New article: On the pure traction problem of linear elasticity: A regularized formulation and its robust approximation
New article: - Kaleem, A. and Gebhardt, C. and Romero, I. (2026). On the pure traction problem of linear elasticity: A regularized formulation and its robust approximation, Computer Methods in Applied Mechanics and Engineering, 459, 119105. link
An old-standing problem in elasticity and other variational problems is finding a solution when only Neumann (traction) boundary conditions are imposed on the solution domain. Traditionally, this very common problem has been solved by selecting some special nodes and imposing special boundary conditions on them to remove the rigid body motions. Alternatively, Lagrange multipliers can be employed for the same purpose, at a much higher cost.
In this article, we propose, for the first time, a convergent (almost cost-free) method for the pure Neumann problem. We describe the intuition behind the idea, the numerical analysis of convergence, and provide some illustrative examples.