Moving finite element analysis for the indentation of elastic beams (Q1118466)

A numerical technique called movig finite element analysis is developed to tackle the indentation of elastic beams whose closed-form solution exist. The governing equation with Lagrange multipliers embedded, derived from the variational principles, is now subjected to the constraint equations and the interface equation. In practice, the constraint equations are used to match both the deflection and the slope of the beam within the contact region with the geometric description of the indentor, while the interface equation is utilized to calculate the incremental movement of the marginal node in one load step. The numerical results calculated from the proposed algorithm incorporated with incremental and iterative procedures are displaced and compared against the closed-form solution obtained from elementary beam theory. A discussion on the inclusion of shear effects is also presented.