Smoothed Finite Element Methods For Interactions Between Large Deformed Solids And Laminar Flows

Fluid-Structure Interactions(FSI)are the most common coupling phenomenon among all multi-physics coupling phenomena in practical engineering systems.It involves the aeroelasticity of aircrafts and structures,the safety of high speed train,wave-ship interactions,interactions between wave and ocean engineering structure,and circulation system in living bodies,etc.The unsteady fluid flow and large deformed solid are usually contained in large scale fluid-structure interactions.The corresponding numerical simulations have drawn the attention of engineers and scholars who have done widely researches in nearly two decades.Traditional numerical simulations of FSI often employ Finite Element Method(FEM)to treat solid phase.However,the linear triangular and tetrahedral elements in FEM have poor accuracies which are not applicable for large scale and complex solid problems.The key point to solve complicate FSI is improving the aforementioned two linear elements in FEM to utilize their low computational costs and easy unstructured meshing.Recently,the Smoothed Finite Element Method(S-FEM)absorbed some techniques used in meshless methods which successfully increased the accuracies of linear triangular and tetrahedral elements.Based on the demands of unstructured mesh in FSI simulation and the advantages of S-FEM in unstructured mesh,the research in this dissertation is the investigation of solving FSI using S-FEM.Besides the usage of S-FEM in solid phase,the S-FEM is also applied to fluid phase of FSI system.Then,combine S-FEM in both solid and fluid phase to solve the large deformation of solid in unsteady fluid flows.The main works and conclusions are given as belows:1.The gradients smoothing and different smoothing domains in S-FEM are reviewed.Based on the characteristics of different smoothing domains,we selected the corresponding S-FEMs for solid and fluid phase which is accurate,stable and suitable for unstructured mesh.2.The explicit S-FEM for hyperelastic solid with large deformation is introduced.The anisotropic hyperelastic incompressible material models are incorporated into selective S-FEM.The isotropic numerical examples have verified the high accuracy,volumetric-locking free,good distorted mesh resistance,good convergence and high computational efficiency of selective S-FEM.It is worth to mention the selective S-FEM can use only linear tetrahedral elements to achieve comparable convergence but better efficiency than second order tetrahedral elements with selective reduced integration in FEM.The calculations of numerical examples with anisotropic materials demonstrated that the developed explicit selective S-FEM has the capability to handle practical applications with complex geometries and complicate fiber distributions.3.A new stabilization which works very well for both S-FEM and FEM is proposed.This stabilization unified the Characteristic-Galerkin(CG)method and Polynomial Pressure Projection(P3)to resolve the numerical oscillations caused by convection and pressure,respectively.Moreover,this stabilization is still keeping pressure to be stable in quite small time step length.From the results of numerical examples,S-FEM exhibits better temporal convergence,spatial convergence and efficiency than FEM in two-dimensional cases.In three-dimensional examples,S-FEM shows just slightly better accuracy in pressure than FEM.In addition,the optimization and parallelization of S-FEM codes have been implemented to equip the basic ability for large scale laminar flows.4.The sharp interface immersed S-FEM is proposed which modified original immersed S-FEM with fluid velocity reconstruction in vicinity of FSI interface.The sharp interface immersed S-FEM also intakes S-FEM for fluid and solid phases to build a computation platform for FSI simulations.The fast octree and neighbour-to-neighbour searching algorithm have also been investigated for complicate large scale problems.The improves in accuracies near solid boundaries of sharp interface immersed S-FEM have been verified by both two and three dimensional FSI examples.The fast seraching algorithms working with paralleled fluid solver make our computational platform can solve FSI problems with relatively large scale.