Multiscale structural, thermal and thermo-structural optimization towards three-dimensional printable structures

This thesis develops a robust framework for the multiscale design of three-dimensional lattices with macroscopically tailored structural and thermal characteristics. The work exploits the high process flexibility and precision of additive manufacturing to the physical realization of complex microstructure of metamaterials by developing and implementing a multiscale approach. Structures derived from such metamaterials exhibit properties which differ from that of the constituent base material. Inspired by the concept of Free Material Optimization (FMO), a periodic microscale model is developed whose geometric parameterization enables smoothly changing properties and for which the connectivity of neighbouring microstructures in the large-scale domain is guaranteed by slowly changing large-scale descriptions of the lattice parameters. The microscale model is evaluated at full factorial design points to discretely populate material property spaces. A property point is fully defined for a micro-architecture when its elasticity matrix, thermal conductivity matrix and volume fraction is determined. The process of property-space population is facilitated by leveraging the existence of micro-architecture symmetries so that there exists a 95% reduction in the simulations required despite a full-factorial design of experiments. The discrete property evaluations are converted to continuous functions by response surface modelling so that the properties exist as continuous functions of the micro-architecture geometry parameters. A lattice-based functional grading of material is derived using the finite element method. The optimization is driven by a chain-rule combination of sensitivities derived by the adjoint method and sensitivities derived from explicit material property expressions. The novelty of the work lies in the use of multiple geometry-based small-scale design parameters for optimization problems in three-dimensional real space. The approach is demonstrated by solving structural, thermal and thermo-structural optimization problems. The results show designs with improved optimality compared to commonly implemented optimization methodologies. The optimal designs obtained are physically realizable by additive manufacturing techniques.Open Acces

Efficient computational strategies for the control process of continuous casting machines

In continuous casting machineries, monitoring the mold is essential for the safety and quality of the process. Then, the objective of this thesis is to develop mathematical tools for the real-time estimation of the mold-steel heat flux which is the quantity of interest when controlling the mold behaviour. We approach this problem by first considering the mold modelling problem (direct problem). Then, we plant the heat flux estimation problem as the inverse problem of estimating a Neumann boundary condition having as data pointwise temperature measurements in the interior of the mold domain given by the thermocouples that are buried inside the mold plates. In formulating the inverse problem, we consider both the steady and unsteady-state case. For the numerical solution of these problems, we develop several methodologies. We consider traditional methods such as Alifanov's regularization as well as novel methodologies that exploit the parametrization of the sought heat flux. We develop the latter methods to have an offline-online decomposition with a computationally efficient online part. Moreover, in the unsteady-state case, we propose a novel, incremental, data-driven model order reduction technique to achieve the real-time performance of the online phase. Finally, we test all discussed methods on academic and industrial benchmark cases. The results show that the proposed novel numerical tools outclass traditional methods both in performance and computational cost. Moreover, they prove to be robust with respect to the measurements noise and confirm that the computational cost is suitable for real-time estimation of the heat flux

Novel methodologies for solving the inverse unsteady heat transfer problem of estimating the boundary heat flux in continuous casting molds

In this article, we investigate the estimation of the transient mold-slab heat flux in continuous casting molds given some thermocouples measurements in the mold plates. Mathematically, we can see this problem as the estimation of a Neumann boundary condition given pointwise state observations in the interior of the domain. We formulate it in a deterministic inverse problem setting. After introducing the industrial problem, we present the mold thermal model and related assumptions. Then, we formulate the boundary heat flux estimation problem in a deterministic inverse problem setting using a sequential approach according to the sequentiality of the temperature measurements. We consider different formulations of the inverse problem. For each one, we develop novel direct methodologies exploiting a space parameterization of the heat flux and the linearity of the mold model. We construct these methods to be divided into a computationally expensive offline phase that can be computed before the process starts, and a cheaper online phase to be performed during the casting process. To conclude, we test the performance of the proposed methods in two benchmark casesAgencia Estatal de Investigación, Grant/Award Number: PID2019-105615RBI00/AEI; European Research Council, Grant/Award Number:765374; H2020 Marie Skłodowska-Curie Actions, Grant/Award Number: 681447; Ministerio de Economía, Industria y Competitividad, Gobierno de España, Grant/Award Number: MTM2015-68275-RS

Applications of Isogeometric Analysis Coupled with Finite Volume Method

In this thesis, a combination of Isogeometric Analysis (IGA) and Finite Volume Method (FVM) on geometries parameterized by Non-Uniform Rational Basis Splines (NURBS) is explored with applications in fluid flow, heat transfer, and shape optimization. An IGA framework supplemented with FVM is created in MATLAB® to solve problems defined over single patch domains with mesh refinement by node insertion. Additionally, a second-order finite difference method is developed using non-orthogonal curvilinear coordinates and a numerical Jacobian of the NURBS geometry. The examples include fully developed laminar flow through ducts, potential flow around a tilted ellipse, transient heat conduction, linear advection-diffusion, and a basic shape optimization example using a particle swarm technique. The numerical results are compared among the methods and verified with available analytical solutions

