Download or read book Discrete Structural Optimization written by W. Gutkowski and published by . This book was released on 2014-09-01 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Discrete Structural Optimization written by W. Gutkowski and published by Springer. This book was released on 2014-05-04 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: The engineering design of structures and machines consists often in finding the best solution among a finite number of feasible decisions. This volume comprises problems and solution methods for discrete structural optimization. Exact, approximate and heuristic methods are presented applying deterministic and stochastic approaches.
Download or read book An Introduction to Structural Optimization written by Peter W. Christensen and published by Springer Science & Business Media. This book was released on 2008-10-20 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book has grown out of lectures and courses given at Linköping University, Sweden, over a period of 15 years. It gives an introductory treatment of problems and methods of structural optimization. The three basic classes of geometrical - timization problems of mechanical structures, i. e. , size, shape and topology op- mization, are treated. The focus is on concrete numerical solution methods for d- crete and (?nite element) discretized linear elastic structures. The style is explicit and practical: mathematical proofs are provided when arguments can be kept e- mentary but are otherwise only cited, while implementation details are frequently provided. Moreover, since the text has an emphasis on geometrical design problems, where the design is represented by continuously varying—frequently very many— variables, so-called ?rst order methods are central to the treatment. These methods are based on sensitivity analysis, i. e. , on establishing ?rst order derivatives for - jectives and constraints. The classical ?rst order methods that we emphasize are CONLIN and MMA, which are based on explicit, convex and separable appro- mations. It should be remarked that the classical and frequently used so-called op- mality criteria method is also of this kind. It may also be noted in this context that zero order methods such as response surface methods, surrogate models, neural n- works, genetic algorithms, etc. , essentially apply to different types of problems than the ones treated here and should be presented elsewhere.
Download or read book Topology Design Methods for Structural Optimization written by Osvaldo M. Querin and published by Butterworth-Heinemann. This book was released on 2017-06-09 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topology Design Methods for Structural Optimization provides engineers with a basic set of design tools for the development of 2D and 3D structures subjected to single and multi-load cases and experiencing linear elastic conditions. Written by an expert team who has collaborated over the past decade to develop the methods presented, the book discusses essential theories with clear guidelines on how to use them. Case studies and worked industry examples are included throughout to illustrate practical applications of topology design tools to achieve innovative structural solutions. The text is intended for professionals who are interested in using the tools provided, but does not require in-depth theoretical knowledge. It is ideal for researchers who want to expand the methods presented to new applications, and includes a companion website with related tools to assist in further study. - Provides design tools and methods for innovative structural design, focusing on the essential theory - Includes case studies and real-life examples to illustrate practical application, challenges, and solutions - Features accompanying software on a companion website to allow users to get up and running fast with the methods introduced - Includes input from an expert team who has collaborated over the past decade to develop the methods presented
Download or read book Discrete Structural Optimization as a Sequential Decision Process Solved Using Deep Reinforcement Learning written by Maximilian Edward Ororbia and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Discretization Methods and Structural Optimization Procedures and Applications written by Hans A. Eschenauer and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Topology Optimization in Structural Mechanics written by G.I.N. Rozvany and published by Springer. This book was released on 2014-05-04 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topology optimization is a relatively new and rapidly expanding field of structural mechanics. It deals with some of the most difficult problems of mechanical sciences but it is also of considerable practical interest, because it can achieve much greater savings than mere cross-section or shape optimization.
Download or read book Guide to Structural Optimization written by Jasbir S. Arora and published by Amer Society of Civil Engineers. This book was released on 1997 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimization methods are perceived to be at the heart of computer methods for designing engineering systems. With these optimization methods, the designer can evaluate more alternatives, resulting in a better and more cost-effective design. This guide describes the use of modern optimization methods with simple yet meaningful structural design examples. Optimum solutions are obtained and, where possible, compared with the solutions obtained using traditional design procedures.
Download or read book Discrete Structural Optimization written by Visarn Chanaratna and published by . This book was released on 1978 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book An Introduction to Structural Optimization written by Peter W. Christensen and published by Springer Science & Business Media. This book was released on 2008-10-14 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book has grown out of lectures and courses given at Linköping University, Sweden, over a period of 15 years. It gives an introductory treatment of problems and methods of structural optimization. The three basic classes of geometrical - timization problems of mechanical structures, i. e. , size, shape and topology op- mization, are treated. The focus is on concrete numerical solution methods for d- crete and (?nite element) discretized linear elastic structures. The style is explicit and practical: mathematical proofs are provided when arguments can be kept e- mentary but are otherwise only cited, while implementation details are frequently provided. Moreover, since the text has an emphasis on geometrical design problems, where the design is represented by continuously varying—frequently very many— variables, so-called ?rst order methods are central to the treatment. These methods are based on sensitivity analysis, i. e. , on establishing ?rst order derivatives for - jectives and constraints. The classical ?rst order methods that we emphasize are CONLIN and MMA, which are based on explicit, convex and separable appro- mations. It should be remarked that the classical and frequently used so-called op- mality criteria method is also of this kind. It may also be noted in this context that zero order methods such as response surface methods, surrogate models, neural n- works, genetic algorithms, etc. , essentially apply to different types of problems than the ones treated here and should be presented elsewhere.
Download or read book Structural Optimization with Nonlinear and Discrete Programming written by Peiming Wu and published by . This book was released on 1986 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Discrete Variable Structural Optimization by the Complex Method written by P. G. van Bladel and published by . This book was released on 1989 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Optimization of Large Structural Systems written by G. I. N. Rozvany and published by Springer Science & Business Media. This book was released on 1993 with total page 594 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second of two volumes which examine structural optimization of large structural systems. Topics covered in these volumes include optimality criteria and topology optimization, decomposition methods and approximation concepts, neural networks and parallel processing.
Download or read book Integrated Structural Optimization of Discrete Framelike Structures for Multiple Load Cases written by Philipp A. Wagenblast and published by . This book was released on 2000 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Structural Optimization of Discrete Systems Represented by Finite Elements written by Dietrich Hartmann and published by . This book was released on 1984 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Recent Advances in Optimal Structural Design written by Scott A. Burns and published by ASCE Publications. This book was released on 2002-01-01 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Stability and Optimization of Structures written by Makoto Ohsaki and published by Springer Science & Business Media. This book was released on 2007-06-10 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on the optimization of a geometrically-nonlinear structure under stability constraint. It presents a deep insight into optimization-based and computer-assisted stability design of discrete structures. Coverage combines design sensitivity analysis developed in structural optimization and imperfection-sensitivity analysis developed in stability analysis.
