Approximate method for local elastic-plastic problems solving

Aeronautical and Space-Rocket Engineering

Strength and thermal conditions of flying vehicles


Svirskii Y. A.*, Bautin A. A.**, Luk’yanchuk A. A., Basov V. N.

Central Aerohydrodynamic Institute named after N.E. Zhukovsky, TsAGI, 1, Zhukovsky str., Zhukovsky, Moscow Region, 140180, Russia



In the last twenty years, durability computing techniques with account for local elastic-plastic strain-stress state have achieved a status of the Industry Standard while producing aviation, automotive, cargo and earth moving equipment all over the world. Although the fundamental concepts of this approach are quite simple, the large-scale automation and this technique application for strength calculation of both large dynamically loaded structures and machines driving gears led, in one hand, to the new possibilities emergence for engineers, but, on the other hand, they created extra challenges for the designers of the durability evaluation software. Presently, there is a possibility of dynamic models application for aviation structure loading computing, finite element models, allowing compute local strains by the applied loads, and techniques for more accurate plasticity computing for damageability estimation.

The article considers one of the methods for solving the elastic-plastic problem at cycle-by-cycle calculation, which can be applied for the durability evaluation with account for non-linear effects of interaction of loads of various values, especially after rare loads of high values. The need for analytical methods for elastic-plastic stresses computation developing and improving is caused by high labor intensity and low computing speed through numerical methods, such as finite element method.

The article proposes a new approximate formula for determining elastic plastic stresses and strains at the point of failure. The proposed approach is based on the solution of the elastic-plastic problem by the finite element method for the static case, as well as the method developed by the authors for fitting the static and cyclic stress-strain curves based on standard constants and the Masing principle. The suggested formula for determining the dependencies of local stresses and strains on nominal stresses for typical concentrators provides the necessary dependencies, close in accuracy to the results determined by the finite element method. This formula application will allow developing effective methods for durability computing based on local elastic-plastic stresses and strains under multi-cycle loading, being typical for aircraft structures.

The article presents comparisons of local stresses dependencies at the most stressed points on nominal stresses, obtained with the proposed formula and the finite element method for typical stress concentrators of the aircraft structure such as strips with free hole, fillet, and stringer runout.


durability computing technique by local tensions, durability of elements with typical concentrators, finite element model of bolted joint, cyclic deformation curve


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