An improved multiscale finite element method for nonlinear bending analysis of stiffened composite structures

Abstract

Stiffened composite structures are commonly composed of skins and stiffeners that are employed to transfer and carry load, respectively. An improved multiscale finite element method is presented for geometrically nonlinear bending analysis of composite grid stiffened laminates. In the developed method, two kinds of strategies for establishing stiffened multiscale models are presented, in which the stiffeners are modeled at different scale. By introducing a virtual degree of freedom and additional coupling terms, multiscale base functions are improved to consider the local effects of stiffeners and coupling effects of composites. To construct the multiscale base functions of stiffened multiscale models, an extended displacement boundary conditions are constructed, in which the displacements of stiffeners are imposed constraints based on the displacement continuous conditions between skin and stiffener. Incremental multiscale finite element formulations are derived based on Total-Lagrange description and von Karman's large deflection plate theory. The incremental displacement boundary conditions are constructed to consider the effect of microscopic unbalanced force on microscopic results. Numerical examples show high efficiency and applicability of the developed method for composite grid stiffened laminates. KEYWORDS displacement boundary conditions, geometrically nonlinear bending analysis, multiscale base functions, multiscale finite element method, stiffened composite structures, stiffened multiscale models Int J Numer Methods Eng. 2019;118:459-481.wileyonlinelibrary.com/journal/nme