2014 IEEE International Conference on BigData (IEEE BigData 2014), Washington DC Evaluating Structural Engineering Finite Element Analysis Data Using Multiway Analysis Matija Radovic Civil Engineering Department University of Delaware Newark, DE. mradovic@udel.edu Jennifer McConnell Civil Engineering Department University of Delaware Newark, DE. righman@udel.edu Abstract- The scope of this paper is to introduce multiway analysis into structural engineering research and to outline methodology used in tensor decomposition of finite element analysis (FEA) data. More specifically, the example evaluated herein evaluates the stress distribution of two different highway bridge structural components (girders and cross frames), being subjected to incrementally increasing forces. Additionally, the paper shows potential advantages of using multiway methods in interpretation of FEA data and makes recommendations for future investigations on the use of multiway methods in FEA post- processing of structural engineering data. Keywords—Multiway analysis, finite element analysis, bridge engineering, structural engineering, Tucker3 model. I. INTRODUCTION In current structural engineering practice, finite element analysis (FEA) is commonly used to predict the structural behavior of various structural members, of assemblies of structural members, and / or of entire structures. For example, FEA can be used to determine the maximum strength or displacements of a structural member under various loading scenarios or to investigate the distribution of stress between various members. It is routinely used to design unique structures such as bridges and buildings and as a research tool. FEA is based on a discretization of structural parts into geometric shapes (elements) that are bounded at their corners or edges with points (nodes). Each element has assigned material properties. The grid lines seen in the left of Fig. 1 denote the element boundaries for an I-shaped member. The response of these elements to an input loading is calculated via a system of partial differential equations with each element containing multiple unknown quantities that are calculated by the FEA method [1]. Since the solution for the set of the partial differential equations is based on numerical approximations, a more detailed set (a finer FEA mesh with a larger number of elements) will theoretically yield more accurate solutions up to a point where the influence of mesh size converges to a common solution. The number of elements in a typical model could vary anywhere from hundreds to millions. As a result of a typical FEA, displacements, stresses, and strains in multiple directions are computed for each element. Furthermore, one FEA may Fig. 1. Finite element model (FEM) of a steel bridge I-girder (on the left) shows the element mesh, where rectangles represent discretized geometrical shapes (elements) that can be numerically modeled with a system of partial differential equations. Stress contours (on the right) the spatial variation of stress magnitudes due to imposed loads. Red colored elements are elements with the largest stresses, while the green colored elements are the elements with the lowest stresses. realistically contain anywhere from one to hundreds of loading conditions, producing a unique data set for each loading. Thus, the potential output from these analyses is immense. Fig 2. shows a subset of potential FEA data, showing one type of output (von Mises stresses) for one part (bottom flange) of one highway bridge member (one girder) that was subjected to 60 load increments. In current practice, only a small fraction of this available data is quantitatively analyzed. For example, it is often the case that only the extreme values in the data set (such as minimum and maximum stresses or maximum displacements) at a particular region of interest are analyzed. A possible exception to this statement are contour plots showing the spatial distribution of the magnitudes of a specific output variable that can be produced by some FEA post-processing software (as seen in Fig 1. on the right). However, an approach for performing a rigorous quantitative analysis of the data has yet to be applied in any published works that could be identified by the authors. For these reasons, this paper explores the use of “big data” applications to analyze a large data set resulting from the FEA of a representative civil engineering structure, a steel bridge. The general goal of this effort is to first determine a methodology using big data analysis techniques to improve upon the current practice of using isolated subsets of the available data and/ or visual data contours that lack a means to readily conduct Center for Innovative Bridge Engineering (CIBrE), University of Delaware, Newark, DE.