Improved Meshfree Methods And Its Application In Structural Damage Analysis Under Fluid-Structure Impact

With the development of guidance technology,the probability of warships being sub-jected to underwater near-field or even contact explosions is increasing.The shock wave,bubble jet and high-speed fragment generated by the near-field underwater explosion will cause fatal damage to the ship structure.This physical process involves strong nonlinear coupling of a variety of materials,accompanied by elastoplastic damage and dynamic frac-ture of the structure.To solve the difficulties in numerical simulation of this problem by tra-ditional mesh-based methods,in this work,the analysis model of structural damage under fluid-structure coupling impact is established based on the Smoothed Particle Method(SPH)and Reproducing Kernel Particle Method(RKPM),and develop the numerical program in-dependently The prediction of structural damage subjected to the underwater explosion is achieved which can provide basic technical support for the design of warship protection structure.In Chapter 2,the basic theory of SPH is expounded,and the improvement of the nu-merical techniques for boundary implementation of SPH method is emphatically studied.On this basis,the correctness and validity of the numerical model are verified by a series of numerical examples.In order to improve the accuracy of the traditional SPH kernel function,the original SPH kernel function is modified based on the reproducing condition in chapter 3,then the two-dimensional reproducing kernel function is obtained.Based on Mindin-Reissner plate theory,the degenerated solid kinematic description of three-dimensional shell structure is established,in which the three-dimensional shell solid are represented by the shell reference surface and a fiber vector,the fiber vector initial vertical to the reference sur-face in the initial configuration.Based on the reproducing kernel interpolation function,the shell kinematics are discretized.Then based on the principle of virtual power,the discrete governing equations of RKPM shell are obtained.Finally,the numerical model of RKPM shell is established.By a series of widely used benchmark,the convergence,stability and accuracy of RKPM shell model are comprehensively verifled.In Chapter 4,based on Timoshenko beam theory,the kinematic description of three-dimensional curved beam is established,the three-dimensional beam solid is represented by the beam reference axis and two fiber vectors,the plane represented by fiber vectors is perpendicular to the reference axis in the initial configuration.Based on the reproducing kernel interpolation and the principle of virtual power,the discrete governing equations of RKPM beam are derived,and the numerical calculation model of RKPM beam is finally es-tablished.Then the effects of interpolation accuracy,integral order,smooth length and par-ticle spacing on the calculation results are systematically studied,which provides guidance for the setting of relevant parameters in numerical practice.The stability and accuracy of the RKPM beam model in the simulation of large deformation problems are verified by several standard numerical examples.The ship hull is a complex stiffened shell structure,and there is little research on the meshfree simulation of the stiffened shell,which greatly limits the ap-plication of the meshfree method in the analysis of complex engineering structures.To solve this problem,in this work,based on the previously established RKPM shell and beam model,the coupling calculation model of the RKPM shell and beam is established.Simultaneously,a numerical algorithm for the truncation of the cross-shell structure is proposed,then the full-shell calculation model of the stiffened shell is established.Finally,the effectiveness of the RKPM stiffened shell numerical model is verified by the simulation of dynamic vibration of the stiffened plate and the stiffened cylindrical shell.In chapter 5,based on Mises yield criterion,the yield function considering plane stress assumption in shell theory is derived.In order to facilitate the analysis,the yield function is expressed as a matrix and diagonalized by eigen analysis.Finally,based on the closest point projection algorithm,the shell plastic return algorithm is established.The correct-ness of the elastic-plastic constitutive model is verified by a series of standard numerical examples.On this basis,in Chapter 6 a damage variable is defined to describe the stress reduction of materials in necking stage based on Lemaitre’s phenomenological damage the-ory,and an elastic-plastic constitutive model coupling with material damage is established.Based on the visibility condition,an algorithm for updating the support domain of stress points around cracks is proposed.Combining the elastic-plastic damage model with the crack discontinuous algorithm,the numerical model for crack initiation and propagation of RKPM shell is established.Several numerical examples are calculated and compared with the experimental results,which verifies the correctness of the RKPM shell carak prop-agation model.Simultaneously,to simulate the impact damage of structures cause by the high-speed fragments,a meshfree contact detection algorithm for RKPM shell is proposed in chapter 6,and the volume strain is calculated according to the distance between the shells invading each other,then the contact force algorithm for the shells is deduced.Finally,a series of numerical examples are studied to verify the applicability and accuracy of the pro-posed contact algorithm in self-contact and multi-object contact problems.On the basis of the previous chapters,in chapter 7,based on the SPH kernel approxi-mation theory,considering the truncation of the support domain of fluid particles caused by the structure boundary,the SPH governing equations considering the fluid-structure cou-pling effect are derived.Then according to the meshfree approximation theory and consid-ering the influence of fluid inertia,an algorithm for calculating the fluid pressure load on the structure surface is proposed.Finally,a fluid-structure interaction model based on SPH and RKPM is established.The SPH-RKPM fluid-structure interaction model is validated by some examples of low-speed flow and underwater explosion,which proves that the fluid-structure interaction model in this work has high accuracy and wide applicability.Finally,the SPH-RKPM fluid-structure interaction model is used to calculate the damage of the light-ning protection broadside subjected to underwater contact explosion.The numerical results are in good agreement with the experimental results,which shows that the SPH-RKPM fluid-structure interaction model in this work has preliminary ability to solve engineering practical problems.