Numerical Non-Equilibrium and Smoothing of Solutions in The Difference Method for Plane 2-Dimensional Adhesive Joints / Nierównowaga Numeryczna i Wygładzanie Rozwiazań w Metodzie Różnicowej Dla Dwuwymiarowych Połączeń Klejowych

Abstract

Abstract The subject of the paper is related to problems with numerical errors in the finite difference method used to solve equations of the theory of elasticity describing 2- dimensional adhesive joints in the plane stress state. Adhesive joints are described in terms of displacements by four elliptic partial differential equations of the second order with static and kinematic boundary conditions. If adhesive joint is constrained as a statically determinate body and is loaded by a self-equilibrated loading, the finite difference solution is sensitive to kinematic boundary conditions. Displacements computed at the constraints are not exactly zero. Thus, the solution features a numerical error as if the adhesive joint was not in equilibrium. Herein this phenomenon is called numerical non-equilibrium. The disturbances in displacements and stress distributions can be decreased or eliminated by a correction of loading acting on the adhesive joint or by smoothing of solutions based on Dirichlet boundary value problem.