Two-scale topology design optimization of stiffened or porous plate subject to out-of-plane buckling constraint

This paper studies maximum out-of-plane buckling load design of thin bending plates for a given amount of material. Two kinds of plates are considered. One is made of periodic homogeneous porous material. Another is uniformly stiffened solid plate. The plate material, thickness, design domain of its...

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Bibliographic Details
Published in:Structural and multidisciplinary optimization 2016-11, Vol.54 (5), p.1283-1296
Main Authors: Cheng, Gengdong, Xu, Liang
Format: Article
Language:English
Subjects:
Asymptotic methods
Boundary conditions
Buckling
Computational Mathematics and Numerical Analysis
Design optimization
Engineering
Engineering Design
Finite element method
Homogenization
Plate material
Plates (structural members)
Porous materials
Porous plates
Research Paper
Search algorithms
Sensitivity analysis
Stiffeners
Stiffness
Theoretical and Applied Mechanics
Topology optimization
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Summary:This paper studies maximum out-of-plane buckling load design of thin bending plates for a given amount of material. Two kinds of plates are considered. One is made of periodic homogeneous porous material. Another is uniformly stiffened solid plate. The plate material, thickness, design domain of its middle plane and boundary conditions are given. The pattern of prescribed in-plane external load or displacements along the part of boundaries, which move freely, is given. Both plate topology and micro-structural topology of porous material or stiffener layout are concurrently optimized. The artificial element material densities in both macro and micro-scale are chosen as design variables. The volume preserving nonlinear density filter is applied to obtain the black-white optimum topology and comparison of its different sensitivities is made to show the reason for oscillation during optimization process in Appendix. The new numerical implementation of asymptotic homogenization method (NIAH, Cheng (Acta Mech Sinica 29(4): 550–556, 2013 ) and Cai (Int J Solids Struct 51(1), 284–292, 2014 ) is applied to homogenization of periodic plate structures and analytic sensitivity analysis of effective stiffness with respect to the topological design variables in both macro-scale and micro-scale. On basis of that, this paper implements the sensitivity analysis of out-of-plane buckling load by using commercial FEA software and enables the application of gradient-based search algorithm in optimization. Several numerical implementation details are discussed. Three numerical examples are given to show the validity of this method.
ISSN:1615-147X
1615-1488
DOI:10.1007/s00158-016-1542-y