This review paper provides an overview of different level-set methods for structural topology optimization. Level-set methods can be categorized with respect to the level-set-function ...parameterization, the geometry mapping, the physical/mechanical model, the information and the procedure to update the design and the applied regularization. Different approaches for each of these interlinked components are outlined and compared. Based on this categorization, the convergence behavior of the optimization process is discussed, as well as control over the slope and smoothness of the level-set function, hole nucleation and the relation of level-set methods to other topology optimization methods. The importance of numerical consistency for understanding and studying the behavior of proposed methods is highlighted. This review concludes with recommendations for future research.
High resolution upwind and centred methods are today a mature generation of computational techniques applicable to a wide range of engineering and scientific disciplines, Computational Fluid Dynamics ...(CFD) being the most prominent up to now. This textbook gives a comprehensive, coherent and practical presentation of this class of techniques. The book is designed to provide readers with an understanding of the basic concepts, some of the underlying theory, the ability to critically use the current research papers on the subject, and, above all, with the required information for the practical implementation of the methods. Direct applicability of the methods include: compressible, steady, unsteady, reactive, viscous, non-viscous and free surface flows. For this third edition the book was thoroughly revised and contains substantially more, and new material both in its fundamental as well as in its applied parts.
Design variables in density-based topology optimization are typically regularized using filtering techniques. In many cases, such as stress optimization, where details at the boundaries are crucially ...important, the filtering in the vicinity of the design domain boundary needs special attention. One well-known technique, often referred to as “padding,” is to extend the design domain with extra layers of elements to mitigate artificial boundary effects. We discuss an alternative to the padding procedure in the context of PDE filtering. To motivate this augmented PDE filter, we make use of the potential form of the PDE filter which allows us to add penalty terms with a clear physical interpretation. The major advantages of the proposed augmentation compared with the conventional padding is the simplicity of the implementation and the possibility to tune the boundary properties using a scalar parameter. Analytical results in 1D and numerical results in 2D and 3D confirm the suitability of this approach for large-scale topology optimization.
Selective laser melting (SLM) is an additive manufacturing process in which multiple, successive layers of metal powders are heated via laser in order to build a part. Modeling of SLM requires ...consideration of both heat transfer and solid mechanics. The present work describes continuum modeling of SLM as envisioned for eventual support of part-scale modeling of this fabrication process to determine end-state information such as residual stresses and distortion. The determination of the evolving temperatures is dependent on the material, the state of the material (powder or solid), the specified heating, and the configuration. Similarly, the current configuration is dependent on the temperatures, the powder-solid state, and the constitutive models. A multi-physics numerical formulation is required to solve such problems. This article describes the problem formulation, numerical method, and constitutive parameters necessary to solve such a problem. Additionally, various verification and example problems are simulated in the parallel, multi-physics finite element code Diablo, and the results presented herein.
Despite the significant progress over the last 50 years in simulating flow problems using numerical discretization of the Navier–Stokes equations (NSE), we still cannot incorporate seamlessly noisy ...data into existing algorithms, mesh-generation is complex, and we cannot tackle high-dimensional problems governed by parametrized NSE. Moreover, solving
inverse flow problems
is often prohibitively expensive and requires complex and expensive formulations and new computer codes. Here, we review
flow physics-informed learning
, integrating seamlessly data and mathematical models, and implement them using physics-informed neural networks (PINNs). We demonstrate the effectiveness of PINNs for inverse problems related to three-dimensional wake flows, supersonic flows, and biomedical flows.
Graphical abstract
Multi-scale structures, as found in nature (e.g., bone and bamboo), hold the promise of achieving superior performance while being intrinsically lightweight, robust, and multi-functional. Recent ...years have seen a rapid development in topology optimization approaches for designing multi-scale structures, but the field actually dates back to the seminal paper by Bendsøe and Kikuchi from 1988 (Computer Methods in Applied Mechanics and Engineering 71(2): pp. 197–224). In this review, we intend to categorize existing approaches, explain the principles of each category, analyze their strengths and applicabilities, and discuss open research questions. The review and associated analyses will hopefully form a basis for future research and development in this exciting field.
This book examines the main theorems in bifurcation theory. It covers both the local and global theory of one-parameter bifurcations for operators acting in infinite-dimensional Banach spaces and ...shows how to apply the theory.
This paper presents a novel bio-inspired algorithm inspired by starlings’ behaviors during their stunning murmuration named starling murmuration optimizer (SMO) to solve complex and engineering ...optimization problems as the most appropriate application of metaheuristic algorithms. The SMO introduces a dynamic multi-flock construction and three new search strategies, separating, diving, and whirling. The separating search strategy aims to enhance the population diversity and local optima avoidance using a new separating operator based on the quantum harmonic oscillator. The diving search strategy aims to explore the search space sufficiently by a new quantum random dive operator, whereas the whirling search strategy exploits the vicinity of promising regions using a new operator called cohesion force. The SMO strikes a balance between exploration and exploitation by selecting either a diving strategy or a whirling strategy based on the flocks’ quality. The SMO was tested using various benchmark functions with dimensions 30, 50, 100. The experimental results prove that the SMO is more competitive than other state-of-the-art algorithms regarding solution quality and convergence rate. Then, the SMO is applied to solve several mechanical engineering problems in which results demonstrate that it can provide more accurate solutions. A statistical analysis shows that SMO is superior to the other contenders.
•Proposing a novel, bio-inspired algorithm named starling murmuration optimizer (SMO).•Introducing a diving strategy and a quantum random dives operator for exploration.•Introducing a whirling strategy and a cohesion operator for exploitation.•Introducing a strategy using quantum harmonic oscillator to enhance diversity.•SMO is superior to other tested algorithms on benchmarks and engineering problems.
Phase-field modeling of
brittle
fracture in elastic solids is a well-established framework that overcomes the limitations of the classical Griffith theory in the prediction of crack nucleation and in ...the identification of complicated crack paths including branching and merging. We propose a novel phase-field model for
ductile
fracture of elasto-plastic solids in the quasi-static kinematically linear regime. The formulation is shown to capture the entire range of behavior of a ductile material exhibiting
J
2
-plasticity, encompassing plasticization, crack initiation, propagation and failure. Several examples demonstrate the ability of the model to reproduce some important phenomenological features of ductile fracture as reported in the experimental literature.
Rubber-like materials consist of chain-like macromolecules that are more or less closely connected to each other via entanglements or cross-links. As an idealisation, this particular structure can be ...described as a completely random three-dimensional network. To capture the elastic and nearly incompressible mechanical behaviour of this material class, numerous phenomenological and micro-mechanically motivated models have been proposed in the literature. This contribution reviews fourteen selected representatives of these models, derives analytical stress–stretch relations for certain homogeneous deformation modes and summarises the details required for stress tensors and consistent tangent operators. The latter, although prevalently missing in the literature, are indispensable ingredients in utilising any kind of constitutive model for the numerical solution of boundary value problems by iterative approaches like the Newton–Raphson scheme. Furthermore, performance and validity of the models with regard to the classical experimental data on vulcanised rubber published by Treloar (Trans Faraday Soc 40:59–70,
1944
) are evaluated. These data are here considered as a prototype or worst-case scenario of highly nonlinear elastic behaviour, although inelastic characteristics are clearly observable but have been tacitly ignored by many other authors.
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