54 research outputs found

    Topology Optimization of Single- and Multi-material Structures: From Single-physics to Multi-physics Designs

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    Topology optimization is a computational design method used to find the optimized geometry of materials or structures meeting some performance criteria while satisfying constraints applied either globally (as usual) or locally (a focus of this work). Topology optimization can be used, for instance, to find lightweight structures that safely carry loads without failing. All you need is a design objective (e.g., minimize the weight) and constraints (e.g., material strength) and, through a nonlinear programming technique, the computer explores the solution space to find the optimized design. Despite the design freedoms afforded by topology optimization, its widespread adoption has primarily been hindered by the inability of current formulations to efficiently handle problems involving, for instance, multi-physics, multiple materials, and local material failure constraints. Thus, this thesis contributes to theoretical formulations, computer algorithms, and numerical implementations for topology optimization with an emphasis on problems subjected to either global constraints (e.g., energy-type constraints) or local constraints (e.g., material failure constraints), and for applications involving single or multiple physical phenomena and single- or multi-material designs. This work can be divided into two parts. In the first part, we present a general multi-material formulation that can handle an arbitrary number of materials and volume constraints (i.e., global-type constraints), and any type of objective function. To handle problems with such generality, we adopt a special linearization of the original optimization problem using a non-monotonous convex approximation of the objective function written in terms of positive and negative components of its gradient. The outcome is a scheme that updates the design variables associated with one constraint independently of the others, leading to an efficient, parallelizable formulation. The new update scheme allows us to design multi-phase viscoelastic microstructures, thermoelastic structures, and structures subjected to general dynamic loading. In the second part of this thesis, we introduce an augmented Lagrangian formulation to solve problems with local stress constraints correctly—a dilemma that has been unresolved thus far. First, we create a formulation to solve stress-constrained problems both for linear and nonlinear structures and provide an educational open-source code aiming to bridge the gap between research and education. Next, to extend the range of applications to structures that can be made of materials other than ductile metals, we introduce a function that unifies several classical strength criteria to predict the failure of a wide spectrum of materials, including either ductile metals or pressure-dependent materials, and use it to solve topology optimization problems with local stress constraints. We then extend the framework to time-dependent problems and address stress-constrained problems for structures subjected to general dynamic loading, in which the stress constraints are satisfied both in space (i.e., locally at every point of the discretized domain) and time (i.e., throughout the duration of the dynamic event). Unlike most work in the literature, this augmented Lagrangian framework leads to a scalable formulation that solves the optimization problem consistently with the local definition of stress and handles thousands or even millions of constraints efficiently. In summary, all components of this work are aimed to address critical challenges that have prevented topology optimization from being embraced as a practical design tool for industry-relevant applications.Ph.D

    Fractional Calculus and the Future of Science

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    Newton foresaw the limitations of geometry’s description of planetary behavior and developed fluxions (differentials) as the new language for celestial mechanics and as the way to implement his laws of mechanics. Two hundred years later Mandelbrot introduced the notion of fractals into the scientific lexicon of geometry, dynamics, and statistics and in so doing suggested ways to see beyond the limitations of Newton’s laws. Mandelbrot’s mathematical essays suggest how fractals may lead to the understanding of turbulence, viscoelasticity, and ultimately to end of dominance of the Newton’s macroscopic world view.Fractional Calculus and the Future of Science examines the nexus of these two game-changing contributions to our scientific understanding of the world. It addresses how non-integer differential equations replace Newton’s laws to describe the many guises of complexity, most of which lay beyond Newton’s experience, and many had even eluded Mandelbrot’s powerful intuition. The book’s authors look behind the mathematics and examine what must be true about a phenomenon’s behavior to justify the replacement of an integer-order with a noninteger-order (fractional) derivative. This window into the future of specific science disciplines using the fractional calculus lens suggests how what is seen entails a difference in scientific thinking and understanding

    Multiscale aeroelastic modelling in porous composite structures

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    Driven by economic, environmental and ergonomic concerns, porous composites are increasingly being adopted by the aeronautical and structural engineering communities for their improved physical and mechanical properties. Such materials often possess highly heterogeneous material descriptions and tessellated/complex geometries. Deploying commercially viable porous composite structures necessitates numerical methods that are capable of accurately and efficiently handling these complexities within the prescribed design iterations. Classical numerical methods, such as the Finite Element Method (FEM), while extremely versatile, incur large computational costs when accounting for heterogeneous inclusions and high frequency waves. This often renders the problem prohibitively expensive, even with the advent of modern high performance computing facilities. Multiscale Finite Element Methods (MsFEM) is an order reduction strategy specifically developed to address such issues. This is done by introducing meshes at different scales. All underlying physics and material descriptions are explicitly resolved at the fine scale. This information is then mapped onto the coarse scale through a set of numerically evaluated multiscale basis functions. The problems are then solved at the coarse scale at a significantly reduced cost and mapped back to the fine scale using the same multiscale shape functions. To this point, the MsFEM has been developed exclusively with quadrilateral/hexahedral coarse and fine elements. This proves highly inefficient when encountering complex coarse scale geometries and fine scale inclusions. A more flexible meshing scheme at all scales is essential for ensuring optimal simulation runtimes. The Virtual Element Method (VEM) is a relatively recent development within the computational mechanics community aimed at handling arbitrary polygonal (potentially non-convex) elements. In this thesis, novel VEM formulations for poromechanical problems (consolidation and vibroacoustics) are developed. This is then integrated at the fine scale into the multiscale procedure to enable versatile meshing possibilities. Further, this enhanced capability is also extended to the coarse scale to allow for efficient macroscale discretizations of complex structures. The resulting Multiscale Virtual Element Method (MsVEM) is originally applied to problems in elastostatics, consolidation and vibroacoustics in porous media to successfully drive down computational run times without significantly affecting accuracy. Following this, a parametric Model Order Reduction scheme for coupled problems is introduced for the first time at the fine scale to obtain a Reduced Basis Multiscale Virtual Element Method. This is used to augment the rate of multiscale basis function evaluation in spectral acoustics problems. The accuracy of all the above novel contributions are investigated in relation to standard numerical methods, i.e., the FEM and MsFEM, analytical solutions and experimental data. The associated efficiency is quantified in terms of computational run-times, complexity analyses and speed-up metrics. Several extended applications of the VEM and the MsVEM are briefly visited, e.g., VEM phase field Methods for brittle fracture, structural and acoustical topology optimization, random vibrations and stochastic dynamics, and structural vibroacoustics

    Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018

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    This open access book features a selection of high-quality papers from the presentations at the International Conference on Spectral and High-Order Methods 2018, offering an overview of the depth and breadth of the activities within this important research area. The carefully reviewed papers provide a snapshot of the state of the art, while the extensive bibliography helps initiate new research directions

    Virtual Element based formulations for computational materials micro-mechanics and homogenization

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    In this thesis, a computational framework for microstructural modelling of transverse behaviour of heterogeneous materials is presented. The context of this research is part of the broad and active field of Computational Micromechanics, which has emerged as an effective tool both to understand the influence of complex microstructure on the macro-mechanical response of engineering materials and to tailor-design innovative materials for specific applications through a proper modification of their microstructure. While the classical continuum approximation does not account for microstructural details within the material, computational micromechanics allows detailed modelling of a heterogeneous material's internal structural arrangement by treating each constituent as a continuum. Such an approach requires modelling a certain material microstructure by considering most of the microstructure's morphological features. The most common numerical technique used in computational micromechanics analysis is the Finite Element Method (FEM). Its use has been driven by the development of mesh generation programs, which lead to the quasi-automatic discretisation of the artificial microstructure domain and the possibility of implementing appropriate constitutive equations for the different phases and their interfaces. In FEM's applications to computational micromechanics, the phase arrangements are discretised using continuum elements. The mesh is created so that element boundaries and, wherever required, special interface elements are located at all interfaces between material's constituents. This approach can be effective in modelling many microstructures, and it is readily available in commercial codes. However, the need to accurately resolve the kinematic and stress fields related to complex material behaviours may lead to very large models that may need prohibitive processing time despite the increasing modern computers' performance. When rather complex microstructure's morphologies are considered, the quasi-automatic discretisation process stated before might fail to generate high-quality meshes. Time-consuming mesh regularisation techniques, both automatic and operator-driven, may be needed to obtain accurate numeric results. Indeed, the preparation of high-quality meshes is today one of the steps requiring more attention, and time, from the analyst. In this respect, the development of computational techniques to deal with complex and evolving geometries and meshes with accuracy, effectiveness, and robustness attracts relevant interest. The computational framework presented in this thesis is based on the Virtual Element Method (VEM), a recently developed numerical technique that has proven to provide robust numerical results even with highly-distorted mesh. These peculiar features have been exploited to analyse two-dimensional representations of heterogeneous materials' microstructures. Ad-hoc polygonal multi-domain meshing strategies have been developed and tested to exploit the discretisation freedom that VEM allows. To further simplify the preprocessing stage of the analysis and reduce the total computational cost, a novel hybrid formulation for analysing multi-domain problems has been developed by combining the Virtual Element Method with the well-known Boundary Element Method (BEM). The hybrid approach has been used to study both composite material's transverse behaviour in the presence of inclusions with complex geometries and damage and crack propagation in the matrix phase. Numerical results are presented that demonstrate the potential of the developed framework

    Seismic Waves

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    The importance of seismic wave research lies not only in our ability to understand and predict earthquakes and tsunamis, it also reveals information on the Earth's composition and features in much the same way as it led to the discovery of Mohorovicic's discontinuity. As our theoretical understanding of the physics behind seismic waves has grown, physical and numerical modeling have greatly advanced and now augment applied seismology for better prediction and engineering practices. This has led to some novel applications such as using artificially-induced shocks for exploration of the Earth's subsurface and seismic stimulation for increasing the productivity of oil wells. This book demonstrates the latest techniques and advances in seismic wave analysis from theoretical approach, data acquisition and interpretation, to analyses and numerical simulations, as well as research applications. A review process was conducted in cooperation with sincere support by Drs. Hiroshi Takenaka, Yoshio Murai, Jun Matsushima, and Genti Toyokuni

    Sensor Signal and Information Processing II

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    In the current age of information explosion, newly invented technological sensors and software are now tightly integrated with our everyday lives. Many sensor processing algorithms have incorporated some forms of computational intelligence as part of their core framework in problem solving. These algorithms have the capacity to generalize and discover knowledge for themselves and learn new information whenever unseen data are captured. The primary aim of sensor processing is to develop techniques to interpret, understand, and act on information contained in the data. The interest of this book is in developing intelligent signal processing in order to pave the way for smart sensors. This involves mathematical advancement of nonlinear signal processing theory and its applications that extend far beyond traditional techniques. It bridges the boundary between theory and application, developing novel theoretically inspired methodologies targeting both longstanding and emergent signal processing applications. The topic ranges from phishing detection to integration of terrestrial laser scanning, and from fault diagnosis to bio-inspiring filtering. The book will appeal to established practitioners, along with researchers and students in the emerging field of smart sensors processing
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