A shell theory with scale effects and higher order gradients

作者：Sansour C^*; Skatulla S; Hjiaj M

来源：International Journal of Solids and Structures, 2013, 50(14-15): 2271-2280.

DOI：10.1016/j.ijsolstr.2013.03.031

• Shell theory
• Scale effects
• Generalised continua
• Strain gradient theory

This works follows a generalised continuum framework developed by Sansour (1998) to derive a strain gradient formulation suitable to address scale effects of structures where one dimension is very small (e.g. thin films, nano tubes etc.). Whereas a previous strain gradient approach by Sansour et al. (2009) considered the fully three-dimensional setting, the approach here proposes a shell theory which aims to run computations of thin structures more efficiently and to include scale effects. The theory features a generalised deformation description, new strain and stress measures. As consequence of these new quantities a corresponding generalised variational principle is formulated. The approach is completed by Dirichlet boundary conditions for the displacement field and its derivatives. A numerical example is presented based on a meshfree formulation which provides the necessary C-1 continuity.

• 出版日期2013-7