Approximation of the critical buckling factor for composite panels

This article is concerned with the approximation of the critical buckling factor for thin composite plates. A new method to improve the approximation of this critical factor is applied based on its behavior with respect to lamination parameters and loading conditions. This method allows accurate approximation of the critical buckling factor for non-orthotropic laminates under complex combined loadings (including shear loading). The influence of the stacking sequence and loading conditions is extensively studied as well as properties of the critical buckling factor behavior (e.g concavity over tensor D or out-of-plane lamination parameters). Moreover, the critical buckling factor is numerically shown to be piecewise linear for orthotropic laminates under combined loading whenever shear remains low and it is also shown to be piecewise continuous in the general case. Based on the numerically observed behavior, a new scheme for the approximation is applied that separates each buckling mode and builds linear, polynomial or rational regressions for each mode. Results of this approach and applications to structural optimization are presented

Large-scale predictive modeling and analytics through regression queries in data management systems

Regression analytics has been the standard approach to modeling the relationship between input and output variables, while recent trends aim to incorporate advanced regression analytics capabilities within data management systems (DMS). Linear regression queries are fundamental to exploratory analytics and predictive modeling. However, computing their exact answers leaves a lot to be desired in terms of efficiency and scalability. We contribute with a novel predictive analytics model and an associated statistical learning methodology, which are efficient, scalable and accurate in discovering piecewise linear dependencies among variables by observing only regression queries and their answers issued to a DMS. We focus on in-DMS piecewise linear regression and specifically in predicting the answers to mean-value aggregate queries, identifying and delivering the piecewise linear dependencies between variables to regression queries and predicting the data dependent variables within specific data subspaces defined by analysts and data scientists. Our goal is to discover a piecewise linear data function approximation over the underlying data only through query–answer pairs that is competitive with the best piecewise linear approximation to the ground truth. Our methodology is analyzed, evaluated and compared with exact solution and near-perfect approximations of the underlying relationships among variables achieving orders of magnitude improvement in analytics processing

A Generalized Multiscale Finite Element Method for the Brinkman Equation

In this paper we consider the numerical upscaling of the Brinkman equation in the presence of high-contrast permeability fields. We develop and analyze a robust and efficient Generalized Multiscale Finite Element Method (GMsFEM) for the Brinkman model. In the fine grid, we use mixed finite element method with the velocity and pressure being continuous piecewise quadratic and piecewise constant finite element spaces, respectively. Using the GMsFEM framework we construct suitable coarse-scale spaces for the velocity and pressure that yield a robust mixed GMsFEM. We develop a novel approach to construct a coarse approximation for the velocity snapshot space and a robust small offline space for the velocity space. The stability of the mixed GMsFEM and a priori error estimates are derived. A variety of two-dimensional numerical examples are presented to illustrate the effectiveness of the algorithm.Comment: 22 page