Recent Achievements in Constitutive Equations of Laminates and Functionally Graded Structures Formulated in the Resultant Nonlinear Shell Theory

  • Stanisław Burzyński
  • Jacek Chróścielewski
  • Karol DaszkiewiczEmail author
  • Agnieszka Sabik
  • Bartosz Sobczyk
  • Wojciech Witkowski
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 110)


The development of constitutive equations formulated in the resultant nonlinear shell theory is presented. The specific features of the present shell theory are drilling rotation naturally included in the formulation and asymmetric measures of strains and stress resultants. The special attention in the chapter is given to recent achievements: progressive failure analysis of laminated shells and elastoplastic constitutive relation for shells made of functionally graded material (FGM). The modified Hashin criterion is used to estimate failure initiation in laminates and stiffness degradation approach in the last ply failure computations. The numerical results obtained for axially compressed C-shaped column are compared with experimental load-deflection curve. The Cosserat plane stress assumption, Tamura-Tomota-Ozawa (TTO) model and improved method of shear correction factor calculation are applied in the elastoplastic constitutive relation for FGM shell. The proposed formulation is tested in numerical examples: rectangular compressed plate and channel section clamped beam. The influence of TTO model parameters and Cosserat characteristic length is investigated.



The research reported in this paper was supported by the National Science Centre, Poland with the grant UMO-2015/17/B/ST8/02190. Parallel solver for CAM elements is developed on the basis of HSL, a collection of Fortran codes for large-scale scientific computation. Abaqus calculations were carried out at the Academic Computer Centre in Gdańsk.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Stanisław Burzyński
    • 1
  • Jacek Chróścielewski
    • 1
  • Karol Daszkiewicz
    • 1
    Email author
  • Agnieszka Sabik
    • 1
  • Bartosz Sobczyk
    • 1
  • Wojciech Witkowski
    • 1
  1. 1.Faculty of Civil and Environmental Engineering, Department of Mechanics of Materials and StructuresGdansk University of TechnologyGdańskPoland

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