On Dynamic Boundary Conditions Within the Linear Steigmann-Ogden Model of Surface Elasticity and Strain Gradient Elasticity

  • Victor A. EremeyevEmail author
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 103)


Within the strain gradient elasticity we discuss the dynamic boundary conditions taking into account surface stresses described by the Steigmann–Ogden model. The variational approach is applied with the use of the least action functional. The functional is represented as a sum of surface and volume integrals. The surface strain and kinetic energy densities are introduced. The Toupin–Mindlin formulation of the strain gradient elasticity is considered. As a result, we derived the motion equations and the natural boundary conditions which include inertia terms.



Authors acknowledges financial support from the Russian Science Foundation under the grant “Methods of microstructural nonlinear analysis, wave dynamics and mechanics of composites for research and design of modern metamaterials and elements of structures made on its base” (No 15-19-10008-P).


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Authors and Affiliations

  1. 1.Faculty of Civil and Environmental EngineeringGdańsk University of TechnologyGdańskPoland
  2. 2.Institute of Mathematics, Mechanics and Computer ScienceSouthern Federal UniversityRostov-on-DonRussia

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