Application of the sensitivity analysis method for the solution of the inverse creep problem of a wingbox structure on the basis of super-element model

Aeronautical and Space-Rocket Engineering

Strength and thermal conditions of flying vehicles


Huang S. *, Kostin V. A.**, Laptevа E. Y.***

Kazan National Research Technical University named after A.N. Tupolev, KNRTU-KAI, 10, Karl Marks str., Kazan, 420111, Russia



The research paper considers the problem of isochronic curves recovery of thin-walled design structures creep referred to deformations measured within the process of full-scale live experiment. It is known that as time passes creep deformations can appear in the construction. They are graphically usually represented as «deformation-time» curves measured by standardized sample testing. However, it has been found out that the deformation curves obtained during testing procedures of the construction differ fr om standard samples due to various reasons: power-based, technological, thermodynamical, etc. The article presents an approach to the corresponding curves construction, based on the processing of the results of the aircraft construction strength experiment.

Setting up the problem for general thin-walled constructions in mathematical terms, we obtain the necessity to optimize the objective functional in the form of the squared residual error of the corresponded theoretical and experimental deformations to the minimum. Working out the solution of the optimization problem is carried out iteratively using the sensitivity matrix, which is the derivative of the deformation function vector along the vector of elastic parameters variables. As the required parameters which control the stress-strained state (SSS) of the structure we choose the secant elastic modulus of the material. To solve a direct problem of the stress-strained state value determination the finite element method (FEM) in the form of a super-element model is used. This makes it possible to reduce the number of diverse required parameters at sufficient accuracy.

Due to the lack of data from the physical experiment, we obtain the numerical deformation values, using the FEM. This is done by solving a direct problem, wh ere measure of inaccuracy typical for strain and load application gauging is introduced. A mathematical calculation has been made for a four-stiffener wingbox operating under the mechanical and temperature load. Figures of the first and second stiffeners show the change of values of the theoretically obtained deformations in case of iterations in the direction of the corresponding experimental values. Isochronic creep curves have been constructed. The application of the sensitivity function has made it possible to purposefully organize the iteration process in the search for elastic parameters and to construct creep curves for the structural elements. The results of the research can be useful for further development of methods of identifying and improving of thin-walled structures according to the testing data, in case of creeping process as well.


thin-wall constructions, isochronous curve, sensitivity analysis, superelement model


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