Analysis of distorted stiffened panels under uniaxial loading using non-linear equivalent single layer formulation

Stiffened panels in ships obtain distortions during manufacturing, and their effect on the panel stiffness may require consideration during the strength assessment. However, modelling the panel distortions while retaining computationally efficient and practical finite element models is challenging. This paper further investigates a one-way multiscale method in which the non-linear stiffness properties of a panel are derived numerically by multiple strain-driven finite element analyses on its smallest repeating Unit Cell (UC). The stiffness properties are used to formulate an Equivalent Single Layer (ESL) representation of the panel, which is implemented in commercial finite element software Abaqus via its UGENS subroutine. Novel aspects of this work include using the panel plate as the ESL reference plane, a practical selection in regards to modelling effort between design iterations and structural connectivity. The paper also highlights the importance of proper distortion modelling and the asymmetry of the stiffness matrix that is obtained using this method. Comparison of unidirectional tension and compression load-response curves between the proposed method and a three-dimensional shell element model show that the method accurately captures the behaviour of a simply supported stiffened panel. Applying the first buckling mode as the distortion shape results in non-conservative load response. Symmetrising the element stiffness matrix may yield additional computational savings, while the effect of the load response remains negligibly small.