Recent Developments in Anisotropic Heterogeneous Shell Theory

Applications of Refined and Three-dimensional Theory—Volume IIA

  • Alexander Ya. Grigorenko
  • Wolfgang H. Müller
  • Yaroslav M. Grigorenko
  • Georgii G. Vlaikov

Part of the SpringerBriefs in Applied Sciences and Technology book series (BRIEFSAPPLSCIENCES)

Also part of the SpringerBriefs in Continuum Mechanics book sub series (BRIEFSCONTINU)

Table of contents

  1. Front Matter
    Pages i-vii
  2. Alexander Ya. Grigorenko, Wolfgang H. Müller, Yaroslav M. Grigorenko, Georgii G. Vlaikov
    Pages 1-42

About this book


This brief book presents solutions of stress-strain problems for a wide class of anisotropic inhomogeneous shells obtained by the refined model. Studying these problems results in severe computational difficulties due to partial differential equations with variable coefficients resulting from the constitutive relations of the original model. To solve this problem the book uses spline-collocation and discrete-orthogonalization methods. It analyses the influence of geometrical and mechanical parameters, of various kinds of boundary conditions, and of the loading conditions on the distributions of stress and displacement fields in shallow, spherical, conical, and noncircular cylindrical shells. The dependence of the stress-strain pattern on shell thickness variations is studied. The authors solve the problem also for the case of the thickness varying in two directions. They study how a variation in shell thickness influences the stress-strain state and consider noncircular cylindrical shells with elliptical and corrugated sections are considered. The results obtained during numerous calculations support the efficiency of the discrete-orthogonalization approach proposed in the monograph for solving static problems for anisotropic inhomogeneous shells when using the refined model.


Refined Shell Theory 3D Elasticity Theory Anisotropy Nonhomogeneity Stress-Strain State Free Vibrations of Shells Cylindrical Shells Noncircular Cylindrical Shells Shallow Shells Conical Shells Spherical Shells Functionally Graded Shells Finite-Length Cylinders

Authors and affiliations

  • Alexander Ya. Grigorenko
    • 1
  • Wolfgang H. Müller
    • 2
  • Yaroslav M. Grigorenko
    • 3
  • Georgii G. Vlaikov
    • 4
  1. 1.National Academy of Sciences of UkraineS.P. Timoshenko Institute of MechanicsKievUkraine
  2. 2.Technische Universität BerlinInstitut für MechanikBerlinGermany
  3. 3.National Academy of Sciences of UkraineS.P. Timoshenko Institute of MechanicsKievUkraine
  4. 4.National Academy Sciences of UkraineTechnical CenterKievUkraine

Bibliographic information

  • DOI
  • Copyright Information The Author(s) 2016
  • Publisher Name Springer, Singapore
  • eBook Packages Engineering Engineering (R0)
  • Print ISBN 978-981-10-0644-9
  • Online ISBN 978-981-10-0645-6
  • Series Print ISSN 2191-530X
  • Series Online ISSN 2191-5318
  • Buy this book on publisher's site