Download Free Effects Of Problem Size On Large Scale Structural Optimization Book in PDF and EPUB Free Download. You can read online Effects Of Problem Size On Large Scale Structural Optimization and write the review.

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.
G.I.N. Rozvany ASI Director, Professor of Structural Design, FB 10, Essen University, Essen, Germany Structural optimization deals with the optimal design of all systems that consist, at least partially, of solids and are subject to stresses and deformations. This inte grated discipline plays an increasingly important role in all branches of technology, including aerospace, structural, mechanical, civil and chemical engineering as well as energy generation and building technology. In fact, the design of most man made objects, ranging from space-ships and long-span bridges to tennis rackets and artificial organs, can be improved considerably if human intuition is enhanced by means of computer-aided, systematic decisions. In analysing highly complex structural systems in practice, discretization is un avoidable because closed-form analytical solutions are only available for relatively simple, idealized problems. To keep discretization errors to a minimum, it is de sirable to use a relatively large number of elements. Modern computer technology enables us to analyse systems with many thousand degrees of freedom. In the optimization of structural systems, however, most currently available methods are restricted to at most a few hundred variables or a few hundred active constraints.
Nowadays in the aircraft industry, structural optimization problemscan be really complex and combine changes in choices of materials, stiffeners, orsizes/types of elements. In this work, it is proposed to solve large scale structural weightminimization problems with both categorical and continuous variables, subject to stressand displacements constraints. Three algorithms have been proposed. As a first attempt,an algorithm based on the branch and bound generic framework has been implemented.A specific formulation to compute lower bounds has been proposed. According to thenumerical tests, the algorithm returned the exact optima. However, the exponentialscalability of the computational cost with respect to the number of structural elementsprevents from an industrial application. The second algorithm relies on a bi-level formulationof the mixed categorical problem. The master full categorical problem consists ofminimizing a first order like approximation of the slave problem with respect to the categoricaldesign variables. The method offers a quasi-linear scaling of the computationalcost with respect to the number of elements and categorical values. Finally, in the thirdapproach the optimization problem is formulated as a bi-level mixed integer non-linearprogram with relaxable design variables. Numerical tests include an optimization casewith more than one hundred structural elements. Also, the computational cost scalingis quasi-independent from the number of available categorical values per element.
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.
Challenges arise when the size of a group of cooperating agents is scaled to hundreds or thousands of members. In domains such as space exploration, military and disaster response, groups of this size (or larger) are required to achieve extremely complex, distributed goals. To effectively and efficiently achieve their goals, members of a group need to cohesively follow a joint course of action while remaining flexible to unforeseen developments in the environment. Coordination of Large-Scale Multiagent Systems provides extensive coverage of the latest research and novel solutions being developed in the field. It describes specific systems, such as SERSE and WIZER, as well as general approaches based on game theory, optimization and other more theoretical frameworks. It will be of interest to researchers in academia and industry, as well as advanced-level students.
Fast algorithms for solving numerical problems involving large sparse matrix computations are investigated. Applications of this work to the areas of structural analysis, constrained optimization and large scale least squares adjustment methods are developed. One of the more important accomplishments is the design and testing on the Denelcor HEP multiprocessor of a parallel algorithm for computing a banded basis matrix for the null space. This algorithm may lead to a new efficient sparse matrix implementation of the force method for the finite element analysis of large-scale structures.