Loss of bifurcation and multiple shapes of thin [0/90] unsymmetric composite plates subject to thermal stress

Abstract

The shape of thermally loaded thin [0/90] composite plates predicted by the classical lamination theory is a saddle, with a value of curvature independent of the in-plane dimensions of the structure. Including the effect of geometrical nonlinearities reveals the occurrence of bifurcation of the saddle solution for a critical value of in-plane dimensions (or temperatures), depending on material properties. In the post-bifurcation regime, the saddle shape becomes unstable, while two cylindrical configurations develop on the stable branches. One cylinder can be snapped into another by applying an external force. In the present paper the behaviour of [0/90] plates under thermal stress is simulated with an ABAQUS Finite Element Model and results are compared to a Rayleigh–Ritz model. For square plates, results from the FEM model are in good agreement with the Rayleigh–Ritz model and only small discrepancies are found. The introduction of imperfections, such as asymmetry in thickness, produces a loss of bifurcation which is predicted by the Rayleigh–Ritz and by the ABAQUS model. The range of existence of the cylindrical solutions can also be predicted. For rectangular plates the FEM model predicts a loss of bifurcation which is not found by the Rayleigh–Ritz model. It is found that the length-to-width ratio (aspect ratio) plays a crucial role in the existence and stability of the cylindrical shapes. Numerical simulations are supported by experimental results on thin [0/90] unsymmetric plates with length-to-width ratio equal to 10.