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Multiscale Structural Topology Optimization

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Multiscale Structural Topology Optimization

Multiscale Structural Topology Optimization Book
Author : Liang Xia
Publisher : Elsevier
Release : 2016-04-27
ISBN : 0081011865
Language : En, Es, Fr & De

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Book Description :

Multiscale Structural Topology Optimization discusses the development of a multiscale design framework for topology optimization of multiscale nonlinear structures. With the intention to alleviate the heavy computational burden of the design framework, the authors present a POD-based adaptive surrogate model for the RVE solutions at the microscopic scale and make a step further towards the design of multiscale elastoviscoplastic structures. Various optimization methods for structural size, shape, and topology designs have been developed and widely employed in engineering applications. Topology optimization has been recognized as one of the most effective tools for least weight and performance design, especially in aeronautics and aerospace engineering. This book focuses on the simultaneous design of both macroscopic structure and microscopic materials. In this model, the material microstructures are optimized in response to the macroscopic solution, which results in the nonlinearity of the equilibrium problem of the interface of the two scales. The authors include a reduce database model from a set of numerical experiments in the space of effective strain. Presents the first attempts towards topology optimization design of nonlinear highly heterogeneous structures Helps with simultaneous design of the topologies of both macroscopic structure and microscopic materials Helps with development of computer codes for the designs of nonlinear structures and of materials with extreme constitutive properties Focuses on the simultaneous design of both macroscopic structure and microscopic materials Includes a reduce database model from a set of numerical experiments in the space of effective strain

Multiscale Topology Optimization of Solid and Fluid Structures

Multiscale Topology Optimization of Solid and Fluid Structures Book
Author : Casper Schousboe Andreasen,Danmarks Tekniske Universitet. DTU Mekanik,Danish Center for Applied Mathematics and Mechanics
Publisher : Unknown
Release : 2021-09-26
ISBN : 9788790416591
Language : En, Es, Fr & De

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Book Description :

Download Multiscale Topology Optimization of Solid and Fluid Structures book written by Casper Schousboe Andreasen,Danmarks Tekniske Universitet. DTU Mekanik,Danish Center for Applied Mathematics and Mechanics, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Nonlinear Structural Design Using Multiscale Topology Optimization

Nonlinear Structural Design Using Multiscale Topology Optimization Book
Author : Anonim
Publisher : Unknown
Release : 2013
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Nonlinear Structural Design Using Multiscale Topology Optimization book written by , available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Topology Optimization Design of Heterogeneous Materials and Structures

Topology Optimization Design of Heterogeneous Materials and Structures Book
Author : Daicong Da
Publisher : John Wiley & Sons
Release : 2020-01-09
ISBN : 1786305585
Language : En, Es, Fr & De

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Book Description :

This book pursues optimal design from the perspective of mechanical properties and resistance to failure caused by cracks and fatigue. The book abandons the scale separation hypothesis and takes up phase-field modeling, which is at the cutting edge of research and is of high industrial and practical relevance. Part 1 starts by testing the limits of the homogenization-based approach when the size of the representative volume element is non-negligible compared to the structure. The book then introduces a non-local homogenization scheme to take into account the strain gradient effects. Using a phase field method, Part 2 offers three significant contributions concerning optimal placement of the inclusion phases. Respectively, these contributions take into account fractures in quasi-brittle materials, interface cracks and periodic composites. The topology optimization proposed has significantly increased the fracture resistance of the composites studied.

DCAMM special report

DCAMM special report Book
Author : Casper Schousboe Andreasen,Danmarks Tekniske Universitet. DTU Mekanik,Danish Center for Applied Mathematics and Mechanics
Publisher : Unknown
Release : 2011
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download DCAMM special report book written by Casper Schousboe Andreasen,Danmarks Tekniske Universitet. DTU Mekanik,Danish Center for Applied Mathematics and Mechanics, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Multiscale Optimization And Materials Design

Multiscale Optimization And Materials Design Book
Author : Jun Yan,Gengdong Cheng
Publisher : World Scientific
Release : 2020-12-29
ISBN : 981121655X
Language : En, Es, Fr & De

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Book Description :

The book presents a set of novel, efficient and systematic concurrent multiscale optimization methods by considering the distribution of the material in macro-scale and the unit-cell configuration design in micro-scale simultaneously. Different from the traditional optimization method that is performed in a single scale, the proposed methods could generate a great deal of improvements in structural performance through the multiscale structure-material concurrent optimum design.The proposed theory and methods are related to statics, dynamics, thermoelastics and the coupling of different physical fields. Therefore, it provides a comprehensive designing scheme when multiple factors are taken into account. For example, the designing scheme can have a great significance on enhancing the structural performances under coupled multi-physical fields, such as load bearing capacity, vibration resistance ability, and safety under thermal stress and so on.Several numerical examples are highlighted in this unique volume based on practical engineering applications. The examples collectively demonstrate drastically improved designs featuring excellent unit-cell configuration and highly regular macroscale material distribution in a variety of industrial applications.

