An analytical formulation for postbuckling and buckling vibration of micro-scale laminated composite beams considering hygrothermal effect

The current paper is concerned with the micro-scale laminated composite Euler-Bernoulli beams under the hygrothermal environment. The aim is mainly focused on the static and dynamical responses of micro-scale beams under consideration in both prebuckling and postbuckling cases. Meanwhile, the mechanism how temperature and hygrothermal concentration affect the critical buckling load is discussed. The material properties are considered to be temperature- and hygroscopic concentration-dependent. And the hygrothermal deformation caused by both variations in temperature and hygroscopic concentration is taken into account. The modified couple stress Euler-Bernoulli beam model involving geometric nonlinearity due to the mid-plane stretching is adopted. Then, an analytical formulation of postbuckling and buckling vibration is derived as a function of the external compressive axial load. Exact solutions for the critical buckling load, the postbuckling configuration and the natural frequency of vibration around the buckling configuration of the beam with various boundary conditions are investigated.