Numerical Investigation of the Elastic Lamina Deformation Based on Radial Layout D2Q9 Lattice Boltzmann Model

Abstract

The radial layout D2Q9 lattice Boltzmann model applied to elastic lamina was investigated. An equivalent differential discursive form for the equation of elastic lamina deformation is provided, and its equivalency to the lattice Boltzmann method (LBM) equation was proved by the Chapman–Enskog expansion. A set of equilibrium distribution functions for the radial layout D2Q9 lattice Boltzmann model and elastic lamina deformation was constructed. The functional form of the external source term is given; thus, the algorithm for the radial layout D2Q9 lattice Boltzmann model was determined. The characteristics of deformations of elastic lamina with different load patterns (loaded evenly on the whole area, loaded linearly on the whole area, loaded evenly on the left half area, and concentrated in the center) were simulated using this model. Numerical tests were conducted to compare the numerical results and the analytical solutions. This work demonstrated that the radial layout D2Q9 lattice Boltzmann model can be used to solve elastic lamina deformations. This paper provides a novel numerical method for computing the deformation of elastic lamina, and has the potential for further application in fluid–structure interaction. A lattice Boltzmann model that can calculate the deformation of elastic thin plates is proposed in this paper. The model adopts the general format of fluid simulations on the lattice format, and this paper shows it to be applicable for solving problems involving elastic systems. The model can be applied to both fluid and solid simulations if appropriate equilibrium distribution functions are selected. Because the general format is adopted in this model, the model has advantages in dealing with the fluid–structure interaction boundary problem, and has the potential to simplify LBM programs involving fluid–structure interaction problems and improve the computation efficiency of the LBM. The model can be applied to fluid–structure interaction computation in fields of civil structures, machinery, biomechanics, and so forth, such as for the displacement of high-rise buildings under a wind field, the response of wind turbines under excitation, the interaction of blood and vessels, and so on.