Robust design optimization of imperfect stiffened shells using an active learning method and a hybrid surrogate model

There are many uncertain factors in aerospace structures, such as variations in manufacturing tolerance, material properties and environmental aspects. Although conventional robust design optimization (RDO) can effectively take into account these uncertainties under the specified robust requirement, it is less satisfactory in addressing these difficulties owing to the prohibitive numerical cost of finite element analysis of stiffened shells. To improve the efficiency of RDO of imperfect stiffened shells, a new hybrid surrogate model (HSM), taking full advantage of the efficiency of the smeared stiffener method and the accuracy of the finite element method, is developed in this article. Then, a new active learning method is constructed based on the HSM. Furthermore, a hybrid bi-stage RDO framework is proposed to alleviate the computational burden incurred by repeated structural analysis. An example of a typical 3 m diameter stiffened shell demonstrates the high efficiency and accuracy of the proposed method.

[1]  Mark W. Hilburger,et al.  Comparison of Methods to Predict Lower Bound Buckling Loads of Cylinders Under Axial Compression , 2010 .

[2]  Mark W. Hilburger,et al.  Toward a Probabilistic Preliminary Design Criterion for Buckling Critical Composite Shells , 2003 .

[3]  Zeng Meng,et al.  Convergence control of single loop approach for reliability-based design optimization , 2018 .

[4]  I. Doltsinis,et al.  ROBUST DESIGN OF STRUCTURES USING OPTIMIZATION METHODS , 2004 .

[5]  Bo Wang,et al.  Non-probabilistic reliability-based design optimization of stiffened shells under buckling constraint , 2015 .

[6]  Mark W. Hilburger,et al.  Shell Buckling Design Criteria Based on Manufacturing Imperfection Signatures , 2003 .

[7]  I. Elishakoff,et al.  Optimization and Antioptimization of Buckling Load for Composite Cylindrical Shells Under Uncertainties , 2012 .

[8]  George Stefanou,et al.  Buckling analysis of imperfect shells with stochastic non-Gaussian material and thickness properties , 2009 .

[9]  Kim J.R. Rasmussen,et al.  Nonlinear buckling optimization of composite structures considering ''worst" shape imperfections , 2010 .

[10]  Z. Qiu,et al.  Comparison of dynamic response of structures with uncertain-but-bounded parameters using non-probabilistic interval analysis method and probabilistic approach , 2003 .

[11]  Bo Wang,et al.  Hierarchical Nondeterministic Optimization of Curvilinearly Stiffened Panel with Multicutouts , 2018, AIAA Journal.

[12]  Raimund Rolfes,et al.  Robust design of composite cylindrical shells under axial compression — Simulation and validation , 2008 .

[13]  Hoang-Anh Pham,et al.  Optimisation of stiffeners for maximum fundamental frequency of cross-ply laminated cylindrical panels using social group optimisation and smeared stiffener method , 2017 .

[14]  James K. Guest,et al.  Robust topology optimization of structures with uncertainties in stiffness - Application to truss structures , 2011 .

[15]  Zeng Meng,et al.  A novel experimental data-driven exponential convex model for reliability assessment with uncertain-but-bounded parameters , 2020 .

[16]  R. Lebrun,et al.  An innovating analysis of the Nataf transformation from the copula viewpoint , 2009 .

[17]  Raimund Rolfes,et al.  Design Optimization of Composite Cylindrical Shells under Uncertainty , 2012 .

[18]  Vissarion Papadopoulos,et al.  The effect of non-uniformity of axial loading on the buckling behaviour of shells with random imperfections , 2007 .

[19]  Su-Seng Pang,et al.  Buckling load analysis of grid stiffened composite cylinders , 2003 .

[20]  Hao Wu,et al.  A novel non-probabilistic reliability-based design optimization algorithm using enhanced chaos control method , 2017 .

[21]  Richard Degenhardt,et al.  The single perturbation load approach applied to imperfection sensitive conical composite structures , 2014 .

