Discrete Structural Optimization
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Discrete Structural Optimization
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Author : W. Gutkowski
language : en
Publisher:
Release Date : 2014-09-01
Discrete Structural Optimization written by W. Gutkowski and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-01 with categories.
Discrete Structural Optimization
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Author : Witold Gutkowski
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-07
Discrete Structural Optimization written by Witold Gutkowski and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-07 with Technology & Engineering categories.
The IUTAM Symposium on "Discrete Structural Optimization" was devoted to discuss optimization problems for which design va riables may not be sought among continuous sets. Optimum sizing from lists of available profiles, segmentation; as well as allocation and number of supports, sensors or actuators, are good exam ples of such problems for which design variables may be chosen only from finite sets. The above problems are having not only important practical applications. They are also inspiring scienti fic research in the field of discrete applied mathematics. Among them are controlled enumeration methods, subgradient approach, genetic programming, multicriteria optimization, neural nets etc. Along with its tradition of promoting and supporting new im portant fields of research in mechanics and its application, General Assembly of IUTAM decided in 1990 to support the Sumposium. It is worthy to note that this is the second IUTAM Symposium on structural optimization, organized in Poland. The first one was held in Warsaw twenty years ago and was organized by Profe ssors Sawczuk and Mroz. It was devoted mostly to problems with continuous design variables. The Symposium which gathered 40 participants from 12 coun tries was sponsored by several institutions listed below. However support by IUTAM should be specially appreciated. It helped se veral scientists to contribute to the Symposium which other way wouldn't attend the meeting.
Discrete Structural Optimization As A Sequential Decision Process Solved Using Deep Reinforcement Learning
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Author : Maximilian Edward Ororbia
language : en
Publisher:
Release Date : 2023
Discrete Structural Optimization As A Sequential Decision Process Solved Using Deep Reinforcement Learning written by Maximilian Edward Ororbia and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023 with categories.
Topology optimization is a mathematical framework that in general seeks to determine the optimal layout of material in a design domain. If the design variables are continuous, then often sensitivities can be derived and used with gradient based optimization techniques. However, for certain applications the design variables are inherently discrete, for example the design of steel structures that are constructed of standardized steel sections. This work focuses on the latter, whereby the optimization of structures with discrete elements and discrete design variables is formulated as a sequential decision process solved using reinforcement learning (RL) and deep reinforcement learning (DRL), which has been shown to efficiently provide adept solutions to a variety of high-dimensional planning and learning problems. Hence, this work mathematically models the discrete optimization of planar structures, including trusses and frames, as a Markov decision process (MDP). By modeling discrete structural optimization as an MDP, the set of all feasible design solutions can be precisely represented and the MDP naturally, but not exclusively, accommodates discrete actions. Within this framing, the MDP states correspond to specific structural designs represented as finite graph configurations and the actions correspond to specific topological and parametric grammars that are applied to alter the structure, transitioning the design to a new state and graph configuration. Key to modeling discrete optimization as an MDP is the relation of the rewards to the change in the design's performance as the agent explores alternate design configurations. Through this relation, the agent learns an optimal policy, that is, a sequence of necessary alteration actions, that maximizes its cumulative reward and simultaneously synthesizes a high-performing design solution, if not the global optimal, with respect to the specified design problem's objective and specified constraints. The discrete MDP model solved using RL and DRL is applied to the discrete optimization of planar truss and frame structures. To demonstrate the merit of the idea and because elements of the MDP tuple are unknown to the agent a priori, a tabular implementation of reinforcement learning (RL), specifically a Q-learning algorithm, was employed to solve the MDP due to its strong convergence properties. However, for problems with high dimensional state and action spaces, that is, with a large set of feasible design solutions, the number of state visits required to converge to the optimal policy becomes intractable, a problem commonly referred to as the curse of dimensionality. Tabular RL algorithms can become inefficient for solving design problems with relatively large state and action spaces due to their memory limitation and need for an excessive number of experiences to learn the optimal policy. Hence by extending the general discrete structural optimization MDP to be solved using DRL, a deep neural network architecture is specifically developed to approximate the state-action value function, such that the network has far fewer parameters than the cardinality of the state space of feasible design solutions. This enables the MDP framework to adeptly solve discrete topology optimization design problems with large state and action spaces. A benefit of the suggested method, in comparison to other discrete optimization approaches, is that the MDP framework is grounded in mathematics and is not dependent on the specifics of the structural model. The framework is evaluated in the context of the discrete structural optimization of planar trusses and frames with discrete elements and multiple discrete cross-sectional areas, and its utility is investigated through several numerical examples, each with different state space cardinalities. The objective of the design task is to determine both the layout of structural elements and the assignment of cross-sectional areas that minimize the displacement at a specified node for a given external force(s) determined using either linear or nonlinear finite element analysis, subject to stability and volume constraints. In this work, both the agent's learned optimal policy and the resulting synthesized design solution are validated against the policy determined by using a state-action value iteration dynamic programming algorithm, chosen for its strong convergence guarantees, and the global optimal design configuration identified from an exhaustive evaluation of all feasible design solutions, respectively. Also through qualitative and quantitative comparison with other considered alternative methods, the MDP framework is observed to adeptly learn optimal policies that synthesize optimal design solutions with lower computational effort.
Elements Of Structural Optimization
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Author : Raphael T. Haftka
language : en
Publisher: Springer Science & Business Media
Release Date : 1991-11-30
Elements Of Structural Optimization written by Raphael T. Haftka and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-11-30 with Technology & Engineering categories.
