No abstract

OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. This is an author-deposited version published in: http://oatao.univ-toulouse.fr/ Eprints ID : 14633 Highlights• We address the issue of modelling local phenomena in a NURBS patch with a global/local non-intrusive algorithm.• The approach provides simplicity and flexibility to treat any case of local enrichment in a NURBS patch.• We propose a strategy to handle non-conforming geometries.• We demonstrate the performance of the method on a range of two-dimensional linear elastic numerical examples. AbstractIn this work, we apply a non-intrusive global/local coupling strategy for the modelling of local phenomena in a NURBS patch. The idea is to consider the NURBS patch to be enriched as the global model. This results in a simple, flexible strategy: first, the global NURBS patch remains unchanged, which completely eliminates the need for costly re-parametrization procedures (even if the local domain is expected to evolve); then, easy merging of a linear NURBS code with any other existing robust codes suitable for the modelling of complex local behaviour is possible. The price to pay is the number of iterations of the non-intrusive solver but we show that this can be strongly reduced by means of acceleration techniques. The main development for NURBS is to be able to handle non-conforming geometries. Only slight changes in the implementation process, including the setting up of suitable quadrature rules for the evaluation of the interface reaction forces, are made in response to this issue. A range of numerical examples in two-dimensional linear elasticity are given to demonstrate the performance of the proposed methodology and its significant potential to treat any case of local enrichment in a NURBS patch simply.

Summary Finite element stereo digital image correlation (FE‐SDIC) requires a crucial calibration phase in which the initial CAD needs to be updated to fit the actual shape of the specimen. On the one hand, the use of a FE mesh facilitates the coupling of measurements with simulation tools, while on the other hand, it provides a unique, fine description of both the geometry and the displacement, which often makes the shape measurement problem highly ill‐posed. As a remedy, we propose a hybrid isogeometric‐FE strategy that can measure a shape in terms of spline functions while considering as an input and output the analysis‐suitable FE mesh. Making use of the appealing spline refinement procedures and of Bézier‐based operators, multilevel smooth spline discretizations are built concurrently with the initial FE subspace and related to the multiscale images used for the initialization of the shape measurement. It results in a geometrically sound regularization which provides a spline parametrization of the optimal shape along with its FE twin. A noninvasive implementation from an existing FE‐SDIC code is also detailed. The performance of the proposed method is assessed on real images and comparisons are made with other published techniques to prove its efficiency.

SUMMARYIn this work, we develop an isogeometric non-uniform rational B-spline (NURBS)-based solid-shell element for the geometrically nonlinear static analysis of elastic shell structures. A single layer of continuous 3D elements through the thickness of the shell is considered, and the order of approximation in that direction is chosen to be equal to two. A complete 3D constitutive relation is assumed. The objective is to develop a highly accurate low-order element for coarse meshes. We propose an extension of the mixed method of Bouclier et al.[11] to deal with locking in the context of large rotations and large displacements. The main idea is to modify the interpolation of the average through the thickness of the stress components. It is also necessary to stabilize the element in order to avoid the occurrence of spurious zero-energy modes. This was achieved, for the quadratic version, through the adjunction of artificial elementary stabilization stiffnesses. The result is an element of order 2, which is at least as accurate as standard NURBS shell elements of order 4. Linear and nonlinear test calculations have been carried out along with comparisons with other published NURBS and classical techniques in order to assess the performance of the element.

No abstract

The aim of this study is to develop a new regularized Digital Image Correlation (DIC) method for time dependent measurements. The correlation problem is written as a minimization problem over the space-time domain in a general formulation including 2D-DIC and Stereo DIC (SDIC). The unknown time-resolved displacement field is found as a sum of products of space and time functions, similarly to the Proper Generalized Decomposition in computational mechanics. It is shown that the space fields are less sensitive to noise as time regularity acts as a physical regularization of the space fields. The proposed method is illustrated by vibration measurement under harmonic excitation in 2D-DIC and SDIC.

The multiscale analysis of large composite aeronautical structures involves the development of robust coupling strategies. Among the latter, non-intrusive coupling is attractive, since it is able to consistently connect a global simplified linear model to a local detailed one, using features available in commercial software. Up to now, such coupling methods were still limited to academic situations where global and local meshes are geometrically and/or topologically conforming and of low geometric complexity. To meet the goal of merging a complex non-planar global shell to a local detailed 3D model, an extension of these techniques is proposed to handle meshes of complex shapes that are not only non-matching but also geometrically and topologically non-conforming. The implemented strategy is original and robust: the innovative nature of the approach is to expand the initial local solid model by generating transitional shell meshing. The generated model incorporates two distinct coupling interfaces: (i) non-intrusive global-local coupling and (ii) shell-solid coupling. The multiscale strategy was successfully validated through different numerical experiments using standard Input/Output of a commercial finite element software. In particular, a representative use-case involving a realistic fuselage section of an aircraft was computed.

of a new, more regular, mortar method for the coupling of NURBS subdomains within a NURBS patch: Application to a non-intrusive local enrichment of NURBS patches. (2017) Highlights• We develop a new mortar method for NURBS that keeps the benefit of using more regular functions.• We propose to match the tractions in addition to the displacements at the coupling interface.• We apply the methodology to perform the non-intrusive local enrichment of NURBS patches.• We demonstrate the performance of the method on a range of two-dimensional linear elastic numerical examples. AbstractIn this work, we develop a mortar method for the coupling of non-conforming NURBS subdomains within a NURBS patch that keeps the benefit of using more regular functions. The idea is to use two Lagrange multipliers to match, across the coupling interface, the tractions coming from the discrete displacements in addition to the discrete displacements. It results in a strategy that is suitable with the continuity of the physical solution: when the physical solution is sufficiently smooth, the strategy enables to represent a C 1 behavior; but, when only a C 0 displacement is expected, no additional errors are introduced since only the traction force is continuous and not the whole derivative fields. Lower stress jumps at the coupling interface can then be observed which allows for a better transition of the information. As an application, a non-intrusive algorithm is also built to solve the proposed coupling method, which enables simple and flexible local enrichments of NURBS patches without losing the interest of using more regular functions. A range of numerical examples in two-dimensional linear elasticity are carried out along with comparisons with other published NURBS coupling techniques to demonstrate the performance of the proposed coupling and its interest when combined to a non-intrusive strategy.