Lattice Boltzmann model for elastic thin plate with small deflection

In this paper, a lattice Boltzmann model for solving problems of elastic thin plate with small deflection is proposed. In order to recover the Sophie–Germain equation for elastic thin plate by lattice Boltzmann method, we transform the equation into a set of Poisson equations. Two sets of distribution functions are employed in the lattice Boltzmann equation to recover the Poisson equations. Based on this model, some problems on the rectangular elastic thin plate with small deflection are simulated. The comparisons between the numerical results and the analysis solutions are given in detail. The numerical examples show that the lattice Boltzmann model can be used to solve problems of the elastic thin plate with small deflection.