In order to accurately evaluate the longitudinal ultimate strength of a hull girder under the cyclic bending moment, the effects of an elastic-perfectly plastic and Chaboche material model on the elastic shakedown and ultimate strength of the hull girder under the cyclic bending moment are studied.

The nonlinear finite element method is used to carry out the ultimate strength numerical simulation of a double bottom bulk carrier considering the elastic shakedown under the cyclic bending moment. In this study, the Bauschinger effect of the material during the reverse loading of the structure and influence of the welding initial deformation and residual stress are considered.

The calculation results show that the welding initial deformation significantly reduces the lower limit of the elastic shakedown of bulk carrier, and the range of the elastic shakedown considering welding initial deformation and residual stress is the largest. After reaching the elastic shakedown under the cyclic bending moment, the ultimate strength of the bulk carrier considering the welding initial deformation and residual stress under hogging and sagging states are 7.15% and 5.68% higher than that under single loading respectively.

The welding initial deformation has a major impact on the elastic shakedown interval and elastic shakedown ultimate strength of the bulk carrier, which should be carefully considered in actual research and analysis.

This study analyzes the impact of initial imperfections and the combined loading of bending and torsion on the ultimate strength, residual bearing capacity, and collapse characteristics of box girders under single/cyclic bending and torsion combined loading.

ABAQUS software is used to conduct nonlinear finite element numerical calculations of the ultimate strength of box girders under single bending, combined loading of single bending moment and torsion, cyclic bending, and combined loading of cyclic bending and torsion. The effects of initial imperfections, materials, and loadings are considered.

The box girder model incorporating five sets of cyclic amplitudes with welding residual stress shows a maximum variation of 0.51% between the box girder models with the highest and lowest ultimate strengths. Similarly, the box girder model without welding residual stress exhibits a maximum variation of 1.94% between the models with the highest and lowest ultimate strengths. Under combined loading of cyclic bending moment and torsion, the ultimate strength of the box girder is lower than that under cyclic bending moment. The combination of cyclic bending moment and torsion loading more effectively relieves welding residual stresses, and the box girder model with four sets of residual stresses in five cyclic amplitudes exhibits higher ultimate strength than that without welding residual stresses. Once the ultimate strength is reached, the box girder model with both torsion and welding residual stresses has slightly higher residual bearing capacity.

The impact of torsion on the ultimate strength of box girders is limited. The findings of this study can provide valuable references for further research on the ultimate strength of ship hull girders under combined loading of cyclic bending moment and torsion.

To accurately assess the ultimate strength of a hull girder, this study analyzes the elastic shakedown characteristics of hull stiffeners under cyclic loading.

Based on the results of nonlinear finite element numerical simulation, the average stress-average strain relationship of the stiffened plate element in Rahman's Beam-Column Method is corrected with full consideration of the elastic shakedown state, type of stiffened plate, and failure mode. A correction method applicable to the average stress-average strain relationship of the stiffened plate in the elastic shakedown limit state is proposed, and a program for Smith’s method for the ultimate strength of hull girders based on the elastic shakedown limit state is compiled and compared with the results of nonlinear finite element numerical simulation.

The results show that the proposed method can effectively evaluate the ultimate strength of a hull girder in the elastic shakedown limit state with greater efficiency than the nonlinear finite element method.

The application of Smith’s method for the ultimate strength of hull girders based on the elastic shakedown limit state can contribute to the accurate and efficient evaluation of the ultimate strength of hull girders.

The aim of this paper is to evaluate the longitudinal ultimate strength of a hull girder more accurately and determine its collapse process.

A bulk carrier is finely modeled in nonlinear finite element software ABAQUS, and the effects of slight, average, and severe welding initial deformations and average welding residual stress on the ultimate strength of the hull girder under hogging and sagging bending moments are fully considered.

The calculation results show that the hull girder's ultimate strength and bending stiffness decrease gradually with the increase of the initial deformation amplitude. Severe welding initial deformation makes the ultimate strength of the bulk carrier decrease by 14.25%, and the bulk carrier's ultimate strength decreases by up to 8.22% under the effect of welding residual stress individually. The combined effect of welding initial deformation and residual stress on the hull girder's ultimate strength is not a linear combination of the effects of the two initial deformations individually.

The combined effect of welding initial deformation and residual stress on a hull girder's ultimate strength should be considered more carefully in research on the ultimate strength of hull girders.

In order to accurately assess the ultimate load-bearing capacity of a hull structure under cyclic loading, it is necessary to consider the effects of the cyclic properties of the load on the ultimate strength of hull stiffened plates.