A Method for Geometry Optimization in a Simple Model of Two-Dimensional Heat Transfer

This investigation is motivated by the problem of optimal design of cooling elements in modern battery systems. We consider a simple model of two-dimensional steady-state heat conduction described by elliptic partial differential equations and involving a one-dimensional cooling element represented by a contour on which interface boundary conditions are specified. The problem consists in finding an optimal shape of the cooling element which will ensure that the solution in a given region is close (in the least squares sense) to some prescribed target distribution. We formulate this problem as PDE-constrained optimization and the locally optimal contour shapes are found using a gradient-based descent algorithm in which the Sobolev shape gradients are obtained using methods of the shape-differential calculus. The main novelty of this work is an accurate and efficient approach to the evaluation of the shape gradients based on a boundary-integral formulation which exploits certain analytical properties of the solution and does not require grids adapted to the contour. This approach is thoroughly validated and optimization results obtained in different test problems exhibit nontrivial shapes of the computed optimal contours.Comment: Accepted for publication in "SIAM Journal on Scientific Computing" (31 pages, 9 figures

Thermal Diffusivity Identification of Distributed Parameter Systems to Sea Ice

A method of optimal control is presented as a numerical tool for solving the sea ice heat transfer problem governed by a parabolic partial differential equation. Taken the deviation between the calculated ice temperature and the measurements as the performance criterion, an optimal control model of distributed parameter systems with specific constraints of thermal properties of sea ice was proposed to determine the thermal diffusivity of sea ice. Based on sea ice physical processes, the parameterization of the thermal diffusivity was derived through field data. The simulation results illustrated that the identified parameterization of the thermal diffusivity is reasonably effective in sea ice thermodynamics. The direct relation between the thermal diffusivity of sea ice and ice porosity is physically significant and can considerably reduce the computational errors. The successful application of this method also explained that the optimal control model of distributed parameter systems in conjunction with the engineering background has great potential in dealing with practical problems

Domain-decomposed Bayesian inversion based on local Karhunen-Lo\`{e}ve expansions

In many Bayesian inverse problems the goal is to recover a spatially varying random field. Such problems are often computationally challenging especially when the forward model is governed by complex partial differential equations (PDEs). The challenge is particularly severe when the spatial domain is large and the unknown random field needs to be represented by a high-dimensional parameter. In this paper, we present a domain-decomposed method to attack the dimensionality issue and the method decomposes the spatial domain and the parameter domain simultaneously. On each subdomain, a local Karhunen-Lo`eve (KL) expansion is constructed, and a local inversion problem is solved independently in a parallel manner, and more importantly, in a lower-dimensional space. After local posterior samples are generated through conducting Markov chain Monte Carlo (MCMC) simulations on subdomains, a novel projection procedure is developed to effectively reconstruct the global field. In addition, the domain decomposition interface conditions are dealt with an adaptive Gaussian process-based fitting strategy. Numerical examples are provided to demonstrate the performance of the proposed method

A review on feature-mapping methods for structural optimization

Acknowledgments We thank Dr. Lukas Pflug from the Department of Mathematics at the Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Germany, for fruitful discussion and support. The initiative for this review goes back to critical yet constructive comments by Prof. Kurt Maute, from the University of Colorado Boulder, USA. We also thank Prof. Horea Ilies from the University of Connecticut, USA, for guidance and insight into some of the geometric aspects of this work. The first author acknowledges support by Deutsche Forschungsgemeinschaft (DFG) in the framework of the collaborative research center CRC 814 (subproject C2). The third author thanks the support of the US National Science Foundation, award CMMI-1634563.Peer reviewedPreprintPostprin

Design of Thermal Structures using Topology Optimization

The design of structures subjected to elevated temperature environments has long been an important area of study in the aerospace industry. This is especially true in the modern day, where new problems related to embedded engine aircraft and high temperature exhaust-washed structures present new structural design challenges not found in past applications. In this work, the response of a class of thermal structures whose responses are characterized by significant amounts of restrained expansion, to which exhaust-washed structures belong, are studied. To address the complex design challenges that become evident in these investigations, structural topology optimization is applied due to its unique ability to identify optimal material layout. Since conventional methods for topology optimization fail to generate effective designs in the presence of thermoelastic effects, new formulations for thermoelastic topology optimization are demonstrated. These include techniques for addressing the amount of reaction loading generated by a structural concept and methods for incorporating stress-based design criteria in topology optimization problems with design-dependent thermal loading. When taken together, the developments in this work provide a design technique in which stresses can be directly treated in thermal structures by identifying the proper arrangement of structural components in a thermal environment