An efficient online successive reanalysis method for dynamic topology optimization

In this study, an efficient reanalysis strategy for dynamic topology optimization is proposed. Compared with other related studies, an online successive dynamic reanalysis method and POD-based approximate dynamic displacement strategy are integrated. In dynamic reanalysis, the storage of the stiffness matrix decomposition can be avoided and the reduced basis vectors should be updated successively according to the structural status in each iteration. Therefore, the bottleneck of combined approximation method for large-scale dynamic topology optimization can be handled. Sequentially, the Proper Orthogonal Decomposition (POD) is employed to obtain the approximate dynamic displacement, in which the Proper Orthogonal Mode (POM) of the displacement field is employed to establish the approximated equivalent static loads of Equivalent Static Load (ESL) method. Compared with the exact equivalent static loads at all the time intervals, the number of equivalent static loads is significantly reduced. Finally, the 2D and 3D test results indicate that the proposed method has remarkable speed-up effect on the premise of small relative error, support the strength of the proposed strategy.

[1]  Ji-Cheng Yin,et al.  A Multigrid Assisted Reanalysis Method for Accelerated Heat Transfer Topology Optimization , 2023, Applied Mathematical Modelling.

[2]  Yaya Zhang,et al.  A novel reduced basis method for adjoint sensitivity analysis of dynamic topology optimization , 2023, Engineering Analysis with Boundary Elements.

[3]  Hu Wang,et al.  An efficient coupling reduction model-based evolutionary topology optimization method , 2023, Adv. Eng. Softw..

[4]  Christian Duriez,et al.  Real-Time Simulation for Control of Soft Robots With Self-Collisions Using Model Order Reduction for Contact Forces , 2021, IEEE Robotics and Automation Letters.

[5]  Jingjie He,et al.  Topology optimization of vibrating structures with frequency band constraints , 2020, Structural and Multidisciplinary Optimization.

[6]  Piotr Breitkopf,et al.  Multi-grid reduced-order topology optimization , 2020, Structural and Multidisciplinary Optimization.

[7]  Enying Li,et al.  An efficient auxiliary projection‐based multigrid isogeometric reanalysis method and its application in an optimization framework , 2020, International Journal for Numerical Methods in Engineering.

[8]  Piotr Breitkopf,et al.  On-the-fly model reduction for large-scale structural topology optimization using principal components analysis , 2020, Structural and Multidisciplinary Optimization.

[9]  P. Breitkopf,et al.  On-the-fly model reduction for large-scale structural topology optimization using principal components analysis , 2020, Structural and Multidisciplinary Optimization.

[10]  Hu Wang,et al.  A novel dynamic isogeometric reanalysis method and its application in closed-loop optimization problems , 2019, Computer Methods in Applied Mechanics and Engineering.

[11]  Shutian Liu,et al.  Topology optimization for minimizing the maximum temperature of transient heat conduction structure , 2019, Structural and Multidisciplinary Optimization.

[12]  Shutian Liu,et al.  Topology optimization for minimizing the maximum temperature of transient heat conduction structure , 2019, Structural and Multidisciplinary Optimization.

[13]  Cheol Kim,et al.  Topology optimization for crashworthiness of thin-walled structures under axial crash considering nonlinear plastic buckling and locations of plastic hinges , 2018, Engineering Optimization.

[14]  Maenghyo Cho,et al.  Efficient design optimization strategy for structural dynamic systems using a reduced basis method combined with an equivalent static load , 2018 .

[15]  M. Cho,et al.  Efficient design optimization strategy for structural dynamic systems using a reduced basis method combined with an equivalent static load , 2018, Structural and Multidisciplinary Optimization.

[16]  Scott T. M. Dawson,et al.  Modal analysis of fluid flows using variants of proper orthogonal decomposition , 2017 .

[17]  Muhammad Abid,et al.  Nonlinear response topology optimization using equivalent static loads—case studies , 2017 .

[18]  Pedro Díez,et al.  An error estimator for real-time simulators based on model order reduction , 2015, Adv. Model. Simul. Eng. Sci..

[19]  F. Chinesta,et al.  An error estimator for real-time simulators based on model order reduction , 2015, Advanced Modeling and Simulation in Engineering Sciences.

[20]  J. Hesthaven,et al.  Certified Reduced Basis Methods for Parametrized Partial Differential Equations , 2015 .

[21]  Kai A. James,et al.  Topology optimization of viscoelastic structures using a time-dependent adjoint method , 2015 .

[22]  Gianluigi Rozza,et al.  Reduced Order Methods for Modeling and Computational Reduction , 2013 .

[23]  O. Sigmund,et al.  Topology optimization approaches , 2013, Structural and Multidisciplinary Optimization.

[24]  Guangyao Li,et al.  An adaptive time-based global method for dynamic reanalysis , 2013 .

[25]  B. Li,et al.  Shift-Relaxation Combined Approximations Method for Structural Vibration Reanalysis of Near Defective Systems , 2013 .

[26]  Serkan Gugercin,et al.  H2 Model Reduction for Large-Scale Linear Dynamical Systems , 2008, SIAM J. Matrix Anal. Appl..

[27]  Jakob S. Jensen,et al.  On maximal eigenfrequency separation in two-material structures: the 1D and 2D scalar cases , 2006 .

[28]  Athanasios C. Antoulas,et al.  Approximation of Large-Scale Dynamical Systems , 2005, Advances in Design and Control.

[29]  Ahsan Kareem,et al.  Proper Orthogonal Decomposition-Based Modeling, Analysis, and Simulation of Dynamic Wind Load Effects on Structures , 2005 .

[30]  H. P. Lee,et al.  PROPER ORTHOGONAL DECOMPOSITION AND ITS APPLICATIONS—PART I: THEORY , 2002 .

[31]  Gyung-Jin Park,et al.  Structural optimization using equivalent static loads at all time intervals , 2002 .

[32]  Raphael T. Haftka,et al.  Fast exact linear and non‐linear structural reanalysis and the Sherman–Morrison–Woodbury formulas , 2001 .

[33]  Y. Tamura,et al.  PROPER ORTHOGONAL DECOMPOSITION OF RANDOM WIND PRESSURE FIELD , 1999 .

[34]  Gyung-Jin Park,et al.  Transformation of dynamic loads into equivalent static loads based on modal analysis , 1999 .

[35]  N. Kikuchi,et al.  Structural design for obtaining desired eigenfrequencies by using the topology and shape optimization method , 1994 .

[36]  N. Kikuchi,et al.  Solutions to shape and topology eigenvalue optimization problems using a homogenization method , 1992 .

[37]  M. Zhou,et al.  The COC algorithm, Part II: Topological, geometrical and generalized shape optimization , 1991 .

[38]  M. Bendsøe.  Optimal shape design as a material distribution problem , 1989 .

[39]  Uri Kirsch,et al.  Approximate structural reanalysis based on series expansion , 1981 .

[40]  Dirk Hartmann,et al.  Model Order Reduction a Key Technology for Digital Twins , 2018 .

[41]  M. Diez,et al.  Design-space dimensionality reduction in shape optimization by Karhunen–Loève expansion , 2015 .

[42]  Gianluigi Rozza,et al.  Model Order Reduction in Fluid Dynamics: Challenges and Perspectives , 2014 .

[43]  Guanxin Huang,et al.  Modified Combined Approximations and the Application in Reanalysis of Vehicle Frame Stiffness , 2011 .

[44]  Uri Kirsch,et al.  Reanalysis and sensitivity reanalysis by combined approximations , 2009 .

[45]  A. Chatterjee.  An introduction to the proper orthogonal decomposition , 2000 .