The buckling response of a variable-length laminated beam constrained by a pair of symmetrical walls in hygrothermal environment is studied in the paper. The constrained wall is rigid but supported by springs that move upwards as a whole after being subjected to a force. The nonlinearly constrained buckling governing equation of the variable-length laminated beam in hygrothermal environment is established based on the principle of minimum potential energy and the Lagrange multiplier method. The buckling responses of the variable-length laminated beam are derived based on the elliptic integral method. Extensive numerical calculations are performed to illustrate the effects of different constraint clearances, spring stiffness, geometry, temperature, humidity, and composite fiber ply angle on the critical buckling load, buckling response, and buckling path.

The nonlinear dynamic responses of an axially moving laminated beam subjected to a blast load in thermal environment is studied considering large-displacement. Firstly, the nonlinear dynamic equilibrium equation is established based on the large-displacement theory and the constitutive relation of the single layer material in thermal environment. Based on the Galerkin method, a set of ordinary differential equations is obtained. Secondly, the multiple scales method is adopted to get the nonlinear free vibration frequency. Then, the stability region of the axial velocity and temperature is derived and the truncation order is approximated by the convergence calculation of the natural frequencies. Finally, numerical calculations are performed to discuss the effects of different kinds of blast loads, axial velocity and temperature on the nonlinear dynamic responses adopting the Runge–Kutta technique.