presents a simple yet flexible method for coupling non-conforming NURBS patches in isogeometric frameworks. It consists of virtually refining bordering patches to derive coupling constraints in a master-slave formulation. These constraints are then enforced via a substitution method for condensation of the slave variables, thereby reducing the model size. In the special case of hierarchical meshes, the method results in an exact connection. For an arbitrary non-conforming configuration, the master-slave formulation takes the interface constraints into account in a least-squares sense. This yields an accurate weak coupling without overconstraining the interface. The coupling relationships only depend on the mesh itself and not on any problem-dependent parameters, allowing them to be generated in a pre-processing step with very limited numerical efforts. Besides this low computational cost, the main merit of the proposed method lies in its simplicity and robustness, yielding good results for arbitrarily strongly non-conforming patch configurations. Several numerical examples are studied for different problem types requiring C0- or C1-continuity, in particular time-harmonic acoustics and (dynamic) thin plate bending. Benchmarking of the proposed approach against existing similar techniques illustrates its superior accuracy and robustness. publisher: Elsevier articletitle: A robust patch coupling method for NURBS-based isogeometric analysis of non-conforming multipatch surfaces journaltitle: Computer Methods in Applied Mechanics and Engineering articlelink: http://dx.doi.org/10.1016/j.cma.2016.06.022 content_type: article copyright: © 2016 Elsevier B.V. All rights reserved. ispartof: Computer Methods in Applied Mechanics and Engineering vol:316 pages:235-260 status: published

This work proposes a hybrid modelling technique for efficient analysis of poroelastic materials, which are widely used for noise reduction in acoustic problems. By combining the finite element method and the wave based method in a direct manner, the proposed hybrid technique maximises the advantages and compensates the drawbacks of both numerical methods. The considered poroelastic domain described by Biot's theory is divided into two groups of domains according to their geometrical characteristics and boundary conditions. The group with complex geometries and/or boundary conditions leading to singularities is discretised into a large number of small finite elements. The other group consisting of large, geometrically moderate poroelastic domains is partitioned into wave based subdomains where the field variables are expanded with analytical poroelastic wave functions. Both groups modelled by the finite element method and the wave based method, respectively, are combined in a hybrid framework in this work to ensure their interacting dynamic behaviours. The properties of the hybrid model are investigated and are compared to existing modeling methods for some numerical examples. The proposed direct hybrid modeling technique provides stable predictions and exhibits fast convergence performances for the analysis of poroelastic materials, especially when singularities arise in the poroelastic domain. publisher: Elsevier articletitle: A direct hybrid finite element–wave based modelling technique for efficient analysis of poroelastic materials in steady-state acoustic problems journaltitle: Computer Methods in Applied Mechanics and Engineering articlelink: http://dx.doi.org/10.1016/j.cma.2016.02.006 content_type: article copyright: © 2016 Elsevier B.V. All rights reserved. ispartof: Computer Methods in Applied Mechanics and Engineering vol:304 pages:55-80 status: published

This work evaluates the performance of a NURBS-based isogeometric finite element formulation for solving stationary acoustic problems in two dimensions. An initial assessment is made by studying eigenvalue problems for a square and a circular domain. The spectral approximation properties of NURBS functions of varying order are compared to those of conventional polynomials and are found to be superior, yielding more accurate representations of eigenvalues as well as eigenmodes. The higher smoothness of NURBS shape functions yields better approximations over an extended frequency range when compared to conventional polynomials. Two numerical case studies, including a geometrically complex domain, are used to benchmark the method versus the traditional finite element method. A convergence analysis confirms the higher efficiency of the isogeometric method on a per-degree-of-freedom basis. Simulations over a wider frequency range also illustrate that the method suffers less from the dispersion effects that deteriorate the acoustic response towards higher frequencies. The tensor product structure of NURBS, however, also imposes practical considerations when modelling a complex geometry consisting of multiple patches. publisher: Elsevier articletitle: A performance study of NURBS-based isogeometric analysis for interior two-dimensional time-harmonic acoustics journaltitle: Computer Methods in Applied Mechanics and Engineering articlelink: http://dx.doi.org/10.1016/j.cma.2016.03.007 content_type: article copyright: © 2016 Elsevier B.V. All rights reserved. ispartof: Computer Methods in Applied Mechanics and Engineering vol:305 pages:441-467 status: published