Shell and Membrane Theories in Mechanics and Biology pp 147-154

Part of the Advanced Structured Materials book series (STRUCTMAT, volume 45) | Cite as

On the Direct Approach in the Theory of Second Gradient Plates



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.


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© 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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