On the removal of rigid body motions in the interior BVP of plane elasticity by using node support in conjunction with least square technique

Abstract

This paper provides an effective technique for removing the rigid body motions in the interior traction BVP (boundary value problem) of plane elasticity. In the technique, we assume three additional node support conditions. After substituting those conditions in the algebraic equations derived from discretization of BIE (boundary integral equation), we will obtain the algebraic equations where the number of the equations is larger than the number of unknowns. The mentioned algebraic equations can be solved by using the least square technique. Finally, the displacement vector can be evaluated. A stress component derived from the suggested technique is compared to the exact one. Excellent accuracy has been found in the suggested technique.