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

Geometrically nonlinear isogeometric analysis of laminated composite plates based on higher-order shear deformation theory

In this paper, we present an effectively numerical approach based on isogeometric analysis (IGA) and higher-order shear deformation theory (HSDT) for geometrically nonlinear analysis of laminated composite plates. The HSDT allows us to approximate displacement field that ensures by itself the realistic shear strain energy part without shear correction factors. IGA utilizing basis functions namely B-splines or non-uniform rational B-splines (NURBS) enables to satisfy easily the stringent continuity requirement of the HSDT model without any additional variables. The nonlinearity of the plates is formed in the total Lagrange approach based on the von-Karman strain assumptions. Numerous numerical validations for the isotropic, orthotropic, cross-ply and angle-ply laminated plates are provided to demonstrate the effectiveness of the proposed method

Computing distances and geodesics between manifold-valued curves in the SRV framework

This paper focuses on the study of open curves in a Riemannian manifold M, and proposes a reparametrization invariant metric on the space of such paths. We use the square root velocity function (SRVF) introduced by Srivastava et al. to define a Riemannian metric on the space of immersions M'=Imm([0,1],M) by pullback of a natural metric on the tangent bundle TM'. This induces a first-order Sobolev metric on M' and leads to a distance which takes into account the distance between the origins in M and the L2-distance between the SRV representations of the curves. The geodesic equations for this metric are given and exploited to define an exponential map on M'. The optimal deformation of one curve into another can then be constructed using geodesic shooting, which requires to characterize the Jacobi fields of M'. The particular case of curves lying in the hyperbolic half-plane is considered as an example, in the setting of radar signal processing

Maximum-likelihood estimation of lithospheric flexural rigidity, initial-loading fraction, and load correlation, under isotropy

Topography and gravity are geophysical fields whose joint statistical structure derives from interface-loading processes modulated by the underlying mechanics of isostatic and flexural compensation in the shallow lithosphere. Under this dual statistical-mechanistic viewpoint an estimation problem can be formulated where the knowns are topography and gravity and the principal unknown the elastic flexural rigidity of the lithosphere. In the guise of an equivalent "effective elastic thickness", this important, geographically varying, structural parameter has been the subject of many interpretative studies, but precisely how well it is known or how best it can be found from the data, abundant nonetheless, has remained contentious and unresolved throughout the last few decades of dedicated study. The popular methods whereby admittance or coherence, both spectral measures of the relation between gravity and topography, are inverted for the flexural rigidity, have revealed themselves to have insufficient power to independently constrain both it and the additional unknown initial-loading fraction and load-correlation fac- tors, respectively. Solving this extremely ill-posed inversion problem leads to non-uniqueness and is further complicated by practical considerations such as the choice of regularizing data tapers to render the analysis sufficiently selective both in the spatial and spectral domains. Here, we rewrite the problem in a form amenable to maximum-likelihood estimation theory, which we show yields unbiased, minimum-variance estimates of flexural rigidity, initial-loading frac- tion and load correlation, each of those separably resolved with little a posteriori correlation between their estimates. We are also able to separately characterize the isotropic spectral shape of the initial loading processes.Comment: 41 pages, 13 figures, accepted for publication by Geophysical Journal Internationa

Simultaneous inference for misaligned multivariate functional data

We consider inference for misaligned multivariate functional data that represents the same underlying curve, but where the functional samples have systematic differences in shape. In this paper we introduce a new class of generally applicable models where warping effects are modeled through nonlinear transformation of latent Gaussian variables and systematic shape differences are modeled by Gaussian processes. To model cross-covariance between sample coordinates we introduce a class of low-dimensional cross-covariance structures suitable for modeling multivariate functional data. We present a method for doing maximum-likelihood estimation in the models and apply the method to three data sets. The first data set is from a motion tracking system where the spatial positions of a large number of body-markers are tracked in three-dimensions over time. The second data set consists of height and weight measurements for Danish boys. The third data set consists of three-dimensional spatial hand paths from a controlled obstacle-avoidance experiment. We use the developed method to estimate the cross-covariance structure, and use a classification setup to demonstrate that the method outperforms state-of-the-art methods for handling misaligned curve data.Comment: 44 pages in total including tables and figures. Additional 9 pages of supplementary material and reference

A priori error for unilateral contact problems with Lagrange multiplier and IsoGeometric Analysis

In this paper, we consider unilateral contact problem without friction between a rigid body and deformable one in the framework of isogeometric analysis. We present the theoretical analysis of the mixed problem using an active-set strategy and for a primal space of NURBS of degree $p$ and $p-2$ for a dual space of B-Spline. A inf-sup stability is proved to ensure a good property of the method. An optimal a priori error estimate is demonstrated without assumption on the unknown contact set. Several numerical examples in two- and three-dimensional and in small and large deformation demonstrate the accuracy of the proposed method

Fragility curves and seismic demand hazard analysis of rocking walls restrained with elasto-plastic ties

AbstractThe dynamic stability of out‐of‐plane masonry walls can be assessed through non‐linear dynamic analysis (rocking analysis), accounting for transverse walls, horizontal diaphragms and tie‐rods. Steel tie‐rods are widely spread in historical constructions to prevent dangerous overturning mechanisms and can be simulated by proper elasto‐plastic models. Conventionally, design guidelines suggest intensity‐based assessment methods, where the seismic demand distribution directly depends upon the selected intensity measure level. Fragility analysis could also be employed as a more advanced procedure able to assess the seismic vulnerability in a probabilistic manner. The boundedness of this approach is herein overcome by applying a robust stochastic seismic performance assessment to obtain seismic demand hazard curves. A sensitivity study is carried out to account for the influence of wall geometry, the minimum number of seismic inputs, and the mechanical parameters of tie‐rods. Fragility analysis, prior to seismic demand hazard analysis is applied on over 6000 analyses, revealing that intensity measures are poorly correlated both for 1‐D and 2‐D correlation, hardly leading to the selection of the optimal intensity measure. The tie‐rod ductility, followed by its axial strength and wall size, is the mechanical parameter mostly influencing the results, whereas the wall slenderness does not play a significant role in the probabilistic response