Application Of The Improved SPH Method In The Dynamic Response Of Shell Structures Under Impact Loads

The hulls subjected to shock waves,bubble pulsating loads,etc in cases of underwater explosions will undergo large deformations,plastic damage and even cracks.When the finite element methods are used for the simulation,the grids are severely distorted and then need remeshing,which will affect the calculation efficiency and reduce the accuracy.However,the meshfree methods,which use a series of particles to construct the shape functions and then solve the corresponding integral equations and differential equations,have a distinctive advantage to deal with large deformations of shells.Smoothed particle hydrodynamics(SPH)is a kind of point collocation meshless methods.The field function is adopted in integral forms.The computational domains will be discretized into Lagrange particles,and the interactions between the particles are established by the kernel functions.Therefore,the particles can move arbitrarily and the mesh distortions can be avoided.Based on the theory of SPH,this paper introduces the main ideas of particle approximation and kernel approximation.The basic conditions that the kernel functions must meet and the accuracy at the boundary is discussed.Then,based on the Mindlin-Reissner plate theory,the equilibrium equations of the SPH three-dimensional shell numerical model are derived and an explicit dynamic algorithm is presented.In order to make the calculations more stable,three kinds of numerical processing techniques are adopted,which include artificial viscosity,smooth filtering technology and stress point technology.The traditional SPH method is not accurate at the boundary and it will cause large errors while predicting the dynamic responses of the three-dimensional shells.In the present work,the K2_SPH method is used to modify the kernel function In order to eliminate the tensile instability,the Eulerian kernel is converted into the Lagrangian kernel.Then,the completeness of the Lagrangian kernel function is discussed and compared with SPH,CSPM(Corrective Smoothed Particle Method),and second order MLSPH(Moving Least Squares Particle Hydrodynamics).Then,the K2_SPH model is used to predict the dynamic response of shells,and the results are compared with the results got from ABAQUS to verify its accuracy.Aiming at the problem that the applicable range of ratio of the thickness to the width is not very clear in the Mindlin-Reissner plate theory,the K2_SPH shell model is used to discuss this problem.Meanwhile the influence of the uniformity of particle distribution and the locations of stress points are studied,and the best way to discrete shells and the best arrangements of stress points are presented.For the plastic response of shells under impact loads,the yield functions of the shells and the plastic return algorithm based on the Mises yield criterion are given.Then,the response of the square plate based on the ideal elastoplastic model is predicted and compared with results predicted by ABAQUS.Because the hardening effect of metal materials has a great impact on its mechanical properties,based on the Johnson-Cook hardening model,the plastic deformations of metal square plate and disc are calculated,and the results are compared with simulation results of ABAQUS.Finally,the K2_SPH elastoplastic shell model is used to study the plastic response of the cylindrical shells under radial impact loads,which can verify the validity and applicability of the plastic model.Finally,the interactions between the underwater explosion bubble and the elastoplastic shells are studied by the SPH-BEM coupling method.The BEM(Boundary Element Method)is used to calculate the explosion bubbles,and the K2_SPH shell model is used for the shells.The elastoplastic responses of the shells and motions of the bubble are obtained by the coupling model.The results are compared with the results from LS-DYNA to verify the effectiveness of the coupled method.