Nonlinear thermoelastic analysis of shell structures: solid-shell modelling and high-performing continuation method

This work presents a cost-effective and reliable numerical framework for geometrically nonlinear thermoelastic analyses of thin-walled structures. Firstly, the structure is discretised using an isogeometric solid-shell formulation, that allows an accurate approximation of geometry and kinematics avoiding the parameterisation of finite rotations. Focus is given to an efficient modelling of thermal strains, temperature-dependent materials and general temperature profiles. Then, a generalised arc-length method is developed for solving the discrete equations with the temperature amplifier as additional unknown. A consistent definition of the tangent operators and a mixed integration point strategy lead to a robust analysis with a reduced iterative burden, even in case of complex nonlinear behaviours where standard simulation tools are outperformed or even fail. Finally, an accurate eigenvalue analysis is derived for a quick estimate of critical temperatures. The overall framework is validated by a number of applications with isotropic and multi-layered composite materials, including variable angle tow laminates.