Data-driven modelling and optimization of stiffeners on undevelopable curved surfaces

Undevelopable stiffened curved shells have been widely used in engineering fields. The shape of the undevelopable curved surface is generally characterized with the non-straight generatrix and variable cross sections, which makes it challenging to automatically model and optimize stiffeners on the undevelopable curved surface. Therefore, the data-driven modelling and optimization framework are proposed for undevelopable stiffened curved shells in this paper. Firstly, a novel mesh deformation method is developed for the data-driven modelling of undevelopable stiffened curved shells based on RBF neural network machine learning method. Its main idea is to firstly define a developable curved shell (background mesh domain) having similar topological characteristics with the undevelopable curved shell (target mesh domain), and then train the mapping relationship between the background mesh domain and the target mesh domain by RBF neural network, and finally the complicated modelling problem of the undevelopable stiffened curved shell can be transformed into a simple modelling problem of developable stiffened curved shell by means of the mapping relationship. Moreover, based on the efficient global optimization (EGO) surrogate method, a data-driven layout optimization method is established for minimizing the structural weight of undevelopable stiffened curved shells. Finally, three representative optimization examples are carried out, including modelling and optimization of stiffeners on hyperbolic parabolic curved surfaces, blade-shaped curved surfaces and S-shaped variable cross-sectional curved surfaces. Optimal results indicate that the structural weight of undevelopable stiffened curved shells decreases significantly after the optimization, indicating the effectiveness of the proposed modelling and optimization framework.

[1]  Nicholas Fantuzzi,et al.  Effect of agglomeration on the natural frequencies of functionally graded carbon nanotube-reinforced laminated composite doubly-curved shells , 2016 .

[2]  Yuanming Xu,et al.  Study on the thermal buckling and post-buckling of metallic sub-stiffening structure and its optimization , 2016 .

[3]  Peng Hao,et al.  A hybrid descent mean value for accurate and efficient performance measure approach of reliability-based design optimization , 2018, Computer Methods in Applied Mechanics and Engineering.

[4]  C. Hühne,et al.  Robust knockdown factors for the design of spherical shells under external pressure: Development and validation , 2018, International Journal of Mechanical Sciences.

[5]  Antonio Tomás,et al.  The influence of initial geometric imperfections on the buckling load of single and double curvature concrete shells , 2012 .

[6]  Bo Wang,et al.  Efficient Optimization of Cylindrical Stiffened Shells with Reinforced Cutouts by Curvilinear Stiffeners , 2016 .

[7]  Peng Hao,et al.  Optimum design of aircraft panels based on adaptive dynamic harmony search , 2017 .

[8]  C. Lee,et al.  Subsonic diffuser design and performance for advanced fighter aircraft , 1985 .

[9]  Shuo Ding,et al.  A MATLAB-Based Study on the Realization and Approximation Performance of RBF Neural Networks , 2013 .

[10]  Zhifeng Liu,et al.  Stiffness design of machine tool structures by a biologically inspired topology optimization method , 2014 .

[11]  Rakesh K. Kapania,et al.  EBF3PanelOpt: An optimization framework for curvilinear blade-stiffened panels , 2013 .

[12]  Dan Wang,et al.  Global and local buckling analysis of grid-stiffened composite panels , 2015 .

[13]  C. Hühne,et al.  Geometric imperfection and lower-bound analysis of spherical shells under external pressure , 2019, Thin-Walled Structures.

[14]  Fan Yang,et al.  Optimal design of hierarchical grid-stiffened cylindrical shell structures based on linear buckling and nonlinear collapse analyses , 2017 .

[15]  Dan Wang,et al.  A parametric mapping method for curve shape optimization on 3D panel structures , 2010 .

[16]  Lei Li,et al.  Reliability based multidisciplinary design optimization of cooling turbine blade considering uncertainty data statistics , 2018, Structural and Multidisciplinary Optimization.

[17]  Daining Fang,et al.  Fabrication and testing of composite orthogrid sandwich cylinder , 2017 .

[18]  Bo Wang,et al.  Numerical-based smeared stiffener method for global buckling analysis of grid-stiffened composite cylindrical shells , 2016 .

[19]  Rakesh K. Kapania,et al.  Vibration Analysis of Curvilinearly Stiffened Composite Panel Subjected to In-Plane Loads , 2017 .

[20]  R. Kapania,et al.  Free Vibration Analysis of Curvilinearly Stiffened Cylindrical Shells , 2015 .

