ERRORS IN QUANTITIES OF INTEREST IN THE LAMINATED PLATE BENDING PROBLEM USING HIERARCHIC SETS OF BASIS FUNCTIONS IN GFEM

A formulation for error estimation is developed for the bending problem of composite laminated plates based on the Mindlin-Reissner kinematic model discritized by the Generalized Finite Element Method (GFEM). The error estimation process starts with an upper bound in energy norm, which is obtained following the basic CRE (Constitutive Relation Error) framework of the Ladev`eze formulation, that is, the estimate is obtained from a statically admissible stress field computed at element level in a Neumann problem where the element boundary forces are equilibrated. The authors have previously shown that an accurate description of the in plane stresses in a laminate is essential to obtain an accurate approximation to the transverse shear stresses at the layers interfaces. Since important failure modes in laminated composite plates, like the delamination, are linked to the transverse stresses, it is essential to develop both, accurate post-processing procedures to compute improved transverse stresses, and also estimate techniques for the discretization errors. The first condition is adequately satisfied by GFEM. Therefore, the aim of the present work is to extend the general CRE technology to develop formulations to estimation of errors in Quantity of Interest (QI) identified preferably with the stress field in the laminated plate problem. One of the steps necessary in the CRE procedure is the computation of and admissible stress field in each element, in a Neumann problem where the boundary forces have been previously equilibrated. For a GFEM basis with high order enrichment, adequate procedures have to be sought. Here we use one single higher order finite element, based on displacement FEM, to obtain an approximation to the equilibrated field. The formulation is implemented for arbitrary degree of the basis, which allows an arbitrarily close approximation to the equilibrium condition. The sharpness of the QI’s error bounds is increased with the accuracy of the primal and dual global energy norm of errors. In the present work we investigate the effectiveness of a local GFEM p-enrichment as a tool to improve the approximability of the model in capturing the local gradients which characterizes response of the dual loading. The GFEM p-enrichment is implemented in a simple and straightforward way, as opposed to some other possible forms of enrichment, e.g. local h-refinement or a sub-domain approach. Numerical tests are performed to asses the effect of the different parameters in the modeling over the errors in the quantities of interest

LARGE DEFLECTION ANALYSIS OF ANISOTROPIC LAMINATED PLATES BY CONTINUOUS AND NON-CONTINUOUS GFEM

This work addresses the application of the GFEM to laminated plates under moderately large transverse displacements by the von K´arm´an’s hypothesis, in the frame of the Kirchhoff-Love and Reissner-Mindlin kinematical plate models. The formulation admits the general case of laminated plates composed of anisotropic layers in the elastic range. The behaviors of two types of GFEM formulations are compared, one based on C0 continuous Partition of Unity (PoU), and the other is based on continuous PoU. The adequate number of integration points in the element is investigated for each degree of enrichment polynomial. For the transverse shear stresses obtained from integration of the local equilibrium equations, a theorem is presented to explain the reason why, in some cases, the null value is not reached at the end of the integration across the laminate thickness. Numerical results are compared with literature

Comparative Analysis of Ck- and C0-GFEM Applied to Two-dimensional Problems of Confined Plasticity

AbstractFor many practical applications in engineering, a complex structure shows linear elastic behavior over almost all its extension, but exhibits confined plasticity contained in some small critical regions, e.g. stress concentrations in fillets and sharp internal corners. The behavior of C0- and Ck-GFEM is investigated in this class of problems. The first goal of this study is to verify the actual formulation of the Ck-GFEM for two-dimensional elastoplasticity, as a modification of the C0-GFEM formulation. The Ck-GFEM is based on a set of basis functions with Ck continuity over the domain. The approximation functions are constructed from a Ck continuous partition of unity, over which polynomial enrichment functions (or any special function) can be applied, in the same fashion as in the usual C0-GFEM. In this way, the finite element approximations show continuous responses for both displacements and stresses across inter-element interfaces. An investigation is performed to assess the behavior of higher-regularity partitions of unity against conventional C0 counterparts. The irreversible response and hardening effects of the material is represented by the rate independent J2 plasticity theory with linear isotropic hardening of material and von Mises yield criteria, being considered only monotonic loading and the kinematics of small displacements and small deformations. The focus herein is to enlighten any possible advantage of smoothness in the presence of plastification phenomena, seeking for improvements in capturing the evolution of the process zone

