On Solving Nonlinear Elasticity Problems Using a Boundary-Elements-Based Solution Method

Abstract

The attractiveness of the boundary element method—the reduction in the problem dimension by one—is lost when solving nonlinear solid mechanics problems. The point collocation method applied to strong-form differential equations is appealing because it is easy to implement. The method becomes inaccurate in the presence of traction boundary conditions, which are inevitable in solid mechanics. A judicious combination of the point collocation and the boundary integral formulation of Navier’s equation allows a pure boundary element method to be obtained for the solution of nonlinear elasticity problems. The potential of the approach is investigated in some simple examples considering isotropic and anisotropic material models in the total Lagrangian framework.

Keywords

• elasticity
• anisotropy
• large deformation
• BEM
• meshfree strong form
• radial basis function