Size-dependent Bending of Geometrically Nonlinear of Micro-Laminated Composite Beam based on Modified Couple Stress Theory

Abstract

In this study, the effect of finite strain on bending of the geometrically nonlinear of micro laminated composite Euler-Bernoulli beam based on Modified Couple Stress Theory (MCST) is studied in thermal environment. The Green-Lagrange strain tensor according to finite strain assumption and the principle of minimum potential energy is applied to obtain governing equation of motion and boundary conditions. The equation of motion with boundary conditions is solved using a generalized differential quadrature method and then, the deflection of the beam in classical elasticity and MCST states is drawn and compared with each other. Considering the bending of the beam, which has been made of carbon/epoxy and glass/epoxy materials specified, it can be seen there is a significant difference between the finite strain and von-Karman assumptions particularly for L =10 h. Also, the results show that the thermal loadings have a remarkable effect on the glass/epoxy beam based on the finite strain particularly for simply supported boundary condition.