First-order shear deformation theory for orthotropic doubly-curved shells based on a modified couple stress elasticity

This paper investigates the micro- and nano-mechanical behavior of orthotropic doubly-curved shells by considering the New Modified Couple Stress Theory (NMCST). The higher order continuum assumed by the NMCST includes three material length scale parameters in order to capture the size-effect of anisotropic and orthotropic materials. The governing equations of the problem are based on the First-order Shear Deformation Theory (FSDT). According to the proposed NMCST, the expressions of the physical components for the strain and curvature tensors are obtained in an orthogonal curvilinear coordinate system. Then, the governing differential equations and boundary conditions are derived by applying the energy method and Hamilton's principle. A comparative investigation between our numerical results and the ones available in the literature proves the capability of the proposed formulation in predicting the micro- and nano-mechanical behavior of orthotropic doubly-curved shells.