On the isogeometric analysis of geometrically nonlinear shell structures with the consideration of surface energies
Faculty of Mechanical Engineering, University of Guilan, P.O. Box 3756, Rasht, Iran
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Accepted: 30 January 2020
Published online: 19 February 2020
Presented in this article is a size-dependent analysis which is aimed to discover the surface stress effects on the large deformation characteristics of small-scaled shell structures. Consideration of surface energies in the micro/nanodimensions, and also in the cases of structures with high ratios of surface to volume like shells, significantly affects the predicted responses. To take the surface stress effects into account, it is assumed that the body is surrounded by thin surface layers at the top and bottom. The first-order shear deformation shell theory with seven parameters is adopted in the Lagrangian configuration system for the bulk part of structure. Also, the effects of surface stresses are captured based on the surface elasticity theory. Because of its unique features, IGA (isogeometric analysis) solution methodology is implemented to solve the governing equations. In this regard, the matrix–vector form of nonlinear relations, including the constitutive equations and energy functionals, is presented to directly utilize IGA for the problem. As case studies and also to show the main contribution of present investigation, i.e., studying the effects of surface energies on the mechanical behavior of geometrically nonlinear shells, the well-known benchmarks in the literature are studied in micro/nanodimensions with the consideration of surface influences.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature, 2020