Nonlinear Thermal Buckling Analysis of Thin‐walled Structures: Solid‐shell Discretization, Continuation Method and Reduction Technique

Abstract

This work presents an accurate and efficient numerical tool for geometrically nonlinear thermoelastic analyses of thin‐walled structures. The structure is discretized by an isogeometric solid‐shell model with an accurate approximation of geometry and kinematics avoiding the parameterization of finite rotations. An efficient modeling of thermal strains, temperature‐dependent materials and general temperature profiles based on a numerical pre‐integration through the shell thickness is proposed. Then, a generalized path‐following method is developed for solving the discrete equations with the temperature amplifier as additional unknown, in order to trace the temperature‐displacement nonlinear curve also in case of limit points and unstable paths. A consistent definition of the tangent operators and a mixed integration point strategy give a robust and efficient analysis. Finally, a reduction technique is derived for a quick estimate of the nonlinear thermal buckling point. The reduced model consists of the initial path tangent, the first linearized buckling modes and their second order corrections. Numerical applications are given.