PSI - Issue 37

L.V. Stepanova et al. / Procedia Structural Integrity 37 (2022) 920–925 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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3. Conclusions The nonlinear problem for the plate with the central hole under creep conditions is studied. The approximate analytical solution to the problem for the infinite plate with the circular hole under uniaxial tension under creep regime is obtained by the quasilinearization method. Three approximations of the solution for the nonlinear problem are found. Using software package SUMULIA Abaqus several numerical solutions for various creep exponent values are obtained. It is worth to note that the tangential stress reaches its maximum value not at the circular hole but at the internal point of the plate. It is shown that quasilinearization method is the effective method for nonlinear problems. Acknowledgements The work was supported by Russian Foundation for Basic Research (project 19-31-90100). References Aznam, S. M., Ghani, N.A.C., Chowdhury M.S.H., 2019. A numerical solution for nonlinear heat transfer of fin problems using the Haar wavelet quasilinearization method. Results in Physics 14, 102393. Bellman, R.E., Kalaba, R.E., 1965. “ Quasilinearization and Nonlinear Boundary Value Problems ”, Elsevier, New York. Koleva N, Vulkov L., 2010. Two-grid quasilinearization approach to ODEs with applications to model problems in physics and mechanics. Computer Physics Communications 181(3), 663-670. Magagula, V.M., Motsa, S.S., Sibanda, P., 2020. On the bivariate spectral quasilinearization method for nonlinear boundary layer partial differential equations, in ” Applications of Heat, Mass and Fluid Boundary Layers ” . Woodhead Publishing, Sawston, pp. 177-190. Malyk I., Shrahili M., Shafay A., Goswami P., Sharma Sh., Dubey R., 2020. Analytical solution of non- linear fractional Burger’s equation in the framework of different fractional derivative operators. Results in Physics 19, 103397. Pandey R.K., Tomar S., 2021. An effective scheme for solving a class of nonlinear doubly singular boundary value problems through quasilinearization approach. Journal of Computational and Applied mathematics 392,113411. Polyanin, A.D., 2019. Construction of exact solutions in implicit form for PDEs: New functional separable solutions of non-linear reaction-diffusion equations with variable coefficients. International Journal of Non-linear Mechanics 111, 95-105. Polyanin, A.D., Sorokin, V,G., 2021. Construction of exact solutions to nonlinear PDEs with delay using solutions of simpler PDEs without delay. Communications in Nonlinear Science and Numerical Simulations 95, 105634. Rani, D., Mishra, V., 2020. Numerical inverse Laplace transform based on Bernoulli polynomials operational matrix for solving nonlinear differential equations. Results in Physics 16. 102836. Singh, R., Guleria, V., Singh M., 2020. Haar wavelet quasilinearization method for numerical solution of Emden-Fowler type equations Mathematics and Computers in Simulations 174, 123-133. Stepanova, L., Yakovleva, E.M., 2015. Asymptotic stress field in the vicinity of mixed-mode crack under plane stress conditions for power-law hardening material. Journal of Mechanics of Materials and Structures 10 (3), 367 – 393. Stepanova, L., Yakovleva, E., 2016. Stress-strain state near the crack tip under mixed-mode loading: Asymptotic approach and numerical solutions of nonlinear eigenvalue problems. AIP Conference Proceedings 1785, 030030. Stepanova, L., Yakovleva, E., 2016. Asymptotics of eigenvalues of the nonlinear eigenvalue problem arising from the near mixed-mode crack tip stress-strain. Numerical Analysis and Applications 9(2) 159-170. Su G., Lu l., Tang B., Liu Z., 2020. Quasilinearisation technique for solving nonlinear Riemann-Liouville fractional-order problems. Applied Mathematics and Computation 378, 125199. Verma, A.K., Tiwari, D., 2019. Higher resolution methods based on quasilinearization and Haar wavelets on Lane – Emden equations. International Journal of Wavelets. Multiresolution and Information Processing 17(3), 1950005.