Asymptotic bounds on the globally optimal positions of orthogonal stiffeners for rectangular plates in elastostatic bending

作者：Perchikov Nathan^*

来源：Optimization and Engineering, 2013, 14(1): 119-153.

DOI：10.1007/s11081-011-9161-3

• Elastic plate bending
• Orthogonal stiffeners
• Fredholm's 2nd kind integral equation
• Asymptotic analysis
• Globally optimal positions

The present paper treats the problem of finding the asymptotic bounds for the globally optimal locations of orthogonal stiffeners minimizing the compliance of a rectangular plate in elastostatic bending. The essence of the paper is the utilization of a method of analysis of orthogonally stiffened rectangular plates first presented by Mazurkiewicz in 1962, and obtained herein in a closed form for several special cases. Asymptotic expansions of the expressions for the deflection field of a stiffened plate are used to derive limit-case globally optimal stiffening layouts for highly flexible and highly rigid stiffeners. A central result obtained in this work is an analytical proof of the fact that an array of flexible enough orthogonal stiffeners of any number, stiffening a simply-supported rectangular plate subjected to any lateral loading, is best to be put in the form of exactly two orthogonal stiffeners, one in each direction.

• 出版日期2013-3