Pointwise Force Equilibrium Preserving Spectral Element Method for Structural Problems

Abstract

In structural mechanics the geometry is a crucial factor in the derivation of the governing force equilibrium equations, which describe the balance of forces in a discrete setting. In conventional discretization techniques the quantities are approximated through nodal expansions, which lead to global force equilibrium, but not local. This paper shows that by considering the geometry of the problem the equilibrium of forces can be satisfied globally as well as locally.