Structural Multiscale Topology Optimization with Stress Constraint for Additive Manufacturing

Structural Multiscale Topology Optimization with Stress Constraint for Additive Manufacturing Book
Author : Ferdinando Auricchio,Elena Bonetti,Massimo Carraturo,Dietmar Hömberg,Alessandro Reali,Elisabetta Rocca
Publisher : Unknown
Release : 2019
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

In this paper a phase-field approach for structural topology optimization for a 3D-printing process which includes stress constraint and potentially multiple materials or multiscales is analyzed. First order necessary optimality conditions are rigorously derived and a numerical algorithm which implements the method is presented. A sensitivity study with respect to some parameters is conducted for a two-dimensional cantilever beam problem. Finally, a possible workflow to obtain a 3D-printed object from the numerical solutions is described and the final structure is printed using a fused deposition modeling (FDM) 3D printer.

Multiscale Topology Optimization

Multiscale Topology Optimization Book
Author : Tej Kumar
Publisher : Unknown
Release : 2021
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Topology optimization (TO) is a mature technique for engineering design and is being incorporated in almost all engineering design software. It is possible to generate high-resolution nature-like structures using topology optimization by exploiting a large number of processors. Such high-resolution designs can also be generated by using multiscale topology optimization (MTO) which involves designs at two length scales. Compared to designs by TO, designing at two length scales in MTO provides additional flexibility in modeling and scope for computational gains. This thesis focuses on various modeling and computational aspects of multiscale topology optimization. Specifically, three distinct models are proposed in this thesis to enhance MTO design capabilities at moderate computational costs enabling their application on a Personal Computer (PC). The first model relies on a novel clustering approach to reduce the number of small scale structures called microstructures. The computational cost of clustered MTO with only a few distinct microstructures is negligible compared to unclustered MTO. However, the performance of the design may be compromised for an "incautious" choice of clustering criteria. To this end, we propose a density-and-strain-based clustering criterion along with the flexibility of rotation for microstructures to reduce the cost of MTO almost without compromising the performance. The proposed criterion features a very high convergence rate, converging in 50 iterations at an average. The second model is pertinent to a graded microstructure MTO wherein a number of fitting functions define the elasticity matrix at all volume fractions of the microstructure. Conventionally, each of these functions define one component of elasticity matrix and are not coupled to one another. This may lead the elasticity matrix to lose positive definiteness, a must-have property for any elasticity matrix. To ensure the positive definiteness, a spectral-decomposition of elasticity matrix is proposed where the fitting functions for eigenvalues and eigenvector orientations define the elasticity matrix. Ensuring the positive value of eigenvalue fitting functions translates to positive definiteness of elasticity matrix. The third model is for graded microstructure as well but instead of single graded microstructure, multiple graded microstructures are modeled together. A number of models inspired by multiple material optimization techniques are compared.

Concurrent Topology Optimization of Structures and Materials

Concurrent Topology Optimization of Structures and Materials Book
Author : Kai Liu
Publisher : Unknown
Release : 2013
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Topology optimization allows designers to obtain lightweight structures considering the binary distribution of a solid material. The introduction of cellular material models in topology optimization allows designers to achieve significant weight reductions in structural applications. However, the traditional topology optimization method is challenged by the use of cellular materials. Furthermore, increased material savings and performance can be achieved if the material and the structure topologies are concurrently designed. Hence, multi-scale topology optimization methodologies are introduced to fulfill this goal. The objective of this investigation is to discuss and compare the design methodologies to obtaining optimal macro-scale structures and the corresponding optimal meso-scale material designs in continuum design domains. These approaches make use of homogenization theory to establish communication bridges between both material and structural scales. The periodicity constraint makes such cellular materials manufacturable while relaxing the periodicity constraint to achieve major improvements of structural performance. Penalization methods are used to obtain binary solutions in both scales. The proposed methodologies are demonstrated in the design of stiff structure and compliant mechanism synthesis. The multiscale results are compared with the traditional structural-level designs in the context of Pareto solutions, demonstrating benefits of ultra-lightweight configurations. Errors involved in the mult-scale topology optimization procedure are also discussed. Errors are mainly classified as mesh refinement errors and homogenization errors. Comparisons between the multi-level designs and uni-level designs of solid structures, structures using periodic cellular materials and non-periodic cellular materials are provided. Error quantifications also indicate the superiority of using non-periodic cellular materials rather than periodic cellular materials.

