An embedded cohesive crack model for finite element analysis of quasi-brittle materials

This paper presents a numerical implementation of the cohesive crack model for the anal-ysis of quasibrittle materials based on the strong discontinuity approach in the framework of the finite element method. A simple central force model is used for the stress versus crack opening curve. The additional degrees of freedom defining the crack opening are determined at the crack level, thus avoiding the need for performing a static condensation at the element level. The need for a tracking algorithm is avoided by using a consistent pro-cedure for the selection of the separated nodes. Such a model is then implemented into a commercial program by means of a user subroutine, consequently being contrasted with the experimental results. The model takes into account the anisotropy of the material. Numerical simulations of well-known experiments are presented to show the ability of the proposed model to simulate the fracture of quasibrittle materials such as mortar, concrete and masonry.

Analysis of plate bending by means of high order finite hyperelements

The possibilities and limitations of high order hyperelements in plate bending analysis are discussed. Explicit shape functions for some types of triangular elements are given. These elements are applied to simple cases to assess their computational efficiency.

A C1 finite element for Kirchhoff plate bending

After a short introduction the possibilities and limitations of polynomial simple elements with C1 continuity are discussed with reference to plate bending analysis. A family of this kind of elements is presented.. These elements are applied to simple cases in order to assess their computational efficiency. Finally some conclusions are shown, and future research is also proposed.

Two-dimensional mesh optimization in the finite element method

The solution to the problem of finding the optimum mesh design in the finite element method with the restriction of a given number of degrees of freedom, is an interesting problem, particularly in the applications method. At present, the usual procedures introduce new degrees of freedom (remeshing) in a given mesh in order to obtain a more adequate one, from the point of view of the calculation results (errors uniformity). However, from the solution of the optimum mesh problem with a specific number of degrees of freedom some useful recommendations and criteria for the mesh construction may be drawn. For 1-D problems, namely for the simple truss and beam elements, analytical solutions have been found and they are given in this paper. For the more complex 2-D problems (plane stress and plane strain) numerical methods to obtain the optimum mesh, based on optimization procedures have to be used. The objective function, used in the minimization process, has been the total potential energy. Some examples are presented. Finally some conclusions and hints about the possible new developments of these techniques are also given.

Finite element simulation of dispersion in the Bay of Santander

Two mathematical models are used to simulate pollution in the Bay of Santander. The first is the hydrodynamic model that provides the velocity field and height of the water. The second gives the pollutant concentration field as a resultant. Both models are formulated in two-dimensional equations. Linear triangular finite elements are used in the Galerkin procedure for spatial discretization. A finite difference scheme is used for the time integration. At each time step the calculated results of the first model are input to the second model as field data. The efficiency and accuracy of the models are tested by their application to a simple illustrative example. Finally a case study in simulation of pollution evolution in the Bay of Santander is presented

Classifying GABAergic interneurons with semi-supervised projected model-based clustering

Objectives: A recently introduced pragmatic scheme promises to be a useful catalog of interneuron names.We sought to automatically classify digitally reconstructed interneuronal morphologies according tothis scheme. Simultaneously, we sought to discover possible subtypes of these types that might emergeduring automatic classification (clustering). We also investigated which morphometric properties weremost relevant for this classification.Materials and methods: A set of 118 digitally reconstructed interneuronal morphologies classified into thecommon basket (CB), horse-tail (HT), large basket (LB), and Martinotti (MA) interneuron types by 42 of theworld?s leading neuroscientists, quantified by five simple morphometric properties of the axon and fourof the dendrites. We labeled each neuron with the type most commonly assigned to it by the experts. Wethen removed this class information for each type separately, and applied semi-supervised clustering tothose cells (keeping the others? cluster membership fixed), to assess separation from other types and lookfor the formation of new groups (subtypes). We performed this same experiment unlabeling the cells oftwo types at a time, and of half the cells of a single type at a time. The clustering model is a finite mixtureof Gaussians which we adapted for the estimation of local (per-cluster) feature relevance. We performedthe described experiments on three different subsets of the data, formed according to how many expertsagreed on type membership: at least 18 experts (the full data set), at least 21 (73 neurons), and at least26 (47 neurons).Results: Interneurons with more reliable type labels were classified more accurately. We classified HTcells with 100% accuracy, MA cells with 73% accuracy, and CB and LB cells with 56% and 58% accuracy,respectively. We identified three subtypes of the MA type, one subtype of CB and LB types each, andno subtypes of HT (it was a single, homogeneous type). We got maximum (adapted) Silhouette widthand ARI values of 1, 0.83, 0.79, and 0.42, when unlabeling the HT, CB, LB, and MA types, respectively,confirming the quality of the formed cluster solutions. The subtypes identified when unlabeling a singletype also emerged when unlabeling two types at a time, confirming their validity. Axonal morphometricproperties were more relevant that dendritic ones, with the axonal polar histogram length in the [pi, 2pi) angle interval being particularly useful.Conclusions: The applied semi-supervised clustering method can accurately discriminate among CB, HT, LB, and MA interneuron types while discovering potential subtypes, and is therefore useful for neuronal classification. The discovery of potential subtypes suggests that some of these types are more heteroge-neous that previously thought. Finally, axonal variables seem to be more relevant than dendritic ones fordistinguishing among the CB, HT, LB, and MA interneuron types.