|Dopov. Nac. akad. nauk Ukr. 2019, 10:38-42|
Within the framework of the theory of linearized elasticity, the formulation and solution of the plane load trans fer problem from periodically located elastic stringers to two identical elastic bands with initial (residual) stresses are given. In general, the study is carried out within the theory of large (finite) initial deformations and various versions of the theory of small initial deformations for an arbitrary form of the elastic potential. The influence of initial stresses on the distribution of contact forces in elastic bands and stringers is studied. Proceeding from the assumption that stringers are simultaneously loaded by vertical and horizontal forces, the problem is formulated mathematically as a system of integro-differential equations for the unknown contact stresses. Using the Fourier transformation, the system is solved in a closed form. The stress expressions are represented by quite simple Fourier integrals.
|Keywords: contact problems, elastic stringer, initial (residual) tensions, initial deformations, linearized elasticity theory|
1. Arutyunyan, N. Kh. & Mhitaryan, S. M. (1968). Periodic contact problem for a half-plane with elastic straps. Prikl. Mekh. 32, No. 4. pp. 632-646 (in Russian). doi: https://doi.org/10.1016/0021-8928(68)90096-8
2. Sarkisyan, V. S. (1983). Contact problems for the half-planes and strips with elastic straps. Yerevan: Yerevan Univ. Press. (in Russian).
3. Guz, A. N., Babich, S. Y. & Rudnitskii, V. B. (1998). Contact problems for elastic bodies with initial stresses: Focus on Ukrainian research. Int. Appl. Mech. Rew., 51, No. 5. pp. 343-371. doi: https://doi.org/10.1115/1.3099009
4. Dihtyaruk, N. N. (2004). Periodic contact problem for an elastic band with initial (residual) stresses. Dopov. Nac. acad. nauk Ukr., No. 3. pp. 46-49 (in Ukrainian).
5. Guz, A. N., Babich, S. Y. & Rudnitskii, V. B. (1995). Contact interaction of bodies with initial stresses. Kyiv: Vysha Shkola (in Ukrainian).
6. Guz, A. N. (1983). Mechanics of brittle fracture of materials with initial stresses. Kiev: Naukova Dumka (in Russian). doi: https://doi.org/10.1016/B978-1-4832-8440-8.50107-1
7. Shtaerman, I. Ya. (1949). Contact problems of the theory of elasticity. Moscow. Gostehizdat (in Russian).