Adjoint design sensitivity analysis of dynamic crack propagation using peridynamic theory

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• 作者：Min-Yeong Moon (1)
  Jae-Hyun Kim (2)
  Youn Doh Ha (3)
  Seonho Cho (2)
  
  1. Department of Mechanical and Industrial Engineering ; University of Iowa ; Iowa City ; Iowa ; USA
  2. Seoul National University ; Seoul ; Republic of Korea
  3. Kunsan National University ; Kunsan ; Republic of Korea
  
• 关键词：Peridynamic theory ; Dynamic crack propagation ; Adjoint variable method ; Design sensitivity analysis ; Path dependent problem ; Parallel computation
• 刊名：Structural and Multidisciplinary Optimization
• 出版年：2015
• 出版时间：March 2015
• 年：2015
• 卷：51
• 期：3
• 页码：585-598
• 全文大小：1,195 KB
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• 刊物类别：Engineering
• 刊物主题：Theoretical and Applied Mechanics
  Computer-Aided Engineering and Design
  Numerical and Computational Methods in Engineering
  Engineering Design
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1615-1488

文摘

Based on the peridynamics of the reformulated continuum theory, an adjoint design sensitivity analysis (DSA) method is developed for the solution of dynamic crack propagation problems using the explicit scheme of time integration. Non-shape DSA problems are considered for the dynamic crack propagation including the successive branching of cracks. The adjoint variable method is generally suitable for path-independent problems but employed in this bond-based peridynamics since its path is readily available. Since both original and adjoint systems possess time-reversal symmetry, the trajectories of systems are symmetric about the u-axis. We take advantage of the time-reversal symmetry for the efficient and concurrent computation of original and adjoint systems. Also, to improve the numerical efficiency of large scale problems, a parallel computation scheme is employed using a binary space decomposition method. The accuracy of analytical design sensitivity is verified by comparing it with the finite difference one. The finite difference method is susceptible to the amount of design perturbations and could result in inaccurate design sensitivity for highly nonlinear peridynamics problems with respect to the design. It is demonstrated that the peridynamic adjoint sensitivity involving history-dependent variables can be accurate only if the path of the adjoint response analysis is identical to that of the original response.