Dynamic Analyses Of Ship Structures Using The Smoothed Point Interpolation Method

Dynamic analysis is an important content of ship structure calculation,which mainly includes the frequency,model analysis and the response analysis.For large complex structure,it is hard to obtain the analytical solutions.Usually use numerical methods such as finite element method(FEM)and the meshfree methods to calculate them.We found that the accuracy of the numerical methods has something to do with the stiffness of the model.The FEM can realize the automatic mesh generation of complicated structure while would get the poor result and high frequency when using the triangular mesh for the stiffer stiffness.The proposed meshfree point interpolation methods using the triangular background elements can improve the accuracy of the results.However it fails to calculate the dynamic problem and the results of the frequencies are too lower because of the softer stiffness.To solve the above problems,this paper from the perspective of the stiffness to do the following works.This paper makes a combination of FEM and node-based smoothed point interpolation method(NS-PIM)by conducting node-locally-based gradient smoothing operation and proposes the node-locally-based smoothed point interpolation method(NLS-PIM).Through the numerical cases,we found that make the combination of the FEM and NS-PIM,the method can not only successfully overcome the temporally instability of NS-PIM and get a more accurate result of frequency and response but also give a much tighter upper and lower bound of natural frequencies by using different parameter values.Then through dividing the smoothing domain into two parts and adding the virtual smoothing domain,we can control the stiffness of the edge-based smoothed point interpolation methods(ES-PIM).Through dividing the smoothing domain into two parts and adding the virtual smoothing domain,the stiffness of ES-PIM can be well controlled and when choosing the proper parameter ? the improved ES-PIM is much better than the traditional ES-PIM in displacement norm error and is a litter better in energy norm error.Making the combination of face-based smoothed point interpolation methods and boundary element methods to calculate the frequency and model of the underwater cylinder and the bracket can get a more accurate frequency results of underwater structures.