plate and shellstructures are widelyused in industrial products and structures such as automotives, vessels and architectures for its good formability and lightweight property. This paper presents a numerical shape o...
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plate and shellstructures are widelyused in industrial products and structures such as automotives, vessels and architectures for its good formability and lightweight property. This paper presents a numerical shapeoptimization method for the rigiditydesign of plate and shellstructures. A solution to a compliance minimization problem subject to a volume constraint is proposed, and its reciprocal problem is also solved. The boundaries are assumed to be movable in the in -plane directions so as to keep the initial curvatures in the design domain. For simplicity, the structures to be optimized are discretized by plane elements based on the Mindlin-Reissner plate theory. The problems are formulated as non-parametric, or distributed shapeoptimizationproblems involving the design of free boundaries. The shape gradient functions are theoretically derived using the material derivative method and the Lagrange multiplier method. With the shape gradient function, the smooth domain variation that minimizes the objective functional is de termined by the traction method developed by the authors. The validity and practical utility of this numerical solution for the rigiditydesign of plate and shellstructures are verified through simple examples and applications to automotive components.
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