Study On Dynamic Response Of Ship Structures Using The Cell-based Smoothed Point Interpolation Method

The vibration of ship structures will lead to many adverse effects,so accurately calculating the dynamic response of ship structures is important for reducing vibration and structural safety assessment.In recent years,numerical methods have become a powerful tool for analyzing complex structural problems,and the finite element method(FEM)is the most widely used one.However,the model of finite element method is too rigid when using simple linear elements that can be automatically segmented.As a result,the solution of FEM has poor accuracy,and free vibration frequency is much higher than exact solution.The cell-based smoothed point interpolation method(CS-PIM)performs strain smoothing processing within the cell,which is the smoothed domain.Because generalized gradient smoothing technique(GGS)can significantly soften the model stiffness,CS-PIM can overcome the ?overly-stiff? property of the finite element method.Based on the traditional cell-based smoothed point interpolation method,this thesis further adjusts the construction method of the condensed RPIM shape function.Newly developed virtual nodes arrangement schemes make the model stiffness more accurate,so the proposed methods could obtain higher precision when solving structural dynamic problems.For two-dimensional problems,the novel method is cell-based smoothed radial point interpolation method using six virtual nodes(CSRPIM-T4-Cd6);for three-dimensional problems,the novel method is cell-based smoothed radial point interpolation method using eight virtual nodes(CSRPIM-T5-Cd8).A series of numerical cases have been studied to test the numerical methods proposed in this thesis.The numerical results show that the addition of two virtual nodes will make the condensed RPIM shape function match the cell-based strain smoothing system better.The stiffness of the calculated model is very close to the real system stiffness.Both CSRPIM-T4-Cd6 and CSRPIM-T5-Cd8 can pass the standard patch test.When calculating the static problem,the strain energy of the structure can be accurately simulated,the displacement error norm and the energy error norm are lower than the former methods;The results of modal analysis is highly accurate,even better than finite element method using high-order elements background mesh with the same degree of freedom.Then,CSRPIM-T5-Cd8 is applied to solve the structural problems of ship structural problems.Combined with the boundary element method(BEM)to obtain the added mass of underwater structure,the free vibration of the underwater cylinder and brackets are analyzed very accurately.Many numerical cases in this work have proved that the proposed methods can obtain high precision results with a sparse mesh,which means these methods are of high precision and efficiency.Compared with the traditional finite element method,the proposed methods have higher precision and computational efficiency under the same conditions.The methods use linear element background meshes that can be automatically generated,so pre-processing of structural analysis is simple.Therefore,the proposed methods have a promising future in numerical simulations for structural dynamic analysis.