Simplified analysis method for deformation of two-way stiffened plates based on orthotropic equivalent theory

Objectives With the continuous development of larger scale and more complex ships, the number of finite element model elements required to model hull structures at the cabin structure level and above is increasing dramatically, resulting in collision, impact, contact and other large-scale non-linear mechanical problems which are difficult to solve. To this end, a simplified method for the deformation of two-way stiffened plate structures based on orthotropic equivalent theory is proposed in order to simplify the modeling of ship structures.

Methods First, the current well-established simplification method for the plane stress of one-way stiffened plates is extended to the more complex plane bending problem of two-way stiffened plates. The ratio of the total moment of inertia of stiffened plates to the moment of inertia of plates in the orthogonal direction is introduced to reflect the structural orthotropism. Next, the moment of inertia ratios are substituted into the equivalent constitutive equation for the plane bending of stiffened plates to achieve the transformation to physical orthotropism, thereby taking into account both the deformation resistance of the structure and the influence of the membrane forces generated by shifting the neutral surface at the mechanical level. Finally, finite element calculations are used to classify the deformation modes of the four-sided fixed stiffened plates according to different displacement distributions, and the actual results of the stiffened plates are analyzed in terms of error comparisons with the equivalent results of this method and the traditional method.

Results The result comparison shows that the proposed method can reduce the number of elements in two-way stiffened plates by up to 84%, and the equivalent errors in all three deformation modes can be controlled within 6%, which is much lower than those of the two traditional methods.

Conclusions With high precision, a wide application range and greatly reduced calculation resources, the proposed method can provide a direct modeling and simulation calculation solution to address the nonlinear mechanical problems of large hull structures for practical engineering applications.