Goal-oriented error estimation for beams on elastic foundation with double shear effect

In this paper, goal-oriented error estimation for Timoshenko beams on Pasternak foundation, which involves double shear effect, is performed. The constitutive relation error (CRE) estimation is used in finite element analysis (FEA) to acquire strict bounds on quantities of interest. Due to the coupling of the displacement field and the internal force field in the equilibrium equations of the beam, the prolongation condition for construction of the admissible internal force field, a pillar of the CRE estimation, is not directly applicable. To overcome this difficulty, an auxiliary approximate problem whose stress solution enables the CRE estimation to proceed is introduced. Thereafter, strict bounds of outputs for the beam are obtained by dual analysis to which a significant adjunct is the circumvention of shear locking in low-order finite element analysis. Numerical results are presented to validate the strict bounding properties for quantities of beams on elastic foundation and accurate estimation of displacement quantities that is impervious to shear locking.