Parallel algorithms for interactive manipulation of digital terrain models

Interactive three-dimensional graphics applications, such as terrain data representation and manipulation, require extensive arithmetic processing. Massively parallel machines are attractive for this application since they offer high computational rates, and grid connected architectures provide a natural mapping for grid based terrain models. Presented here are algorithms for data movement on the massive parallel processor (MPP) in support of pan and zoom functions over large data grids. It is an extension of earlier work that demonstrated real-time performance of graphics functions on grids that were equal in size to the physical dimensions of the MPP. When the dimensions of a data grid exceed the processing array size, data is packed in the array memory. Windows of the total data grid are interactively selected for processing. Movement of packed data is needed to distribute items across the array for efficient parallel processing. Execution time for data movement was found to exceed that for arithmetic aspects of graphics functions. Performance figures are given for routines written in MPP Pascal

Seshadri constants and Grassmann bundles over curves

Let $X$ be a smooth complex projective curve, and let $E$ be a vector bundle on $X$ which is not semistable. For a suitably chosen integer $r$, let $\text{Gr}(E)$ be the Grassmann bundle over $X$ that parametrizes the quotients of the fibers of $E$ of dimension $r$. Assuming some numerical conditions on the Harder-Narasimhan filtration of $E$, we study Seshadri constants of ample line bundles on $\text{Gr}(E)$. In many cases, we give the precise value of Seshadri constant. Our results generalize various known results for ${\rm rank}(E)=2$.Comment: Final version; Annales Inst. Fourier (to appear

Passive elasto-magnetic suspensions: nonlinear models and experimental outcomes

The paper presents a passive elasto-magnetic suspension based on rare-earth permanent magnets: the dynamical system is described with theoretical and numerical nonlinear models, whose results are validated through experimental compar- ison. The goal is to minimize the dependence on mass of the natural frequency of a single degree of freedom system. For a system with variable mass, static configuration and dynamical behaviour are compared for classic linear elastic systems, for purely magnetic suspensions and for a combination of the two. In particular the dynamics of the magneto-mechanic inter- action is predicted by use of nonlinear and linearised models and experimentally observed through a suitable single degree of freedom test ri

Second fundamental form of the Prym map in the ramified case

In this paper we study the second fundamental form of the Prym map $P_{g,r}: R_{g,r} \rightarrow {\mathcal A}^{\delta}_{g-1+r}$ in the ramified case $r>0$. We give an expression of it in terms of the second fundamental form of the Torelli map of the covering curves. We use this expression to give an upper bound for the dimension of a germ of a totally geodesic submanifold, and hence of a Shimura subvariety of ${\mathcal A}^{\delta}_{g-1+r}$, contained in the Prym locus.Comment: To appear in Galois Covers, Grothendieck-Teichmueller Theory and Dessins d'Enfants - Interactions between Geometry, Topology, Number Theory and Algebra. Springer Proceedings in Mathematics & Statistics. arXiv admin note: text overlap with arXiv:1711.0342

Identification Techniques Applied to a Passive Elasto-magnetic Suspension

The paper presents an experimental passive elasto-magnetic suspension based on rare-earth permanent magnets, characterized by negligible dependence on mass of its natural frequency. The nonlinear behaviour of this system, equipped with a traditional linear elastic spring coupled to a magnetic spring, is analysed in time domain, for non-zero initial conditions, and in frequency domain, by applying sweep excitations to the test rig base. The dynamics of the system is very complex in dependence of the magnetic contribution, showing both hardening behaviour in the elasto-magnetic setup, and softening motion amplitude dependent behaviour in the purely magnetic case. Hence it is necessary to adopt nonlinear identification techniques, such as non-parametric restoring force mapping method and direct parametric estimation technique, in order to identify the system parameters in the different configurations. Finally, it is discussed the ability of identified versus analytical models in reproducing the nonlinear dependency of frequency on motion amplitude and the presence of jump phenomen

A global–local approach for progressive damage analysis of fiber-reinforced composite laminates

