4.7 Article

Accurate equilibrium-based interlaminar stress recovery for isogeometric laminated composite Kirchhoff plates

Journal

COMPOSITE STRUCTURES
Volume 256, Issue -, Pages -

Publisher

ELSEVIER SCI LTD
DOI: 10.1016/j.compstruct.2020.112976

Keywords

Kirchhoff plates; B-Splines; Isogeometric analysis; Collocation methods; Stress recovery procedure; Equilibrium

Funding

  1. Ministero dell'Istruzione, dell'Universita e della Ricerca through the project XFAST-SIMS: Extra fast and accurate simulation of complex structural systems, within the program Progetti di ricerca di Rilevante Interesse Nazionale (PRIN)
  2. European Research Council through the H2020 ERC Advanced Grant 2015 [694515 CHANGE]
  3. Swiss National Science Foundation through the project Design-through-Analysis (of PDEs): the litmus test [40B2-0 187094]
  4. European Research Council through the H2020 ERC Consolidator Grant 2019 [864482 FDM2]
  5. Swiss National Science Foundation (SNF) [40B2-0_187094] Funding Source: Swiss National Science Foundation (SNF)

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This paper introduces a fast and accurate stress recovery strategy for modeling the out-of-plane behavior of Kirchhoff laminated plates. The method is a two-step approach that utilizes classical composite plates theory followed by isogeometric analysis to recover out-of-plane stresses, with the effectiveness proven through extensive numerical tests.
Despite the accelerated deployment of laminated composites in a wide variety of markets due to their peculiar engineering features, the design of those materials is often restrained by the lack of cost-efficient modeling techniques. In fact, the existing strategies allowing for cheap simulations usually fail to directly capture out of-plane through-the-thickness stresses, which prove to be typically responsible of delamination failure modes. In this paper, we introduce a fast and accurate stress recovery strategy to model the out-of-plane behavior of Kirchhoff laminated plates. The proposed technique can be regarded as a two-step approach: First, the classical composite plates theory, providing the lowest computational cost among known literature strategies, is applied to obtain a coarse displacement solution; afterwards, this solution is used to compute the necessary in-plane derivatives to recover the out-of-plane stresses directly imposing equilibrium in strong form. Since this a posteriori step relies on high-order in-plane continuity requirements, isogeometric analysis (IGA) represents a natural simulation framework given its accuracy and higher continuity properties. Both isogeometric Galerkin and collocation formulations are herein considered. The effectiveness of the proposed approach is proven by extensive numerical tests.

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