Constrained optimization of structures with displacement constraints under various loading conditions |
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| Affiliation: | 1. Université de Nantes, Nantes Atlantique Universités, Laboratoire de Thermocinétique de Nantes, UMR CNRS 6607, La Chantrerie, Rue Christian Pauc, BP 50609, 44306 Nantes Cedex 3, France;2. Institut de Recherche en Génie Civil et Mécanique (GeM), UMR CNRS 6183 Ecole Centrale de Nantes, BP 92101, 44321 Nantes Cedex 3, France;1. Department of Mechanical and Electrical Engineering, Ocean University of China, Qingdao 266100, China;2. Key Laboratory of Ocean Engineering of Shangdong Province, Ocean University of China, Qingdao 266100, China;1. Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA;2. Massachusetts Institute of Technology, Cambridge, MA 02139, USA;3. Pacific Northwest National Laboratory, Richland, WA 99352, USA;4. Karlsruhe Institute of Technology, Karlsruhe, Germany;1. Department of Mechanical and Construction Engineering, Northumbria University, Newcastle upon Tyne NE1 8ST, United Kingdom;2. Department of Architectural Engineering, Sejong University, 98 Gunja Dong, Gwangjin Gu, Seoul 143-747, South Korea;3. Department of Engineering Mechanics, Faculty of Engineering, University of Rijeka, Vukovarska 58, HR-51000 Rijeka, Croatia;1. College of Mechanical & Power Engineering, China Three Gorges University, Yichang 443002, China;2. Key Laboratory of Hydroelectric Machinery Design and Maintenance, Yichang 443002, China |
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| Abstract: | Optimization problems often involve constraints and restrictions which must be considered in order to obtain an optimum result and the resultant solution should not deviate from any of the imposed constraints. These constraints and restrictions are imposed either on the design variables or on the algebraic relations between them. Constraints of allowable stress, minimum size and buckling of members in the absence of allowable displacement constraint are the most important factors in optimization of the cross-sectional area of structural elements. When the allowable displacement constraint is included in the problem as a determinant parameter, since the specifications of most of elements affect the displacement rate, the way of imposing and considering this constraint requires special care. In this research the way of simultaneous imposition of multi displacement constraints for optimum design of truss structures in several load cases is described. In this method various constraints for different load cases are divided into active and passive constraints. The mathematical formulation is based on the classical method of Lagrange Multipliers. Overall, this simple method can be employed along with other constraints such as buckling, allowable stress and minimum size of members for imposing the displacement constraint in various load cases. |
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