Minimization of maximum failure criterion of laminated composite shell structure by optimizing distributed-material orie
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RESEARCH PAPER
Minimization of maximum failure criterion of laminated composite shell structure by optimizing distributed-material orientation Masatoshi Shimoda 1
&
Yoshiaki Muramatsu 2 & Ryosuke Tsukihara 1
Received: 13 May 2019 / Revised: 15 October 2019 / Accepted: 15 October 2019 / Published online: 29 February 2020 # Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract In this study, we propose a distributed-parameter optimization method for the material-orientation design aiming at maximizing the strength of a laminated composite shell structure with anisotropic material, which is homogenized based on a laminate theory. The modified Tsai–Hill criterion is employed as a failure criterion in this study, and its maximum value is minimized with the state equation constraint. The issue of non-differentiability inherent in this min–max problem is avoided by transforming the singular local measure to a smooth differentiable integral functional using the Kreisselmeier–Steinhauser function. The optimum design problem is formulated as a distributed-parameter optimization problem, and the sensitivity function with respect to the material-orientation variation is theoretically derived based on a variational method. The optimal material-orientation variation is determined using the H1 gradient method with Poisson’s equation proposed by the authors, where the sensitivity function are applied as Robin condition to vary and optimize the material-orientation distribution. We transfer the sensitivity function to the internal heat generation and determine the material-orientation variation using Poisson’s equation to ensure continuous distribution of material orientation. The optimum design examples show that the proposed optimization method can effectively and efficiently obtain the optimum material orientation with the smooth curvilinear distribution and minimize the maximum strength measured by a failure criterion. Keywords Laminated shell structures . Material orientation . Optimization . Tsai–Hill failure criterion . Strength design . H1 gradient method
1 Introduction Laminated composite shell structures are used in a variety of industrial products and structures, especially in vehicles for their lightweight design, where the usage of carbon-fiberreinforced plastics (CFRP) in shell structures has been increasing, since they have higher specific mechanical performances compared to metals. Moreover, “Automated fiber placement Responsible Editor: Helder C. Rodrigues * Masatoshi Shimoda [email protected] 1
Department of Advanced Science and Technology, Toyota Technological Institute, 2-12-1 Hisakata, Tenpaku-ku, Nagoya, Aichi 468-8511, Japan
2
Department of Advanced Science and Technology, Graduate School of Engineering, Toyota Technological Institute, 2-12-1 Hisakata, Tenpaku-ku, Nagoya, Aichi 468-8511, Japan
(AFP)” has enabled the manufacture of curvilinear-distributed material orientation, which can derive out their potential and improve the structural performances. Previously, the authors (Mura
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