[22]  B. Gangadhara Prusty,et al.  Stochastic analysis of imperfection sensitive unstiffened composite cylinders using realistic imperfection models , 2015 .

[23]  R. Velmurugan,et al.  Buckling Analysis of Composite Hexagonal Lattice Cylindrical Shell using Smeared Stiffener Model , 2009 .

[24]  Bo Wang,et al.  Two-stage size-layout optimization of axially compressed stiffened panels , 2014 .

[25]  Gang Li,et al.  An active weight learning method for efficient reliability assessment with small failure probability , 2020 .

[26]  I. Elishakoff.  Uncertain buckling: its past, present and future , 2000 .

[27]  Z. Qiu,et al.  Novel reliability-based optimization method for thermal structure with hybrid random, interval and fuzzy parameters , 2017 .

[28]  Wei Chen,et al.  Towards a Better Understanding of Modeling Feasibility Robustness in Engineering Design , 2000 .

[29]  Nicolas Gayton,et al.  AK-MCS: An active learning reliability method combining Kriging and Monte Carlo Simulation , 2011 .

[30]  Chiara Bisagni,et al.  Perturbation-based imperfection analysis for composite cylindrical shells buckling in compression , 2013 .

[31]  Z. Qiu,et al.  Post-buckling analysis of a thin stiffened plate with uncertain initial deflection via interval analysis , 2009 .

[32]  Manolis Papadrakakis,et al.  The effect of material and thickness variability on the buckling load of shells with random initial imperfections , 2005 .

[33]  Johann Arbocz,et al.  Collapse of axially compressed cylindrical shells with random imperfections , 1995 .

[34]  Ahmed K. Noor,et al.  Uncertainty analysis of stiffened composite panels , 2001 .

[35]  J. Williams,et al.  Imperfection Surveys on a 10-ft-Diameter Shell Structure , 1977 .

[36]  Tae Hee Lee,et al.  Robust Design: An Overview , 2006 .

[37]  Luca Lanzi,et al.  A numerical and experimental investigation on composite stiffened panels into post-buckling , 2004 .

[38]  Raimund Rolfes,et al.  PROBABILISTIC DESIGN OF AXIALLY COMPRESSED COMPOSITE CYLINDERS WITH GEOMETRIC AND LOADING IMPERFECTIONS , 2010 .

[39]  Dao Huy Bich,et al.  Nonlinear static and dynamic buckling analysis of imperfect eccentrically stiffened functionally graded circular cylindrical thin shells under axial compression , 2013 .

[40]  Yunlong Ma,et al.  Numerically and experimentally predicted knockdown factors for stiffened shells under axial compression , 2016 .

[41]  Yutian Wang,et al.  Simultaneous buckling design of stiffened shells with multiple cutouts , 2017 .

[42]  Aleksandrs Korjakins,et al.  Surrogate Models for Optimum Design of Stiffened Composite Shells , 2004 .

[43]  Gang Li,et al.  Hybrid Framework for Reliability-Based Design Optimization of Imperfect Stiffened Shells , 2015 .

[44]  C. Guedes Soares,et al.  Reliability assessment of post-buckling compressive strength of laminated composite plates and stiffened panels under axial compression , 2007 .

[45]  Zeng Meng,et al.  Adaptive conjugate single-loop method for efficient reliability-based design and topology optimization , 2019, Computer Methods in Applied Mechanics and Engineering.

[46]  Luca Lanzi,et al.  Post-buckling optimization of composite stiffened panels: Computations and experiments , 2006 .

[47]  Chen Jiang,et al.  An active failure-pursuing Kriging modeling method for time-dependent reliability analysis , 2019, Mechanical Systems and Signal Processing.

[48]  Sankaran Mahadevan,et al.  Efficient Global Surrogate Modeling for Reliability-Based Design Optimization , 2013 .

[49]  Bernhard Sendhoff,et al.  Robust Optimization - A Comprehensive Survey , 2007 .

[50]  Ioan Cristian Trelea,et al.  The particle swarm optimization algorithm: convergence analysis and parameter selection , 2003, Inf. Process. Lett..