Titlebook: An Introduction to Structural Optimization; Peter W. Christensen,Anders Klarbring Textbook 2009 Springer Science+Business Media B.V. 2009

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https://doi.org/10.1007/978-3-662-41310-4 6.3.2, the sensitivity analysis for shape optimization of sheets was described. It was concluded that the nodal sensitivities, i.e. the partial derivatives of the nodal positions with respect to the design variables were needed. These sensitivities will depend on how the shape is represented and al

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https://doi.org/10.1007/978-3-662-41310-4discrete, like trusses, or we have made them discrete by a finite element discretization. In this chapter, on the other hand, we will look at some techniques of mathematics, from an area usually referred to as calculus of variations, that can handle some continuous optimization problems such as thos

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Die Zukunft des MINT-Lernens – Band 1e formulate the problem of optimizing stiffness of a sheet by finding an optimal thickness distribution, which is basically a special case of the general stiffness optimization problem of the previous chapter and which relates closely to the truss problem of Chap. 5. The classical optimality criteri

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Examples of Optimization of Discrete Parameter Systems, finding the cross-sectional areas of bars or beams, i.e. they are sizing problems. The list of such examples is the following: . A simple example of combined shape and sizing optimization of a two-bar truss is given in Exercise 2.5. Despite their simplicity, it turns out that these problems display

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Basics of Convex Programming,ptimization problem under study. This works fine for problems with only two design variables, but when trying to solve real-life problems, where the number of design variables may vary from the order of 10 to the order of 100 000 or more, one needs more systematic solution methods. In this and the f

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Two-Dimensional Shape Optimization, 6.3.2, the sensitivity analysis for shape optimization of sheets was described. It was concluded that the nodal sensitivities, i.e. the partial derivatives of the nodal positions with respect to the design variables were needed. These sensitivities will depend on how the shape is represented and al

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Stiffness Optimization of Distributed Parameter Systems,discrete, like trusses, or we have made them discrete by a finite element discretization. In this chapter, on the other hand, we will look at some techniques of mathematics, from an area usually referred to as calculus of variations, that can handle some continuous optimization problems such as thos