Discrete Structural Optimization PDF Download
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Author: W. Gutkowski
Publisher:
ISBN: 9783709127551
Category :
Languages : en
Pages : 260
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Book Description
Author: W. Gutkowski
Publisher:
ISBN: 9783709127551
Category :
Languages : en
Pages : 260
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Book Description
Author: Osvaldo M. Querin
Publisher: Butterworth-Heinemann
ISBN: 0080999891
Category : Technology & Engineering
Languages : en
Pages : 205
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Book Description
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
Author: W. Gutkowski
Publisher: Springer
ISBN: 3709127548
Category : Technology & Engineering
Languages : en
Pages : 253
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Book Description
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.
Author: Peter W. Christensen
Publisher: Springer Science & Business Media
ISBN: 1402086652
Category : Technology & Engineering
Languages : en
Pages : 214
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Book Description
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.
Author: G.I.N. Rozvany
Publisher: Springer
ISBN: 3709125669
Category : Technology & Engineering
Languages : en
Pages : 325
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Book Description
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.
Author: Maximilian Edward Ororbia
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
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.
Author: Hans A. Eschenauer
Publisher: Springer Science & Business Media
ISBN: 3642837077
Category : Technology & Engineering
Languages : en
Pages : 377
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Book Description
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.
Author: Visarn Chanaratna
Publisher:
ISBN:
Category :
Languages : en
Pages : 378
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Book Description
Author: Peter W. Christensen
Publisher: Springer Science & Business Media
ISBN: 1402086660
Category : Technology & Engineering
Languages : en
Pages : 214
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Book Description
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.
Author: Jasbir S. Arora
Publisher: Amer Society of Civil Engineers
ISBN: 9780784402207
Category : Technology & Engineering
Languages : en
Pages : 347
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Book Description
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.
