An improved quadrilateral flat element with drilling degrees of freedom for shell structural analysis

This paper reports the development of a simple and efficient 4-node flat shell element with six degrees of freedom per node for the analysis of arbitrary shell structures. The element is developed by incorporating a strain smoothing technique into a flat shell finite element approach. The membrane part is formulated by applying the smoothing operation on a quadrilateral membrane element using Allman-type interpolation functions with drilling DOFs. The plate-bending component is established by a combination of the smoothed curvature and the substitute shear strain fields. As a result, the bending and a part of membrane stiffness matrices are computed on the boundaries of smoothing cells which leads to very accurate solutions, even with distorted meshes, and possible reduction in computational cost. The performance of the proposed element is validated and demonstrated through several numerical benchmark problems. Convergence studies and comparison with other existing solutions in the literature suggest that the present element is efficient, accurate and free of lockings

Applications of Graph Embedding in Mesh Untangling

The subject of this thesis is mesh untangling through graph embedding, a method of laying out graphs on a planar surface, using an algorithm based on the work of Fruchterman and Reingold[1]. Meshes are a variety of graph used to represent surfaces with a wide number of applications, particularly in simulation and modelling. In the process of simulation, simulated forces can tangle the mesh through deformation and stress. The goal of this thesis was to create a tool to untangle structured meshes of complicated shapes and surfaces, including meshes with holes or concave sides. The goals of graph embedding, such as minimizing edge crossings align very well with the objectives of mesh untangling. I have designed and tested a tool which I named MUT (Mesh Untangling Tool) on meshes of various types including triangular, polygonal, and hybrid meshes. Previous methods of mesh untangling have largely been numeric or optimizationbased. Additionally, most untangling methods produce low quality graphs which must be smoothed separately to produce good meshes. Currently graph embedding techniques have only been used for smoothing of untangled meshes. I have developed a tool based on the Fruchterman-Reingold algorithm for force-directed layout[1] that effectively untangles and smooths meshes simultaneously using graph embedding techniques. It can untangle complicated meshes with irregular polygonal frames, internal holes, and other complications that previous methods struggle with. The MUT does this by using several different approaches: untangling the mesh in stages from the frame in and anchoring the mesh at corner points to stabilize the untangling

ITEM: Inter-Texture Error Measurement for 3D Meshes

We introduce a simple and innovative method to compare any two texture maps, regardless of their sizes, aspect ratios, or even masks, as long as they are both meant to be mapped onto the same 3D mesh. Our system is based on a zero-distortion 3D mesh unwrapping technique which compares two new adapted texture atlases with the same mask but different texel colors, and whose every texel covers the same area in 3D. Once these adapted atlases are created, we measure their difference with ITEM-RMSE, a slightly modified version of the standard RMSE defined for images. ITEM-RMSE is more meaningful and reliable than RMSE because it only takes into account the texels inside the mask, since they are the only ones that will actually be used during rendering. Our method is not only very useful to compare the space efficiency of different texture atlas generation algorithms, but also to quantify texture loss in compression schemes for multi-resolution textured 3D meshes

Deep drawing simulations of Tailored Blanks and experimental verification

Tailored Blanks are increasingly used in the automotive industry.\ud A combination of different materials, thickness, and coatings can be welded\ud together to form a blank for stamping car body panels. The main advantage\ud of using Tailored Blanks is to have specific characteristics at particular parts\ud of the blank in order to reduce the material weight and costs.\ud To investigate the behaviour of Tailored Blanks during deep drawing, the\ud finite element code DiekA is used. In this paper, simulations of the deep\ud drawing of two products using Tailored Blanks are discussed. For\ud verification, the two products are stamped to gain experimental information.\ud The correlation between the experimental results and the simulation results\ud appears to be satisfactory

A Parallel Solver for Graph Laplacians

Problems from graph drawing, spectral clustering, network flow and graph partitioning can all be expressed in terms of graph Laplacian matrices. There are a variety of practical approaches to solving these problems in serial. However, as problem sizes increase and single core speeds stagnate, parallelism is essential to solve such problems quickly. We present an unsmoothed aggregation multigrid method for solving graph Laplacians in a distributed memory setting. We introduce new parallel aggregation and low degree elimination algorithms targeted specifically at irregular degree graphs. These algorithms are expressed in terms of sparse matrix-vector products using generalized sum and product operations. This formulation is amenable to linear algebra using arbitrary distributions and allows us to operate on a 2D sparse matrix distribution, which is necessary for parallel scalability. Our solver outperforms the natural parallel extension of the current state of the art in an algorithmic comparison. We demonstrate scalability to 576 processes and graphs with up to 1.7 billion edges.Comment: PASC '18, Code: https://github.com/ligmg/ligm

Contour Processing and 3-D Image Processing of Sea Beam Bathymetric Data

The Sea Beam system was installed aboard the survey vessel Takuyo (Nakanishi, 1985), in September 1983. It is currently used for continental shelf surveys, bathymetric surveys for predicting earthquakes and other survey activities. Besides these activities, we have been engaged in the development of a computerized system for drawing precise bathymetric charts based on digital Sea Beam data logged on magnetic tapes. So far we have completed two programs — one for drawing bathymetric contour charts aboard a survey vessel and the other for drawing bathymetric contour charts on shore. By means of the former program one can gradually draw depth contours covering the swath width of Sea Beam along the track of the survey vessel. The latter program enables one to draw very precise bathymetric charts through batch processing of all Sea Beam data of the area surveyed. Incorporated in the latter program are data processing steps to delete defective data, reduce dispersion of data, make a mesh system and adjust the mesh size according to the depth of water. Furthermore, taking advantage of the precision and high density of Sea Beam data, the author developed a three-dimensional image processing program to represent clearly the topography of the seafloor. We have used these programs with the Sea Beam data obtained in bathymetric surveys, and as a result have confirmed their practicability and validity