An improved interval finite element method based on the element-by-element technique for large truss system and plane problems

The interval finite element method based on the element-by-element technique is proved to be a rigorous and efficient method for considering interval uncertainties. The structural internal force of the same accuracy as the interval response displacement can be obtained by combining the variational method and the Lagrange multiplier method. However, the increase of the Lagrange multiplier reduces the efficiency of solving the equation, especially for a large truss system. In addition, the method is mostly used to analyse truss system, and the applications in plane problems are still rare. In this article, an improved method involving modification of the Lagrange multiplier interval equations is proposed to calculate interval displacements and interval internal forces at the same time. In this proposed method, the increase of the unknown Lagrange interval does not affect the solution of the equations. For plane problems, a new method for solving the stress interval of the element is proposed. This proposed method can effectively reduce the expansion of the stress interval of the element. Finally, the correctness and rationality of the proposed method are verified by numerical examples.