Topology Optimization in Engineering Structure Design

Topology Optimization in Engineering Structure Design Book
Author : Jihong Zhu,Tong Gao
Publisher : Elsevier
Release : 2016-11-08
ISBN : 0081021194
Language : En, Es, Fr & De

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Book Description :

Topology Optimization in Engineering Structure Design explores the recent advances and applications of topology optimization in engineering structures design, with a particular focus on aircraft and aerospace structural systems. To meet the increasingly complex engineering challenges provided by rapid developments in these industries, structural optimization techniques have developed in conjunction with them over the past two decades. The latest methods and theories to improve mechanical performances and save structural weight under static, dynamic and thermal loads are summarized and explained in detail here, in addition to potential applications of topology optimization techniques such as shape preserving design, smart structure design and additive manufacturing. These new design strategies are illustrated by a host of worked examples, which are inspired by real engineering situations, some of which have been applied to practical structure design with significant effects. Written from a forward-looking applied engineering perspective, the authors not only summarize the latest developments in this field of structure design but also provide both theoretical knowledge and a practical guideline. This book should appeal to graduate students, researchers and engineers, in detailing how to use topology optimization methods to improve product design. Combines practical applications and topology optimization methodologies Provides problems inspired by real engineering difficulties Designed to help researchers in universities acquire more engineering requirements

Multi scale Topological Design of Structural Materials an Integrated Approach

Multi scale Topological Design of Structural Materials   an Integrated Approach Book
Author : Àlex Ferrer Ferré
Publisher : Unknown
Release : 2017
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

The present dissertation aims at addressing multiscale topology optimization problems. For this purpose, the concept of topology derivative in conjunction with the computational homogenization method is considered. In this study, the topological derivative algorithm, which is clearly non standard in topology optimization, and the optimality conditions are first introduced in order to a provide a better insight. Then, a precise treatment of the interface elements is proposed to reduce the numerical instabilities and the time-consuming computations that appear when using the topological derivative algorithm. The resulting strategy is examined and compared with current methodologies collected in the literature by means of some numerical tests of different nature. Then, a closed formula of the anisotropic topological derivative is obtained by solving analytically the exterior elastic problem. To this aim, complex variable theory and symbolic computation is considered. The resulting expression is validated through some numerical tests. In addition, different anisotropic topology optimization problems are solved to show the macroscopic topological implications of considering anisotropic materials. Finally, the two-scale topology optimization problem is tackled. As a first approach, an structural stiffness increase is achieved by considering the microscopic topologies as design variables of the problem. An alternate direction algorithm is proposed to address the high non-linearities of the problem. In addition, to mitigate the unaffordable time-consuming computations, a reduction technique is presented by means of pre-computing the optimal microscopic topologies in a computational material catalogue. As an extension of the first approach, besides designing the microscopic topologies, the macroscopic topology is also considered as a design variable, leading to even more optimal solutions. In addition, the proposed algorithms are modified in order to obtain manufacturable optimal designs. Two-scale topology optimization examples exhibit the potential of the proposed methodology.

Design Optimisation and Validation of Phononic Crystal Plates for Manipulation of Elastodynamic Guided Waves

Design Optimisation and Validation of Phononic Crystal Plates for Manipulation of Elastodynamic Guided Waves Book
Author : Saeid Hedayatrasa
Publisher : Springer
Release : 2018-01-09
ISBN : 3319729594
Language : En, Es, Fr & De

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Book Description :

