Some specific aspects of linear homogenization shell theory

Abstract

In this paper we propose a multiscale linear shell theory for simulating the mechanical response of a highly heterogeneous shell of varying thickness. To resolve this issue, a higher-order stress-resultant shell formulation based on multiscale homogenization is considered. At the macroscopic scale level, we approximate the displacement field by a fourth-order Taylor–Young expansion in thickness. The transition between both the microscopic and the macroscopic scales is obtained through the introduction of a specific Hill–Mandel condition. Since we adopt the standard assumption of small strain which is used in linear elasticity, we can present a variant of the homogenization scheme which is valid for small strain. The nonlinearity of the previous model occurs from the assumption of large rotation of the transverse normal.