The field of structural optimization is still a relatively new field undergoing rapid changes in methods and focus. Until recently there was a severe imbalance between the enormous amount of literature on the subject, and the paucity of applications to practical design problems. This imbalance is being gradually redressed. There is still no shortage of new publications, but there are also exciting applications of the methods of structural optimizations in the automotive, aerospace, civil engineering, machine design and other engineering fields. As a result of the growing pace of applications, research into structural optimization methods is increasingly driven by real-life problems. t-.Jost engineers who design structures employ complex general-purpose software packages for structural analysis. Often they do not have any access to the source program, and even more frequently they have only scant knowledge of the details of the structural analysis algorithms used in this software packages. Therefore the major challenge faced by researchers in structural optimization is to develop methods that are suitable for use with such software packages. Another major challenge is the high computational cost associated with the analysis of many complex real-life problems. In many cases the engineer who has the task of designing a structure cannot afford to analyze it more than a handful of times.
Recent Advances In Optimal Structural Design
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Author : Scott A. Burns
language : en
Publisher: ASCE Publications
Release Date : 2002-01-01
Recent Advances In Optimal Structural Design written by Scott A. Burns and has been published by ASCE Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-01-01 with Technology & Engineering categories.
Sponsored by the Technical Committee on Structural Design of the Technical Administrative Committee on Analysis and Computation of the Technical Activities Division of the Structural Engineering Institute of ASCE. This report documents the dramatic new developments in the field of structural optimization over the last two decades. Changes in both computational techniques and applications can be seen by developments in computational methods and solution algorithms, the role of optimization during the various stages of structural design, and the stochastic nature of design in relation to structural optimization. Topics include: Ømethods for discrete variable structural optimization; Ødecomposition methods in structural optimization; Østate of the art on the use of genetic algorithms in design of steel structures; Øconceptual design optimization of engineering structures; Øtopology and geometry optimization of trusses and frames; Øevolutionary structural optimization; Ødesign and optimization of semi-rigid framed structures; Øoptimized performance-based design for buildings; Ømulti-objective optimum design of seismic-resistant structures; and Øreliability- and cost-oriented optimal bridge maintenance planning. The book concludes with an extensive bibliography of journal papers on structural optimization published between 1987 and 1999.
The Application Of Discrete Programming Techniques In The Structural Optimization
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Author : Mehmet Rifat Sağlam
language : en
Publisher:
Release Date : 1976
The Application Of Discrete Programming Techniques In The Structural Optimization written by Mehmet Rifat Sağlam and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976 with categories.
Discretization Methods And Structural Optimization Procedures And Applications
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Author : Hans A. Eschenauer
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Discretization Methods And Structural Optimization Procedures And Applications written by Hans A. Eschenauer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Technology & Engineering categories.
In recent years, the Finite Element Methods FEM were more and more employed in development and design departments as very fast working tools in order to determine stresses, deformations, eigenfrequencies etc. for all kinds of constructions under complex loading conditions. Meanwhile. very effective software systems have been developed by various research teams although some mathematical problems (e. g. convergence) have not been solved satisfac torily yet. In order to make further advances and to find a common language between mathe maticians and mechanicians the "Society for Applied Mathematics and Mechanics" (GAMM) agreed on the foundation of a special Committee: "Discretization Methods in Solid Mechanics" focussing on the following problems: - Structuring of various methods (displacement functions, hybrid and mixed approaches, etc. >, - Survey of approach functions (Lagrange-/Hermite-polynominals, Spline-functions), - Description of singularities, - Convergence and stability, - Practical and theoretical optimality to all mentioned issues (single and interacting). One of the basic aims of the GAMM-Committee is the interdisciplinary cooperation between mechanicians, mathematicians, and users which shall be intensified. Thus, on September 22, 1985 the committee decided to hold a seminar on "Structural Optimization" in order to allow an exchange of experiences and thoughts between the experts of finite element methods and those of structural optimization. A GAMM-seminar entitled "Discretization Methods and Structural Optimization - Procedures and Applications" was hold on October 5-7, 1988 at the Unversity of Siegen.
Structural Optimization With Nonlinear And Discrete Programming
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Author : Peiming Wu
language : en
Publisher:
Release Date : 1986
Structural Optimization With Nonlinear And Discrete Programming written by Peiming Wu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with categories.
Constraint Handling In Cohort Intelligence Algorithm
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Author : Ishaan R. Kale
language : en
Publisher: CRC Press
Release Date : 2021-12-26
Constraint Handling In Cohort Intelligence Algorithm written by Ishaan R. Kale and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-26 with Business & Economics categories.
Mechanical Engineering domain problems are generally complex, consisting of different design variables and constraints. These problems may not be solved using gradient-based optimization techniques. The stochastic nature-inspired optimization techniques have been proposed in this book to efficiently handle the complex problems. The nature-inspired algorithms are classified as bio-inspired, swarm, and physics/chemical-based algorithms. Socio-inspired is one of the subdomains of bio-inspired algorithms, and Cohort Intelligence (CI) models the social tendencies of learning candidates with an inherent goal to achieve the best possible position. In this book, CI is investigated by solving ten discrete variable truss structural problems, eleven mixed variable design engineering problems, seventeen linear and nonlinear constrained test problems and two real-world applications from manufacturing domain. Static Penalty Function (SPF) is also adopted to handle the linear and nonlinear constraints, and limitations in CI and SPF approaches are examined. Constraint Handling in Cohort Intelligence Algorithm is a valuable reference to practitioners working in the industry as well as to students and researchers in the area of optimization methods.
Properties Of Discrete Optima In Structural Optimization
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Author : A. Cella
language : en
Publisher:
Release Date : 1972
Properties Of Discrete Optima In Structural Optimization written by A. Cella and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972 with categories.