An isogeometric solid-shell framework for transient thermal and thermo-mechanical large-deformation analysis of homogeneous and multilayered shells

This work presents an isogeometric solid-shell framework for transient thermo-mechanical analysis of homogeneous and multilayered thin-walled structures under large deformations and thermally induced buckling. The main contribution is a generalized shell model for both heat conduction and thermoelasticity: by introducing a piecewise-linear through-thickness representation within each layer, the governing equations are reformulated in terms of generalized through-thickness quantities that depend only on the in-plane coordinates of a reference surface. As a result, the discrete problem requires a purely two-dimensional spatial discretization, implemented here with bivariate NURBS basis functions, while the effects of three-dimensional temperature gradients and temperature-dependent constitutive behavior are captured through efficient layer-wise thickness pre-integration. Time integration of the thermal problem is performed via a modified Crank–Nicolson scheme. Nonlinear time/temperature–displacement equilibrium paths are computed using a generalized arc-length continuation method capable of traversing limit and turning points in transient simulations. This is a major novelty, as conventional Riks analyses are restricted to proportional temperature fields and cannot account for the transient thermal history. A staggered strategy is adopted to eliminate the thermal degrees of freedom by explicit condensation, yielding a reduced mechanical system at each iteration, and robustness is enhanced by the mixed integration-point (MIP) technique and deriving algorithmically consistent tangent operators. Benchmark problems on plates and shells subjected to transient thermal loads and fire exposure demonstrate accuracy and efficiency against fully three-dimensional ABAQUS solutions, with a drastic reduction in degrees of freedom and computational time.