This thesis proposes novel designs of phononic crystal plates (PhPs) allowing ultra-wide controllability frequency ranges of guided waves at low frequencies, with promising structural and tunability characteristics. It reports on topology optimization of bi-material-layered (1D) PhPs allowing maximized relative bandgap width (RBW) at target filling fractions and demonstrates multiscale functionality of gradient PhPs. It also introduces a multi-objective topology optimization method for 2D porous PhPs allowing both maximized RBW and in-plane stiffness and addresses the critical role of considering stiffness in designing porous PhPs. The multi-objective topology optimization method is then expanded for designing 2D porous PhPs with deformation induced tunability. A variety of innovative designs are introduced which their maximized broadband RBW is enhanced by, is degraded by or is insensitive to external finite deformation. Not only does this book address the challenges of new topology optimization methods for computational design of phononic crystals; yet, it demonstrated the suitability and applicability of the topological designs by experimental validation. Furthermore, it offers a comprehensive review of the existing optimization-based approaches for the design of finite non-periodic acoustic metamaterial structures, acoustic metamaterial lattice structures and acoustic metamaterials under perfect periodicity.

Optimization of Structural Topology in the High Porosity Regime

Optimization of Structural Topology in the High Porosity Regime Book
Author : Anonim
Publisher : Unknown
Release : 2004
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

This project explores homogenization-based design as a systematic approach to the optimization of high- porosity materials and structures. We have shown that when the goal is maximal stiffness, extremal effective behavior does not require multiscale architecture. In fact, optimal structures can be found within a simple class of closed-cell, high-porosity composites we call "single-scale laminates." Moreover there is a simple formula for the Hooke's law of a single-scale laminate. It reduces the task of structural optimization for minimum weight and maximal stiffness to a convex optimization specifically, a problem of semidefinite programming. The optimal structures are not in general unique - indeed, there is a high degree of degeneracy. It is natural to use simplicity and/or continuity as selection mechanisms. We have developed efficient schemes for doing so.

Integrated Design of Multiscale Multifunctional Materials and Products

Integrated Design of Multiscale  Multifunctional Materials and Products Book
Author : David L. McDowell,Jitesh Panchal,Hae-Jin Choi,Carolyn Seepersad,Janet Allen,Farrokh Mistree
Publisher : Butterworth-Heinemann
Release : 2009-09-30
ISBN : 9780080952208
Language : En, Es, Fr & De

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Book Description :

Integrated Design of Multiscale, Multifunctional Materials and Products is the first of its type to consider not only design of materials, but concurrent design of materials and products. In other words, materials are not just selected on the basis of properties, but the composition and/or microstructure iw designed to satisfy specific ranged sets of performance requirements. This book presents the motivation for pursuing concurrent design of materials and products, thoroughly discussing the details of multiscale modeling and multilevel robust design and provides details of the design methods/strategies along with selected examples of designing material attributes for specified system performance. It is intended as a monograph to serve as a foundational reference for instructors of courses at the senior and introductory graduate level in departments of materials science and engineering, mechanical engineering, aerospace engineering and civil engineering who are interested in next generation systems-based design of materials. First of its kind to consider not only design of materials, but concurrent design of materials and products Treatment of uncertainty via robust design of materials Integrates the "materials by design approach" of Olson/Ques Tek LLC with the "materials selection" approach of Ashby/Granta Distinquishes the processes of concurrent design of materials and products as an overall systems design problem from the field of multiscale modeling Systematic mathematical algorithms and methods are introduced for robust design of materials, rather than ad hoc heuristics--it is oriented towards a true systems approach to design of materials and products

An Introduction to the Topological Derivative Method

An Introduction to the Topological Derivative Method Book
Author : Antonio André Novotny,Jan Sokołowski
Publisher : Springer Nature
Release : 2020-01-21
ISBN : 3030369153
Language : En, Es, Fr & De

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Book Description :

This book presents the topological derivative method through selected examples, using a direct approach based on calculus of variations combined with compound asymptotic analysis. This new concept in shape optimization has applications in many different fields such as topology optimization, inverse problems, imaging processing, multi-scale material design and mechanical modeling including damage and fracture evolution phenomena. In particular, the topological derivative is used here in numerical methods of shape optimization, with applications in the context of compliance structural topology optimization and topology design of compliant mechanisms. Some exercises are offered at the end of each chapter, helping the reader to better understand the involved concepts.

Advances in Computational Plasticity

Advances in Computational Plasticity Book
Author : Eugenio Oñate,Djordje Peric,Eduardo de Souza Neto,Michele Chiumenti
Publisher : Springer
Release : 2017-09-09
ISBN : 3319608851
Language : En, Es, Fr & De

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Book Description :

This book brings together some 20 chapters on state-of-the-art research in the broad field of computational plasticity with applications in civil and mechanical engineering, metal forming processes, geomechanics, nonlinear structural analysis, composites, biomechanics and multi-scale analysis of materials, among others. The chapters are written by world leaders in the different fields of computational plasticity.

