Effect of spatially varying material properties on the post-buckling behaviour of composite panels utilising geodesic stochastic fields

The post-buckling behaviour of panels can be very sensitive to imperfections or variations in materials or geometry. This paper presents an ecient numerical model to calculate the eects of material stiffness variations on the non-linear response of a structure. This is done by first defining a geodesic mesh on which a unit variance random field is generated. This field uses the true geodesic distance on the structure to calculate how points in the field should be correlated. The fields generated are projected onto a 3D structural mesh which is used for assembly and post-processing of the structural model. The structural model, based on the Unified Formulation is capable of accurate non-linear calculations of both straight and curved elements. Baseline results generated using the implementation are compared to those in literature, and verified using Abaqus. Random material variations are then applied to the structure in a Monte Carlo analysis. The analyses show that the local variation of stiffness can have a variety of effects on the non-linear response of structures. Aside from the change of mean stiffness causing a change in bifurcation or limit point load, the different stiffness distributions can affect and trigger competing buckling modes and post-buckling modes and affect their corresponding post-buckling load-deflection paths

A minimalistic approach for fast computation of geodesic distances on triangular meshes

The computation of geodesic distances is an important research topic in Geometry Processing and 3D Shape Analysis as it is a basic component of many methods used in these areas. In this work, we present a minimalistic parallel algorithm based on front propagation to compute approximate geodesic distances on meshes. Our method is practical and simple to implement and does not require any heavy pre-processing. The convergence of our algorithm depends on the number of discrete level sets around the source points from which distance information propagates. To appropriately implement our method on GPUs taking into account memory coalescence problems, we take advantage of a graph representation based on a breadth-first search traversal that works harmoniously with our parallel front propagation approach. We report experiments that show how our method scales with the size of the problem. We compare the mean error and processing time obtained by our method with such measures computed using other methods. Our method produces results in competitive times with almost the same accuracy, especially for large meshes. We also demonstrate its use for solving two classical geometry processing problems: the regular sampling problem and the Voronoi tessellation on meshes.Comment: Preprint submitted to Computers & Graphic

ZerNet: Convolutional Neural Networks on Arbitrary Surfaces via Zernike Local Tangent Space Estimation

In this paper, we propose a novel formulation to extend CNNs to two-dimensional (2D) manifolds using orthogonal basis functions, called Zernike polynomials. In many areas, geometric features play a key role in understanding scientific phenomena. Thus, an ability to codify geometric features into a mathematical quantity can be critical. Recently, convolutional neural networks (CNNs) have demonstrated the promising capability of extracting and codifying features from visual information. However, the progress has been concentrated in computer vision applications where there exists an inherent grid-like structure. In contrast, many geometry processing problems are defined on curved surfaces, and the generalization of CNNs is not quite trivial. The difficulties are rooted in the lack of key ingredients such as the canonical grid-like representation, the notion of consistent orientation, and a compatible local topology across the domain. In this paper, we prove that the convolution of two functions can be represented as a simple dot product between Zernike polynomial coefficients; and the rotation of a convolution kernel is essentially a set of 2-by-2 rotation matrices applied to the coefficients. As such, the key contribution of this work resides in a concise but rigorous mathematical generalization of the CNN building blocks