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

Victor Eremeev

doi:10.1007/978-3-030-11665-1_10

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

Abstract

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.

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Victor Eremeev prof. dr hab.

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Category:: Monographic publication
Type:: rozdział, artykuł w książce - dziele zbiorowym /podręczniku w języku o zasięgu międzynarodowym
Title of issue:: Dynamical Processes in Generalized Continua and Structures strony 195 - 207
Language:: English
Publication year:: 2019
Bibliographic description:: Eremeev V.: On Dynamic Boundary Conditions Within the Linear Steigmann-Ogden Model of Surface Elasticity and Strain Gradient Elasticity// Dynamical Processes in Generalized Continua and Structures/ ed. Altenbach H., Belyaev A., Eremeyev V., Krivtsov A., Porubov A. Cham: Springer, 2019, s.195-207
DOI:: Digital Object Identifier (open in new tab) 10.1007/978-3-030-11665-1_10
Verified by:: Gdańsk University of Technology