A novel and general reduced-order method for nonlinear thermoelastic analysis considering temperature-dependent composite materials

Abstract

The Koiter–Newton method has been developed to significantly reduce the computational cost of nonlinear thermoelastic buckling analysis of thin-walled structures subjected to a constant initial temperature field. Although the temperature-dependent material properties can be considered by analytically stripping the thermal effect from equilibrium equations, it is only applicable to isotropic materials and does not work for composite materials. This work proposes a novel and general reduced-order finite element framework for nonlinear thermoelastic buckling analysis in the Koiter–Newton method, which can consider temperature-dependent orthotropic composite materials. During the construction of the reduced-order model, the main obstacle for the nonlinear thermoelastic analysis considering temperature-dependent materials is the strain energy nonlinearity with respect to the temperature variation. This obstacle is addressed by expanding the equilibrium conditions with respect to both the displacement field and temperature variation. The displacement and force spaces are projected into the subspace which is represented using the generalized displacement and temperature variation. Nine sets of linear systems of equations can be obtained by equating the coefficients of various powers of the generalized displacement and temperature variation. A thermal–mechanical reduced-order model is constructed by solving the nine sets of linear systems of equations. Four different thermal–mechanical coupling cases can be easily considered in the reduced system. The accuracy and efficiency of the proposed reduced-order method are demonstrated through six numerical examples.