A new, enhanced asymptotic expansion applicable to stability of structures made of
nonlinear elastic materials is established. The method utilizes “hyperbolic”
terms instead of the conventional polynomial terms, covers full kinematic
nonlinearity and is applied to nonlinear elastic Euler columns with two different
types of cross-section. Comparison with numerical results show that our
expansion provides more accurate predictions of the behavior than usual
expansions.
The method is based on an extended version of the principle of virtual
displacements that covers cases with auxiliary conditions, such as inextensibility.
Membrane locking and similar problems are also handled by the method.
Keywords
elastic stability, full nonlinearity, asymptotic expansion