On the Direct Approach in the Theory of Second Gradient Plates

  • Victor A. EremeyevEmail author
  • Holm Altenbach
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 45)


The aim of the paper is to formulate the two-dimensional governing equations in the theory of elastic second gradient plates, that is plates which constitutive equations include second gradients of strain and/or stress measures. Here we use so-called direct approach to modeling of plates and shells. According to the approach a plate is considered as a material deformed surface and all equations are written as for two-dimensional continuum. Here we use the six-parameter theory of shells.Within the framework of the six-parameter theory the kinematics of a shell is described by two independent fields of translations and rotations. We introduce the linear constitutive equations of six-parameter second gradient plates. Considering a deflection of a plate we discuss peculiarities of these models.


Constitutive Equation Surface Stress Gradient Theory Gradient Elasticity Isotropic Shell 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The first author was supported by the RFBR with the grant No. 12-01-00038


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Lehrstuhl für Technische MechanikInstitut für Mechanik, Fakultät für Maschinenbau, Otto-von-Guericke-Universität MagdeburgMagdeburgGermany
  2. 2.Southern Scientific Center of Russian Academy of ScienceSouth Federal UniversityRostov-on-DonRussia

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