The present work applies the global–local technique to the progressive damage analysis of fiber-reinforced composite laminates. A one-way, loosely-coupled global–local approach is developed as a combination of a low-fidelity linear global analysis and a high-fidelity local nonlinear analysis of specific regions within the structure, where damage is expected to occur. The local model is based on higher-order structural theories derived using the Carrera Unified Formulation (CUF), and specifically, Lagrange polynomials are used to model each ply through its thickness, leading to a layer-wise model. Composite damage is described using the CODAM2 material model, which is based on continuum damage mechanics. Initial assessments compare the relative performance of 3D finite elements (FE), 1D-CUF, and the proposed global–local approach via the freeedge stress analysis of a stiffened composite plate. The proposed technique is then used to predict the tensile strength of an open-hole specimen. The last assessment simulates damage progression within an over-height compact tension specimen using the global–local approach. Verification and validation of results are carried out via refined models and experiments from literature. The results demonstrate the accurate evaluation of 3D stress fields and composite laminates’ mechanical response in the progressive damage regime. A multi-fold improvement in the computational cost is shown when compared to full-scale CUF analyses and indicates this technique’s strong potential towards the computationally-efficient high-fidelity analysis of complex and large-scale composite structures

Progressive damage analysis of composite laminates subjected to low-velocity impact using 2D layer-wise structural models

The present work deals with the progressive damage analysis of composite laminates subjected to low-velocity impact. We develop a numerical model using higher-order structural theories based on the Carrera Unified Formulation (CUF) with Lagrange polynomials and resulting in a 2D refined layer-wise model. To model damage, we use a combination of the continuum damage-based CODAM2 intralaminar damage model to account for fibre and matrix damage within the ply, and cohesive elements to account for delamination between successive composite plies. We carry out numerical assessments for the case of a linear elastic composite plate subjected to impact, to compare the current framework with standard approaches based on 3D finite element (FE) analysis. We, then, consider the elastoplastic analysis of a bimetallic laminated plate to compare the performance of the proposed layer-wise model and 3D-FE approaches, for the case of nonlinear impact analysis. The final assessment considers progressive damage due to low-velocity impact, and the results are compared with available literature data. The numerical predictions show a good correlation with reference experimental and simulation results, thus validating the current framework for impact analysis of composite structures. Comparisons of the proposed layer-wise structural models with those based on 3D finite elements demonstrate the improved computational efficiency of the CUF models in terms of model size and analysis time

A global–local approach to the high-fidelity impact analysis of composite structures based on node-dependent kinematics

The objective of the present work is to investigate progressive damage in fibre-reinforced composites under varying load conditions, and in particular transverse impact loads, using a global–local approach. The numerical models are built using higher-order structural theories based on the Carrera Unified Formulation (CUF). The Node-Dependent Kinematics (NDK) technique, an intrinsic feature of CUF models, is employed which enables the selective refinement of critical regions of interest within the structure and results in a global–local analysis. Progressive damage is governed by the CODAM2 material model, which is based on continuum damage mechanics. A series of numerical assessments are performed on composite laminates under varying load conditions, and predicted results of the global–local analysis are found to be in good agreement with experimental data, thereby validating the proposed approach. A comparison of its performance with reference high-fidelity CUF models of the full structure demonstrates the computational efficiency that can be achieved using the CUF-NDK global–local approach

Global/local capabilities of MUL2 for the nonlinear analysis of composite structures

MUL2 is an in-house finite element (FE) platform whose structural formulation is based on the Carrera Unified Formulation (CUF). This work presents some of the latest capabilities of CUF and MUL2 concerning the structural analysis of complex composite structures. The modelling exploits global/local techniques and the node-dependent-kinematics (NDK) recently proposed within CUF. Assessments consider the evaluation of failure indexes along free edges, the tensile strength of notched specimens, and failure progression. Performances are evaluated in terms of accuracy and computational costs, and perspectives on advanced NDK modelling are drawn