| Lattice Boltzmann Method (LBM) has become an important numericalsimulation method. Unlike the traditional macroscopic numerical methods of solvingthe Navier-Stokes equations, LBM is based on the mesoscopic kinetic equations of theparticle distribution function to simulate partial differential equations. Therefore,LBM has simple algorithm and easy implementation of boundary conditions.In this paper, we use the lattice Boltzmann method to study Lame equation. Thelattice Boltzmann model for Lame equation is constructed. And the numericalsimulations are given.In chapter1, we reviewed the history and current research of the latticeBoltzmann method.In chapter2, we introduce the basic theory of the lattice Boltzmann method.Then, A series of partial differential equations in different time and in space scales arepresented. The lattice Boltzmann model for Lame equation and dynamic Lameequation are introduced. And we give the different processing methods and theassociated error analysis.In chapter3, we mainly propose a lattice Boltzmann model for solving the elasticthin plate with small deflection. In the conditions of uniformly distributed load,concentrated load and non-uniform load, the simulation results of two-dimensionalelastic thin plate with small deflection are obtained. The comparisons between the numerical results and the analysis solutions are given in detail. The numericalexamples show that the lattice Boltzmann model can be used to solve problems of theelastic thin plate with small deflection.In chapter4, firstly, the two-dimensional elasticity problems are simulated bylattice Boltzmann model. Displacement distributions and distributions of stress andstrain are given in Numerical results. Compared with the analytical results, theaccuracies of the numerical results have acceptable error. Secondly, the3D elasticityproblems are studied by numerical simulation, including the cube compression andthe expansion of concentric cylinders.We draw the conclusions in chapter5. |
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