A Koiter reduction technique for the nonlinear thermoelastic analysis of shell structures prone to buckling

The multi-modal Koiter method is a reduction technique for estimating quickly the nonlinear buckling response of structures under mechanical loads requiring a fine discretization. The reduced model is based on a quadratic approximation of the full model using a few linear buckling modes and their second order corrections, followed by the projection of the equilibrium equations onto the modal subspace. In this article, the method is reformulated for geometrically nonlinear thermoelastic analyses of shell structures. The starting point is an isogeometric solid-shell discretization with an accurate modeling of thermal strains, temperature-dependent materials and general temperature distributions. The equilibrium path is defined as a displacement versus temperature amplifier curve, while mechanical loads are kept constant. The strain energy nonlinearity with respect to the temperature amplifier is the main obstacle in the definition of an accurate reduced model. This task is achieved by coherent asymptotic expansions in mixed form using independent stress variables at the integration points and accurate linear buckling modes obtained by a two-point mixed eigenvalue problem. Structures made of isotropic and multi-layered composite materials, including variable angle tow laminates, are considered to show the accuracy of the proposed method.