A traction-based equilibrium finite element free from spurious kinematic modes for linear elasticity problems

This paper presents equilibrium elements for dual analysis. A traction-based equilibrium element is proposed in which tractions of an element instead of stresses are chosen as DOFs, and therefore, the interelement continuity and the Neumann boundary balance are directly satisfied. To be solvable, equilibrated tractions with respect to the space of rigid body motion are required for each element. As a result, spurious kinematic modes that may inflict troubles on stress-based equilibrium elements do not appear in the element because only equilibrium constraints on tractions are required. An admissible stress field is eventually constructed in terms of the equilibrated tractions for the element, and hence, equilibrium finite element procedures can proceed. The element is also generalized to accommodate non-zero body forces, nonlinear boundary tractions and curved Neumann boundaries. Numerical tests including a single equilibrium element, error estimation of a cantilever beam and an infinite plate with a circular hole are conducted, displaying excellent convergence and effectiveness of the element for error estimation. Copyright (C) 2014 John Wiley & Sons, Ltd.