Multicriteria optimization of cold-formed thin-walled beams with generalized open shape under different loads |
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| Affiliation: | 1. Université Tunis El Manar, Ecole Nationale d’Ingénieurs de Tunis, Laboratoire de génie civil, BP 37, Tunis Belvédère 1002, Tunisia;2. Institut supérieur des études technologiques de Sfax, Route de Mahdia, km 2.5, BP 88, El Bustan, Sfax 3099, Tunisia;1. School of Automation Science and Electrical Engineering, Beihang University, Beijing 100191, China;2. Beijing Institute of Aerospace Control Devices, Beijing 100039, China;1. Key Laboratory of Oil and Gas Fine Chemicals, Ministry of Education & Xinjiang Uygur Autonomous Region, Xinjiang University, Urumqi 830046, Xinjiang, China;2. College of Chemistry and Chemical Engineering, Central South University, Changsha 410083, Hunan, China;1. Key Laboratory of Oil and Gas Fine Chemicals, Ministry of Education & Xinjiang Uygur Autonomous Region, Xinjiang University, Urumqi 830046, Xinjiang, China;2. Petroleum Chemical Engineering Department, Xinjiang Career Technical College, Kuitun 833200, Xinjiang, China |
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| Abstract: | The paper presents an analysis of the optimal design of cold-formed beams with generalized open shapes under pure bending, uniformly distributed loads, concentrated loads and axial loads with constant bending moment. The optimization problem includes the cross section area as the first objective function and the deflection of a beam as the second one. The geometric parameters of cross sections are selected as design variables. The set of constraints includes global stability condition, selected forms of local stability conditions, strength condition and technological and constructional requirements in a form of geometric relations. The strength and stability conditions are formulated and analytically solved using mathematical equations. The optimization problem is formulated and solved with help of the Pareto concept of optimality. The numerical procedure, based on the Messac normalized constraint method, include discrete, continuous and discrete-continuous sets of design variables. Results of the numerical analysis for different loads of beams with monosymmetrical cross section shapes are presented in tables. |
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