PSI - Issue 72

Alexander Kamenskikh et al. / Procedia Structural Integrity 72 (2025) 252–259

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Numerical and experimental studies of the dynamic and static behavior of plates and shells under the action of temperature loads are described by Azzara et al. (2022), Álvarez and Bisagni (2021), Kuo (2016), Silva et al. (2019). Modeling and experimental study aimed to construct the dependence of flexural behavior of a clamped-clamped plate on the temperature load were carried out by Álvarez and Bisagni (2021). The results show that in composite plates heated to a certain temperature there is a change in the shape of buckling, whereas this feature is not observed in isotropic aluminum plates. Unlike finite element calculations, the experimental studies have revealed much greater deflections and smaller critical loads for the examined specimens. This discrepancy has been attributed to the non-ideal manufacturing of specimens and the lack of accurate material characteristics. Silva et al. (2019) analyze the behavior of a plate fixed at the center and having free edges under the action of inhomogeneous temperature. It is shown that temperature and its distribution dramatically influence the spectrum of natural frequencies of vibration. It has been stressed that consideration of temperature loads in numerical modeling of aerospace structures is rather important not only because of their effect on the mechanical parameters of the material, but also on their dynamic characteristics and geometry. It should be noted that the buckling is not always considered a negative factor. There are studies, in which this phenomenon adds specific functionality to structures, which allows us to create smart-systems and meta-materials, to accumulate energy and solve many other problems of innovative material technologies. A review of these studies is carried out by Champneys et al. (2019) and Reis (2015). This study is devoted to the numerical analysis of free vibration of a temperature-loaded segment of a cylindrical shell before and after buckling. Panel structures with different curvature, including plates, with two variants of edge fixing are investigated. The obtained dependences allow us to conclude that, after buckling occurs, the lowest natural frequency of these shells increases with rising temperature load. 2. Mathematical formulation We consider a segment of a shallow cylindrical shell of length L , width (chord) C , and thickness h (Fig. 1 a ). Its convexity (rise) relative to the O xy plane is characterized by the parameter H . The structure is subjected to a temperature load Δ T in the range of – 40 to +40°C, which together with kinematic boundary conditions leads to a stress-strain state. In the case when the temperature load re aches a critical value Δ T cr the buckling of shell occurs. The purpose of this section is to develop and verify on a simple example the developed numerical algorithm that allows us to estimate the change of the lowest natural frequency of structure vibration under the influence of temperature load in the pre-critical and subcritical states.

a

b

Fig. 1. Shallow cylindrical shell ( a ) and its finite element model ( b ).

The geometrically nonlinear problem of dynamic deformation of a structure under temperature load is formulated using the equations of motion:   , , , kj ij i j i k u u         (1)