Finite element software ANSYS is used to carry out the numerical simulation of ultimate strength based on the elastic shakedown limit state under in-plane cyclic loading for 200 T-bar stiffened plates and flat-bar stiffened plates. The material Bauschinger effect, welding initial deformation and residual stresses of the hull stiffened plates under in-plane cyclic loading are considered in detail. Based on the stiffened plate nonlinear finite element numerical simulation results of the elastic shakedown limit state, the dimensionless ultimate strength of the stiffened plates is taken as the objective function, the flexibility coefficients of the plates and stiffeners are taken as the independent variables, and a formula for predicting the ultimate strength of hull stiffened plates under in-plane cyclic loading based on the elastic shakedown limit state is proposed.

The accuracy of the formula is verified through comparison with the nonlinear finite element simulation results.

This study has positive theoretical and engineering significance for the ultimate strength assessment of hull stiffened plates under cyclic loading.

To fully consider intact initial imperfections, including welding initial deformation and residual stress, it is necessary to conduct a study on the plastic deformation distribution and ultimate strength of a box girder under different cyclic bending moments.

First, an isotropic material model and the Chaboche material model are chosen. Using the Python language, programs are developed to directly apply the initial deformation in finite element software. Subsequently, ABAQUS software is employed to conduct nonlinear finite element numerical simulations of the ultimate strength of a box girder under different cyclic bending moment patterns. The analysis considers the influence of welding initial deformation, residual stress, material hardening and the Bauschinger effect.

The results show that under unidirectional cyclic bending moments, the bending stiffness and ultimate strength of the box girder decrease continuously as the number of cycles increases. The plastic deformation extends from the upper deck of the box girder to the side plate region. The plastic distribution region of the box girder with welding initial deformation and residual stress is wider in the ultimate state. Compared to a single loading and considering only the initial deformation, after three bidirectional cycles, the ultimate strength of the box girder decreases by 10.44% to 15.15%. Considering intact initial imperfections, the ultimate strength decreases by 8.41% to 14.50%.

The ultimate strength of a box girder considering intact initial imperfections under different cyclic bending moments decreases more moderately. The obtained results can serve as a reference for the study of the ultimate strength of box girders under different cyclic bending moments.

In order to improve the accuracy of the ultimate strength evaluation of hull plates, this study carries out a nonlinear finite element numerical simulation of the ultimate strength of ship hull plates under cyclic loading based on the critical state of elastic shakedown.

Finite element software ANSYS is used to primarily investigate the effects of elastic-perfectly plastic and cyclic-plastic Chaboche material models on the release of welding residual stress and ultimate strength of hull plates after reaching the critical state of elastic shakedown.

The results show that after the first cycle, the welding residual stress is basically released and tends to become stable after reaching the elastic shakedown state under cyclic loading, at which point the ultimate strength of the Chaboche model is greater than that of the elastic-perfectly plastic model.

When performing the nonlinear finite element numerical simulation of the ultimate strength of ship hull plates under cyclic loading based on the critical state of elastic shakedown, it is necessary to select a material model that takes into account material hardening and the Bauschinger effect. The obtained results have a certain reference value for further research on the ultimate strength of hull structures under cyclic loading.

This study seeks to grasp the effects of the initial deflection shape on the plastic accumulation characteristics of hull plates with circular holes under cyclic loading.

Finite element software ABAQUS is used to carry out the nonlinear elastic-plastic large deflection numerical simulation of hull plates with circular holes of different slenderness ratios and perforation sizes under axial cyclic loading. The plastic accumulation and fracture characteristics of the plates under axial cyclic loading are studied with the initial deflection shape made by the first-order buckling mode and commonly used initial deflection formula respectively.

The plastic accumulation of plates with the initial deflection shape made by the initial deflection formula is relatively moderate. When the axial cyclic loading amplitude is relatively low, the number of fracturing cycles of plates with the initial deflection shape made by the first-order buckling mode is relatively small, but the difference decreases as the amplitude increases.

The influence of different initial deflection shapes on the plastic accumulation and fracture characteristics of plates with circular holes depends on the slenderness coefficient, perforation size and axial cyclic loading amplitude.

In order to improve the accuracy of nonlinear numerical simulation of the ultimate load-bearing behavior of a hull stiffened plate, the effects of ideal elastoplastic, isotropic hardening and cyclic plastic Chaboche material models on the plastic yield distribution, compression and tensile ultimate strength of stiffened plates in their ultimate state are studied.

For a stiffened plate of the same size, ANSYS software is used to carried out non-linear finite element numerical simulation of ultimate bearing performance under axial cyclic compression and cyclic compression-tension loads.

The results show that different material properties have a significant impact on the ultimate bearing capacity of stiffened plates and the plastic yield distribution in the ultimate state. When carrying out nonlinear finite element numerical simulation of the ultimate bearing behavior of a hull stiffened plate, it is necessary to select the appropriate material model according to different load forms.

The results of this study can provide valuable references for further research on the ultimate strength characteristics and cumulative plastic failure mechanisms of hull structures under cyclic loading.