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Optimization problems are relevant in many areas of technical, industrial, and economic applications. At the same time, they pose challenging mathematical research problems in numerical analysis and optimization. Harald Held considers an elastic body subjected to uncertain internal and external forces. Since simply averaging the possible loadings will result in a structure that might not be robust for the individual loadings, he uses techniques from level set based shape optimization and two-stage stochastic programming. Taking advantage of the PDE’s linearity, he is able to compute solutions for an arbitrary number of scenarios without significantly increasing the computational effort. The author applies a gradient method using the shape derivative and the topological gradient to minimize, e.g., the compliance . and shows that the obtained solutions strongly depend on the initial guess, in particular its topology. The stochastic programming perspective also allows incorporating risk measures into the model which might be a more appropriate objective in many practical applications.
Fluid dynamics -- Mathematics. --- Mathematical optimization. --- Shape theory (Topology). --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Theory --- Stochastic programming. --- Mathematics. --- Probabilities. --- Probability Theory and Stochastic Processes. --- Mathematics, general. --- Linear programming --- Distribution (Probability theory. --- Math --- Science --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk
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The design, construction and verification of complex two- and three-dimensional shapes in architecture and ship geometry have always been a particularly demanding part of the art of engineering. Before science-based structural design and analysis were applied in the construction industries, id est, before 1800, the task of conceiving, documenting and fabricating such shapes constituted the most significant interface between practitioner's knowledge and learned knowledge, above all in geometry. The history of shape development in these two disciplines therefore promises especially valuable insights into the knowledge history of shape creation. This volume is a collection of contributions by outstanding scholars in their fields of study, archaeology, history of architecture and ship design, in classic antiquity, the Middle Ages and the early modern period. The volume presents a comparative knowledge history in these two distinct branches of construction engineering.
Naval architecture --- Hulls (Naval architecture) --- Shape theory (Topology) --- Structural optimization. --- Shipbuilding --- History. --- Design and construction --- Architecture navale --- Coques (Architecture navale) --- Théorie de la forme (Topologie) --- Optimisation des structures --- Construction navale --- Histoire --- Conception et construction --- Optimal structural design --- Optimization, Structural --- Optimization of structural systems --- Optimum design of structures --- Optimum structural design --- Optimum structures --- Structures, Optimum design of --- Structural design --- Homotopy theory --- Mappings (Mathematics) --- Topological manifolds --- Topological spaces --- Shipfitting --- Architecture, Naval --- Marine architecture --- Ships --- Architecture --- Nautical influences
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