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Patch based stress recovery for plate structures

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Abstract

In this paper we address the application of recovery procedures in advanced problems in structural mechanics. The attention is focused on the recovery by compatibility in patches procedure (RCP) and shear deformable plate structures. The formulation of RCP procedure is extended to shear deformable plate problems (Reissner–Mindlin theory) and is applied to recover stresses from mixed and hybrid stress finite elements. These elements offer new possibilities, for recovery procedures in general, which deserve to be discussed. A comprehensive investigation on which finite element solution can be used as input for the recovery procedures is given through standard benchmark problems, obtained for several values of the thickness on structured and unstructured meshes. The numerical results confirm the effectiveness of the recovery procedure extended to plates problems.

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References

  1. Alfano G, Auricchio F, Rosati L, Sacco E (2001) MITC finite elements for laminated composite plates. Int J Numer Methods Eng 50(3): 707–738

    Article  MATH  Google Scholar 

  2. Auricchio F, Sacco E, Vairo G (2006) A mixed FSDT finite element for monoclinic laminated plates. Comput Struct 84(8–9): 624–639

    Article  Google Scholar 

  3. Auricchio F, Taylor R (1994) A shear deformable plate element with an exact thin limit. Comput Methods Appl Mech Eng 118(3–4): 393–412

    Article  MATH  MathSciNet  Google Scholar 

  4. Benedetti A, de Miranda S, Ubertini F (2006) A posteriori error estimation based on the superconvergent recovery by compatibility in patches. Int J Numer Methods Eng 67(1): 108–131

    Article  MATH  Google Scholar 

  5. Boroomand B, Ghaffarian M, Zienkiewicz OC (2004) On application of two superconvergent recovery procedures to plate problems. Int J Numer Methods Eng 61(10): 1644–1673

    Article  MATH  MathSciNet  Google Scholar 

  6. Castellazzi G, Krysl P (2009) Displacement-based finite elements with nodal integration for Reissner-Mindlin plates. Int J Numer Methods Eng 80(2): 135–162

    Article  MATH  MathSciNet  Google Scholar 

  7. Castellazzi G, de Miranda S, Ubertini F (2010) Adaptivity based on the recovery by compatibility in patches. Finite Elem Anal Des 46(5): 379–390

    Article  Google Scholar 

  8. Crisfield MA (1984) A quadratic mindlin element using shear constraints. Comput Struct 18(5): 833–852

    Article  MATH  Google Scholar 

  9. Daghia F, de Miranda S, Ubertini F, Viola E (2008) A hybrid stress approach for laminated composite plates within the first-order shear deformation theory. Int J Solids Struct 45(6): 1766–1787

    MATH  Google Scholar 

  10. Dobyns AL (1981) Analysis of simply-supported orthotropic plates subject to static and dynamic loads. AIAA J 19: 642–650

    Article  MATH  Google Scholar 

  11. de Miranda S, Ubertini F (2006) A simple hybrid stress element for shear deformable plates. Int J Numer Methods Eng 65(6): 808–833

    Article  MATH  Google Scholar 

  12. Tessler A, Hughes TJR (1983) An improved treatment of transverse shear in the mindlin-type four-node quadrilateral element. Comput Methods Appl Mech Eng 39(3): 311–335

    Article  MATH  Google Scholar 

  13. Timoshenko SP (1964) Theory of plates and shells, 2 edn. McGraw-Hill Higher Education, New York

    Google Scholar 

  14. Ubertini F (2004) Patch recovery based on complementary energy. Int J Numer Methods Eng 59(11): 1501–1538

    Article  MATH  Google Scholar 

  15. Yuan K, Huang Y, Pian THH (1993) New strategy for assumed stresses for 4-node hybrid stress membrane element. Int J Numer Methods Eng 36(10): 1747–1763

    Article  MATH  Google Scholar 

  16. Zienkiewicz OC, Zhu JZ (1992) The superconvergent patch recovery and a posteriori error estimates. Part 1: the recovery technique. Int J Numer Methods Eng 33(7): 1331–1364

    Article  MATH  MathSciNet  Google Scholar 

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Correspondence to G. Castellazzi.

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Castellazzi, G., de Miranda, S. & Ubertini, F. Patch based stress recovery for plate structures. Comput Mech 47, 379–394 (2011). https://doi.org/10.1007/s00466-010-0548-3

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  • DOI: https://doi.org/10.1007/s00466-010-0548-3

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