Dilated Polyhedron Based Discrete Element Method And Its Applications On The Analysis Of Ice Loads On Marine Structures

Granular materials,widely existing in nature and engineering practice,have an important impact on human activities.It exhibits extremely complex features,such as strong nonlinearities and quasi-solid-liquid properties.There are still many deficiencies in the study of the physical mechanism of the mechanical properties of granular matter.It is necessary to refine the interaction mechanism and dynamic process between the internal particles of granular materials.The discrete element method(DEM)takes the single particle as the research object,establishes the constitutive relationship of the interaction between particles,and thus describes the macroscopic mechanical behavior of the granular material.This method can perform multi-scale analysis on the granular materials.Besides,the establishment of bond-break model in DEM can analyze the breaking process of sea ice since the distribution and morphology of sea ice show distinct dispersion on different scales.This approach has been widely applied in the simulations of the interaction between sea ice and offshore structure.As the main method of numerical analysis for granular materials,DEM has been developed rapidly in the terms of particle morphology,contact model and bond-break model.At present,the spherical element is still predominantly adopted as the geometric representation of element in DEM.due to the simple geometric structure and the maturity of the contact and bond model of the spherical element.However,most of the real particles appear as irregular shape,while it is difficult for the spherical element to describe the special phenomena,such as occlusion and self-locking of irregular shaped elements.It is an important direction for the development of DEM to generate irregular shaped elements,establish corresponding contact detection methods and contact force models.In this thesis,the study focuses on the dilated polyhedral element based on the Minkowski sum theory for the generation of irregular shape elements.The research of the dilated polyhedral element mainly includes the contact detection,contact force model,bond-break model and fluid-solid coupling model.The main works in this thesis are listed:(1)The dilated polyhedral element is generated based on the Minkowski sum theory.The contact detection based on the geometry due to the surface geometric characteristics of the dilated polyhedron.Meanwhile,the contact stiffness is calculated according to the surface curvature of the two elements at the contact point,and thus the contact force between elements can be determined by the classical Hertzian model.The analytical solution of typical example is adopted to verify the simulation results.(2)The weighted summation of the second-order dilated polyhedron function and spherical function is employed as the envelope function of dilated polyhedron.The contact center is solved by the optimization model between the corresponding envelope functions of dilated polyhedron,while the contact normal and overlap can be determined by simple geometric calculations.Accordingly,the contact force model of single contact point can be employed to calculate the contact force between elements.Some examples are simulated to verify the simulation results.(3)The bonding between elements can be conducted by setting up bond nodes on the interface between elements and calculating the strain and stress between bond nodes.The ultimate strength criterion is developed by employing the tensile and shear strength.The damage process is considered,while the hybrid fracture energy is calculated between bonded elements with the Benzeggagh-Kenane model to determine the ultimate deformation for the failure between bond nodes.Therefore,a hybrid fracture criterion is established.The fracture parameters are studied by analyzing the fracture mode and strength in Brazilian tests.(4)The weakly compressible smoothed particle hydrodynamics(WCSPH)is developed for the hydrodynamic simulation,while the tension correction and artificial viscosity term are considered.Since the geometric interface between the dilated polyhedron and fluid is complex,the repulsive force model considering deep correction is adopted to calculate the force between dilated polyhedra and SPH particles.Hence,the solid-fluid coupling method is established with the dilated polyhedron based DEM and SPH.(5)The generation of the initial field of sea ice is developed with the 2D Voronoi tessellation algorithm.The interaction processes between broken/level ice and floating structure,inclined slope,ship hull are simulated with the dilated polyhedron based DEM.The ice loads on structures in DEM simulations are validated with the field data and ISO standard.The failure mode of ice cover is analyzed under multi-ship conditions.The breaking process of level ice against wave is simulated with DEM-SPH coupling method.Moreover,the ice loads are also simulated with DEM-SPH coupling method during the interaction between broken ice and vertical structure in wave field.At last,research summary of this thesis on the dilated polyhedron based DEM,and some future work are pointed out.