Non-parametric shape optimization method for natural vibration design of stiffened shells. (January 2015)

• Record Type: Journal Article
• Authors: Liu, Yang; Shimoda, Masatoshi
• Is Part Of: Computers & structures. Volume 146(2015)
• Page Start: 20
• Page End: 31
• Publication Date: 2015-01
• Subjects: Natural vibration -- Eigenvalue maximization -- Volume minimization -- Shape optimization -- Non-parametric -- Stiffened shells; Structural engineering -- Data processing -- Periodicals; Electronic data processing -- Structures, Theory of -- Periodicals; 624.171
• DOI: 10.1016/j.compstruc.2014.08.003
• Languages: English
• ISSNs: 0045-7949

Abstract

Highlights: A non-parametric shape optimization method is proposed for natural vibration problems of stiffened thin-walled structures. Solutions are given to deal with a specified eigenvalue maximization problem and its reciprocal volume minimization problem. Mesh smoothing is implemented simultaneously with shape updating. It can be easily implemented in combination with a commercial FEM code. Abstract: In this paper, we newly present an effective shape optimization method for natural vibration design of stiffened thin-walled or shell structures. Both the stiffeners and their basic structures are optimized by solving two kinds of optimization problems. The first is a specified eigenvalue maximization problem subject to a volume constraint, and the second is its reciprocal volume minimization problem subject to a specified eigenvalue constraint. The boundary shapes of a thin-walled structure are determined under the condition where the stiffeners and the basic structure are movable in the in-plane direction to their surface. Both problems are formulated as distributed-parameter shape optimization problems, and the shape gradient functions are derived using the material derivative method and the adjoint variable method. The optimal free-boundary shapes are determined by applying the derived shape gradient function to the H 1 gradient method for shells, which is a parameter-free shape optimization method proposed by one of the authors. Several design examples are presented to validate the proposed method and demonstrate its practical usages.