Reduced order Process aware Design of Multiscale Structures with Architected Materials

Reduced order Process aware Design of Multiscale Structures with Architected Materials Book
Author : Conner Terry Sharpe
Publisher : Unknown
Release : 2020
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Advances in additive manufacturing (AM) techniques have enabled the production of parts with ever increasing geometric complexity across multiple length scales. However, while expanding the space of possible designs is exciting from an engineering perspective, it also presents new challenges that the design community must address to fully take advantage of these capabilities. Analyzing and searching through potential designs in a multiscale setting can quickly become intractable. This work seeks to alleviate these concerns by decoupling the design process across hierarchical length scales and developing surrogate models that can link these scales in a computationally efficient manner. Reduced-order design representations are used at each length scale to render a more tractable search space. Surrogate optimization combined with geometric projection approaches are used to yield architected materials (or unit cell geometries) with desirable homogenized mechanical properties. The macroscale material density field is parameterized using B-Spline surfaces to design lattice structures for stiffness and strength. Many of the most popular AM processes also produce inherently anisotropic properties that depend on geometric design parameters such as feature orientation or size. This factor is often ignored in the design process and consequently causes deviations in manufactured performance from desired outcomes, thus limiting the adoption of AM. This work builds a data-driven method to incorporate design-dependent properties produced by particular AM processes into a multiscale design optimization workflow. A study of the mechanical properties of struts built at various orientations and sizes in metal powder bed fusion is used to build a process-aware material model. Accounting for these manufacturing concerns through design is shown to result in significant improvements in the effective properties of architected materials and lattice structures. Finally, AM allows for an unprecedented freedom in the topology or material layout within a given design domain. However, it is often difficult for engineers to utilize this freedom by fully considering design possibilities as there is a dearth of tools that allow for efficient topology exploration. This work explores the use of deep learning algorithms as generative design tools, allowing for quick visual exploration of design options in the early stages of design. Specifically, conditional generative adversarial networks are used to encode a diverse suite of complex topologies derived from structural optimization in a compact latent space to enable many design options to be considered for the problem at hand. Design factors such as type of architected material, allowable mass, and loading conditions can be included in the exploration. These tools can also be used as reduced-order design parameterizations in themselves to enable further directed design when traditional optimization approaches may be difficult to implement effectively

Optimization of Structures and Components

Optimization of Structures and Components Book
Author : Pablo Andrés Muñoz-Rojas
Publisher : Springer Science & Business Media
Release : 2013-09-03
ISBN : 3319007173
Language : En, Es, Fr & De

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Book Description :

Written by an international group of active researchers in the field, this volume presents innovative formulations and applied procedures for sensitivity analysis and structural design optimization. Eight chapters discuss subjects ranging from recent developments in the determination and application of topological gradients, to the use of evolutionary algorithms and meta-models to solve practical engineering problems. With such a comprehensive set of contributions, the book is a valuable source of information for graduate students and researchers entering or working in the matter.

Multiscale Lattices and Composite Materials Optimal Design Modeling and Characterization

Multiscale Lattices and Composite Materials  Optimal Design  Modeling and Characterization Book
Author : Fernando Fraternali,Chiara Daraio,Julian J. Rimoli
Publisher : Frontiers Media SA
Release : 2019-11-26
ISBN : 2889631850
Language : En, Es, Fr & De

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Book Description :

Download Multiscale Lattices and Composite Materials Optimal Design Modeling and Characterization book written by Fernando Fraternali,Chiara Daraio,Julian J. Rimoli, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Advances in Mechanical Design

Advances in Mechanical Design Book
Author : Jianrong Tan,Feng Gao,Changle Xiang
Publisher : Springer
Release : 2017-11-14
ISBN : 9811065535
Language : En, Es, Fr & De

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Book Description :

Focusing on innovation, these proceedings present recent advances in the field of mechanical design in China and offer researchers, scholars and scientists an international platform to present their research findings and exchange their ideas. In the context of the “Made in China 2025” development strategy, one central aspect of the ICMD2017 was Innovative Design Pushes “Made in China 2025.” The book highlights research hotspots in mechanical design, such as design methodology, green design, robotics and mechanics, and reliability design, while also combining industrial design and mechanical design.