A Multi-Dimensional Lagrange Multiplier Method to Identify the Load Distribution on 3D Special-Shaped Surface in the Strength Analysis of Aircraft Structure

In the process of aircraft structural design, the aerodynamic load and inertial load need to be distributed from single loading points to distributed finite element (FE) nodes before strength analysis. The most commonly used loading distribution method is a Multi-Point Arrangement (MPA) method, which introduces a one-dimensional Lagrange multiplier based on the principle of minimum deformation energy, and simplifies the special-shaped 3D surface in aircraft structure to a plane. However, the actual aircraft structure contains a large number of special-shaped surfaces, and the MPA method cannot accurately distribute the loads on these complex special-shaped surfaces, affecting the accuracy of strength analysis. This paper developed a new 3D load distribution method based on multi-dimensional Lagrange multipliers (MDLM), which can simultaneously achieve an efficient and accurate distribution of surface aerodynamic loads and inertial loads in all directions. Typical numerical cases showed that when an aircraft structure model is a plane, this MDLM method converges to the traditional MPA method. For 3D special-shaped surfaces, the average error of this MDLM method is 0.77–2.28%, which is significantly smaller than the average error of the traditional MPA method (3.30–7.40%).