Formulation of an isogeometric shell element for crash simulation

In this paper, we propose, for the isogeometric analysis, a shell model based on a degenerated three dimensional approach. It uses a first order kinematic description in the thickness with transverse shear (Reissner-Mindlin theory). We examine various approaches to describe the geometry and compare them on various linear and non-linear benchmark problems. Both geometric and material non-linearities are treated. The obtained results are compared with the solutions of isogeometric solid model and with other numerical solutions found in the literature

The DKMQ-SS Solid-Shell Element: Formulation Aspects and Applications

In this paper we present the formulation of a solid-shell element with 24 dof (the three cartesian components of displacement at the eight nodes of a solid hexahedron element), taking into account previous contributions to avoid shear, trapezoidal and thickness locking. But we also enhance the 3D displacement field by incomplete quadratic terms to improve the bending and transverse shear energies as was done for the performing DKMQ plate bending element proposed by Katili. After the formulation aspects, we present the results for some classical benchmark problems and for the linear analysis of a particular shallow foundation system called 'spider net system footing' used in Indonesia

Formulation of an isogeometric shell element for crash simulation

In this paper, we propose, for the isogeometric analysis, a shell model based on a degenerated three dimensional approach. It uses a first order kinematic description in the thickness with transverse shear (Reissner-Mindlin theory). We examine various approaches to describe the geometry and compare them on various linear and non-linear benchmark problems. Both geometric and material non-linearities are treated. The obtained results are compared with the solutions of isogeometric solid model and with other numerical solutions found in the literature

A Reduced Integration for Reissner-Mindlin Non-linear Shell Analysis Using T-Splines

International audienceWe propose a reduced shell element for Reissner-Mindlin geometric non-linear analysis within the context of T-spline analysis. The shell formulation is based on the displacements and a first order kinematic in the thickness is used for the transverse shear strains. A total Lagrangian formulation is considered for the finite transformations. The update of the incremental rotations is made using the quaternion algebra. The standard two-dimensional reduced quadrature rules for structured B-spline and NURBS basis functions are extended to the more flexible T-meshes. The non-uniform Gauss-Legendre and patchwise reduced integrations for quadratic shape functions are both presented and compared to the standard full Gauss-Legendre scheme. The performance of the element is assessed with linear and geometric non-linear two-dimensional problems in structural analysis. The effects of mesh distortion and local refinement, using both full and reduced numerical quadratures, are evaluated

Improved numerical integration for locking treatment in isogeometric structural elements. Part II: Plates and shells

International audienceHighlights • We model Reissner–Mindlin isogeometric plates and shells. • We examine membrane and shear locking in bending dominated problems. • Higher continuity elements exhibit superior accuracy when no locking occurs. • We extend one-dimensional reduced quadrature rules to two-dimensional rules. • We assess the performance of the schemes using the shell obstacle course problems. Abstrac

Improved numerical integration for locking treatment in isogeometric structural elements, Part I: Beams

International audienceA general mathematical framework is proposed, in this paper, to define new quadrature rules in the context of BB-spline/NURBS-based isogeometric analysis. High order continuity across the elements within a patch turned out to have higher accuracy than C0C0 finite elements, as well as a better time efficiency. Unfortunately, a maximum regularity accentuates the shear and membrane locking in thick structural elements. The improved selective reduced integration schemes are given for uni-dimensional beam problems, with basis functions of order two and three, and can be easily extended to higher orders. The resulting BB-spline/NURBS finite elements are free from membrane and transverse shear locking. Moreover, no zero energy modes are generated. The performance of the approach is evaluated on the classical test of a cantilever beam subjected to a distributed moment, and compared to Lagrange under-integrated finite elements

Formulation d'un élément coque en analyse isogéométrique pour la simulation du choc

International audienceDans cet article, nous proposons, pour l'analyse isogéométrique, un modèle de coque tridimensionnel dégénéré basé sur une cinématique du premier ordre dans l'épaisseur avec prise en compte du cisaillement transversal (théorie de Reissner-Mindlin). Nous examinons diverses approches pour la description de la géométrie et nous les comparons sur des cas tests linéaires et non-linéaires. Le résultats présentés sont comparés à ceux obtenus avec un modèle volumique ainsi qu'aux solutions de référence données dans la bibliographie

Intégration réduite d'un élément de coque isogéométrique de type Reissner-Mindlin dans le cadre de l'analyse non-linéaire par T-splines

International audienceL'intégration réduite d'un élément de coque géométriquement non linéaire de ReissnerMindlin est proposée dans le cadre de l'analyse des structures par T-splines. La formulation de coque est basée sur les déplacements et une approximation du premier ordre est utilisée dans l'épaisseur pour prendre en compte le cisaillement transverse. La formulation Lagrangienne totale est utilisée pour prendre en non linéarités en déplacements finis. La mise à jour des grandes rotations est traitée par la théorie des quaternions

Stable time step estimates for NURBS-based explicit dynamics

International audienceAutomobile crashworthiness is a complex application for numerical methods in dynamics of structures which includes many high non-linearities. Explicit techniques are widely used for structural dynamics dealing with difficult and large problems that prevent the use of implicit methods. We propose, in this paper, a deep study of the stable time step, which guarantees the stability of the method, and its estimates, for one-dimensional and two-dimensional problems. Element and nodal time steps are presented and adapted to highly regular B-spline and NURBS functions, in the context of isogeometric analysis. The size of the proposed stable time estimates benefits from the properties of regularity and extended support of the basis. Their performance is assessed and compared in several examples, with an arbitrary mesh, uniform or non-uniform, and considering polynomial orders from one to five. The smoothness and order of the polynomials have a significant effect on the stable time step and its estimates. Several lumping schemes of the mass matrix are presented and their accuracy is assessed

Selective and reduced numerical integrations for NURBS-based isogeometric analysis

International audienceWe propose a new approach to construct selective and reduced integration rules for isogeometric analysis based on NURBS elements. The notion of an approximation space that approximates the target space is introduced. We explore the use of various approximation spaces associated with optimal patch-wise numerical quadratures that exactly integrate the polynomials in approximation spaces with the minimum number of quadrature points. Patch rules exploit the higher continuity of spline basis functions. The tendency of smooth spline functions to exhibit numerical locking in nearly-incompressible problems when using a full Gauss–Legendre quadrature is alleviated with selective or reduced integration. Stability and accuracy of the schemes are examined analyzing the discrete spectrum in a generalized eigenvalue problem. We propose a local algorithm, which is robust and computationally efficient, to compute element-by-element the quadrature points and weights in patch rules. The performance of the methods is assessed on several numerical examples in two-dimensional elasticity and Reissner–Mindlin shell structures