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It is possible to create laminates, composed of plies with spatially varying fiber orientation, which have stiffness properties that vary as a function of position. Previous work had modeled such variable stiffness laminae by taking a reference fiber path and creating subsequent paths by shifting the reference path. We introduce a method where subsequent paths are truly parallel to the reference fiber path. The primary manufacturing constraint considered in the analysis of variable-stiffness laminates was limits on fiber curvature, which proved to be more restrictive for parallel-fiber laminae than for shifted-fiber laminae. The in-plane responses of shifted-and parallel-fiber variable-stiffness laminates to applied uniform end shortening were determined. Both shifted and parallel-fiber variable-stiffness laminates can redistribute the applied load, thereby increasing critical buckling loads compared to traditional straight-fiber laminates. The primary difference between the two methods is that parallel-fiber laminates are not able to redistribute the loading to the degree of the shifted fiber; this significantly reduces the increase in critical buckling load for parallel-fiber variable-stiffness laminates over straight-fiber laminates. (Author) Abstract Using advanced manufacturing techniques it is possible to create laminates, composed of plies' with spatially varying fiber orientation, which have stiffness properties that vary as a function of position. Previous work had modeled such variable stiffness laminae by taking a reference fiber path and creating subsequent paths by shifting the reference path. This paper introduces a method where subsequent paths are truly parallel to the reference fiber path. The primary manufacturing constraint considered in the analysis of variable stiffness laminates was limits on fiber curvature which proved to be more restrictive for parallel fiber laminae than for shifted fiber. The in-plane responses of shifted and parallel fiber variable stiffness laminates to applied uniform end shortening were determined. Both shifted and parallel fiber variable stiffness laminates can redistribute the applied load thereby increasing critical buckling loads compared to traditional straight fiber laminates. The primary differences between the two methods is that parallel fiber laminates are not able to redistribute the loading to the degree of the shifted fiber. This significantly reduces the increase in critical buckling load for parallel fiber variable stiffness laminates over straight fiber laminates.

Pattern-based Representation (PBR) is a novel approach to improving the performance of Sparse Matrix-Vector Multiply (SMVM) numerical kernels. Motivated by our observation that many matrices can be divided into blocks that share a small number of distinct patterns, we generate custom multiplication kernels for frequently recurring block patterns. The resulting reduction in index overhead significantly reduces memory bandwidth requirements and improves performance. Unlike existing methods, PBR requires neither detection of dense blocks nor zero filling, making it particularly advantageous for matrices that lack dense nonzero concentrations. SMVM kernels for PBR can benefit from explicit prefetching and vectorization, and are amenable to parallelization. We present sequential and parallel performance results for PBR on two current multicore architectures, which show that PBR outperforms available alternatives for the matrices to which it is applicable.

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