[21]  Ke Zhang,et al.  Tailoring the optimal load-carrying efficiency of hierarchical stiffened shells by competitive sampling , 2018, Thin-Walled Structures.

[22]  Wang Zhanxue,et al.  Influences of Design Parameters on a Double Serpentine Convergent Nozzle , 2016 .

[23]  Christian B. Allen,et al.  Efficient mesh motion using radial basis functions with data reduction algorithms , 2008, J. Comput. Phys..

[24]  Dan Wang,et al.  Streamline stiffener path optimization (SSPO) for embedded stiffener layout design of non-uniform curved grid-stiffened composite (NCGC) structures , 2019, Computer Methods in Applied Mechanics and Engineering.

[25]  J. Batina.  Unsteady Euler airfoil solutions using unstructured dynamic meshes , 1989 .

[26]  Weihong Zhang,et al.  A bispace parameterization method for shape optimization of thin‐walled curved shell structures with openings , 2012 .

[27]  D. Fang,et al.  A novel hierarchical thermoplastic composite honeycomb cylindrical structure: Fabrication and axial compressive properties , 2018, Composites Science and Technology.

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

[29]  Nima Amjady,et al.  Short-term load forecast of electrical power system by radial basis function neural network and new stochastic search algorithm , 2016 .

[30]  Zhou Quan,et al.  RBF Neural Network and ANFIS-Based Short-Term Load Forecasting Approach in Real-Time Price Environment , 2008, IEEE Transactions on Power Systems.

[31]  Ning Qin,et al.  Fast dynamic grid deformation based on Delaunay graph mapping , 2006 .

[32]  G. Rahimi,et al.  Analysis of the effect of stiffener profile on buckling strength in composite isogrid stiffened shell under axial loading , 2013 .

[33]  Ramana V. Grandhi,et al.  Thermal-Structural Analysis of Engine Exhaust-Washed Structures , 2010 .

[34]  Li Zhou,et al.  Influences of shield ratio on the infrared signature of serpentine nozzle , 2017 .

[35]  Hao Wu,et al.  Carbon fiber reinforced hierarchical orthogrid stiffened cylinder: Fabrication and testing , 2018 .

[36]  Min Xiong,et al.  Optimal stiffener layout of plate/shell structures by bionic growth method , 2014 .

[37]  Chao Hu,et al.  Sequential exploration-exploitation with dynamic trade-off for efficient reliability analysis of complex engineered systems , 2017 .

[38]  Bret Stanford,et al.  Aeroelastic Topology Optimization of Blade-Stiffened Panels , 2013 .

[39]  Gang Li,et al.  Fast procedure for Non-uniform optimum design of stiffened shells under buckling constraint , 2017 .

[40]  Lei Li,et al.  Multidisciplinary Design Optimization Based on Parameterized Free-Form Deformation for Single Turbine , 2019, AIAA Journal.

[41]  Esther Andrés-Pérez,et al.  A novel surface mesh deformation method for handling wing-fuselage intersections , 2017 .

[42]  Chris Lacor,et al.  Robust parameter design optimization using Kriging, RBF and RBFNN with gradient-based and evolutionary optimization techniques , 2014, Appl. Math. Comput..

[43]  S. Pellegrino,et al.  Imperfection-insensitive axially loaded thin cylindrical shells , 2015 .

[44]  Gang Wang,et al.  Mesh deformation on 3D complex configurations using multistep radial basis functions interpolation , 2018 .

[45]  Yang Liu,et al.  Non-parametric shape optimization method for natural vibration design of stiffened shells , 2015 .

[46]  Rakesh K. Kapania,et al.  Free Vibration of Curvilinearly Stiffened Shallow Shells , 2013 .

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

[48]  D. Fang,et al.  Fabrication and testing of composite hierarchical Isogrid stiffened cylinder , 2018 .

[49]  Donald R. Jones,et al.  Efficient Global Optimization of Expensive Black-Box Functions , 1998, J. Glob. Optim..

[50]  Peng Hao,et al.  Improved reliability-based design optimization of non-uniformly stiffened spherical dome , 2019, Structural and Multidisciplinary Optimization.

[51]  Bo Wang,et al.  Generatrix shape optimization of stiffened shells for low imperfection sensitivity , 2014 .

[52]  Peng Hao,et al.  Enhanced single-loop method for efficient reliability-based design optimization with complex constraints , 2018 .