Nonlinear Bending and Snapthrough Response of Doubly Curved Laminated Shells

Abstract

Shell structures made up of conventional fiber reinforced composite (FRC) laminates find many applications in engineering fields. In contrary to plate structures, shells exhibit two stable equilibrium configurations. Due to excessive loading, shells may largely deform and hence snap from one equilibrium position to the other. Snapthrough or snapback motion involves large deflections and hence it is inherently a nonlinear phenomenon. In this thesis, the nonlinear static response of simply supported doubly curved FRC shells is explored according to the classical laminated theory (CLT) with von Karman geometric nonlinearity. Various types of composites are considered: unidirectional [0₄], symmetric [0,90]ₛ, unsymmetric [0,0,90,90] and antisymmetric [0,90,0,90] laminates. The equations of motion and the associated boundary conditions are derived using the Hamilton’s principle. The axial displacements are eliminated from equations of motion by utilizing the Airy stress function and the nonlinear compatibility equation. This reduces the governing equations to two: the compatibility equation and the equation of motion governing the transverse deformation. The Galerkin’s approach is used to obtain a reduced-order model (ROM). This discretization leads to a set of nonlinear coupled ordinary differential equations (ODEs). Three modes are retained in the discretization. By setting all time-dependent terms equal to zero, the system of ODEs reduces to a set of nonlinearly coupled algebraic equations which are solved by means of the Newton-Raphson method for the static equilibrium positions and the Jacobian method is used to assess their stability. The effect of the stacking sequence, radii of curvature, curvature ratio and the shell thickness on the nonlinear bending and snapthrough response are investigated.