The Koiter–Newton approach using von Kármán kinematics for buckling analyses of imperfection sensitive structures

The Koiter–Newton approach is a reduced-basis method for nonlinear structural analyses. The method combines Koiter’s approach as a predictor step and the Newton arc-length technique as a corrector step to trace the entire load–displacement equilibrium path of a structure in a step by step manner. This computationally highly efficient and accurate solution method has recently demonstrated a superior performance in nonlinear analyses compared to standard techniques. In this paper we propose an extension to buckling imperfection sensitivity analyses exploiting the method’s stability and reliability. We present two different modeling techniques for imperfection loads that both profit from the Koiter–Newton approach reducing the initial computation steps to a small fraction thereof. We introduce von Kármán kinematics which neglect some nonlinear terms of the Green strain–displacement relations to further increase the computational efficiency of the analysis by an essential reduction of the computation effort required to obtain higher order derivatives of the strain energy. Using various numerical examples and benchmark tests we demonstrate the overall high quality and performance of the proposed method.