NEOTROPICAL CARNIVORES: a data set on carnivore distribution in the Neotropics

Mammalian carnivores are considered a key group in maintaining ecological health and can indicate potential ecological integrity in landscapes where they occur. Carnivores also hold high conservation value and their habitat requirements can guide management and conservation plans. The order Carnivora has 84 species from 8 families in the Neotropical region: Canidae; Felidae; Mephitidae; Mustelidae; Otariidae; Phocidae; Procyonidae; and Ursidae. Herein, we include published and unpublished data on native terrestrial Neotropical carnivores (Canidae; Felidae; Mephitidae; Mustelidae; Procyonidae; and Ursidae). NEOTROPICAL CARNIVORES is a publicly available data set that includes 99,605 data entries from 35,511 unique georeferenced coordinates. Detection/non-detection and quantitative data were obtained from 1818 to 2018 by researchers, governmental agencies, non-governmental organizations, and private consultants. Data were collected using several methods including camera trapping, museum collections, roadkill, line transect, and opportunistic records. Literature (peer-reviewed and grey literature) from Portuguese, Spanish and English were incorporated in this compilation. Most of the data set consists of detection data entries (n = 79,343; 79.7%) but also includes non-detection data (n = 20,262; 20.3%). Of those, 43.3% also include count data (n = 43,151). The information available in NEOTROPICAL CARNIVORES will contribute to macroecological, ecological, and conservation questions in multiple spatio-temporal perspectives. As carnivores play key roles in trophic interactions, a better understanding of their distribution and habitat requirements are essential to establish conservation management plans and safeguard the future ecological health of Neotropical ecosystems. Our data paper, combined with other large-scale data sets, has great potential to clarify species distribution and related ecological processes within the Neotropics. There are no copyright restrictions and no restriction for using data from this data paper, as long as the data paper is cited as the source of the information used. We also request that users inform us of how they intend to use the data

NEOTROPICAL XENARTHRANS: a data set of occurrence of xenarthran species in the Neotropics

Xenarthrans—anteaters, sloths, and armadillos—have essential functions for ecosystem maintenance, such as insect control and nutrient cycling, playing key roles as ecosystem engineers. Because of habitat loss and fragmentation, hunting pressure, and conflicts with domestic dogs, these species have been threatened locally, regionally, or even across their full distribution ranges. The Neotropics harbor 21 species of armadillos, 10 anteaters, and 6 sloths. Our data set includes the families Chlamyphoridae (13), Dasypodidae (7), Myrmecophagidae (3), Bradypodidae (4), and Megalonychidae (2). We have no occurrence data on Dasypus pilosus (Dasypodidae). Regarding Cyclopedidae, until recently, only one species was recognized, but new genetic studies have revealed that the group is represented by seven species. In this data paper, we compiled a total of 42,528 records of 31 species, represented by occurrence and quantitative data, totaling 24,847 unique georeferenced records. The geographic range is from the southern United States, Mexico, and Caribbean countries at the northern portion of the Neotropics, to the austral distribution in Argentina, Paraguay, Chile, and Uruguay. Regarding anteaters, Myrmecophaga tridactyla has the most records (n = 5,941), and Cyclopes sp. have the fewest (n = 240). The armadillo species with the most data is Dasypus novemcinctus (n = 11,588), and the fewest data are recorded for Calyptophractus retusus (n = 33). With regard to sloth species, Bradypus variegatus has the most records (n = 962), and Bradypus pygmaeus has the fewest (n = 12). Our main objective with Neotropical Xenarthrans is to make occurrence and quantitative data available to facilitate more ecological research, particularly if we integrate the xenarthran data with other data sets of Neotropical Series that will become available very soon (i.e., Neotropical Carnivores, Neotropical Invasive Mammals, and Neotropical Hunters and Dogs). Therefore, studies on trophic cascades, hunting pressure, habitat loss, fragmentation effects, species invasion, and climate change effects will be possible with the Neotropical Xenarthrans data set. Please cite this data paper when using its data in publications. We also request that researchers and teachers inform us of how they are using these data