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291
124. Tikhonov, A.N., Arsenin, V.Ya.: Methods of Solution of the Non-corrected Problems. Nauka,
Moscow (1979) (in Russian)
125. Krysko, V.A., Awrejcewicz, J., Komarov, S.A.: Nonlinear deformations of spherical panels
subjected to transversal load action. Comput. Methods Appl. Mech. Eng. 194(27–29), 3108–
3126 (2005)
126. Franklin, J.N.: On Tikhonov’s method for ill-posed problems. Math. Comput. 28(128), 889–
907 (1974)
127. Miller, K.: Least squares methods for ill-posed problems with a prescribed bound. SIAM J.
Math. Anal. 1(6), 52–74 (1970)
128. Phillips, D.L.: A technique for the numerical solution of certain integral equations of the first
kind. J. Assoc. Comput. Mach. 9(6), 84–97 (1962)
129. Wolf, A., Swift, J.B., Swinney, H.L., Vastano, J.A.: Determining Lyapunov exponents from
a time series. Phys. D 16, 285–317 (1985)
130. Rosenstein, M.T., Collins, J.J., De Luca, C.J.: A practical method for calculating largest
Lyapunov exponents from small data sets. Phys. D 65, 117–134 (1993)
131. Kantz, H.: A robust method to estimate the maximal Lyapunov exponent of a time series.
Phys. Lett. A 185, 77–87 (1994)
132. Awrejcewicz, J., Krysko, V.A.: Feigenbaum scenario exhibited by thin plate dynamics. Nonlinear Dyn. 24, 373–398 (2006)
133. Awrejcewicz, J.A., Krysko, V.A., Zhigalov, M.V., Saltykova, O.A., Krysko, A.V.: Chaotic
vibrations in flexible multilayered Bernoulli-Euler and Timoshenko type beams. Lat. Am. J.
Solids Struct. 5(4), 319–363 (2008)
134. Ke, L.L., Wang, Y.S.: Size effect on dynamic stability of functionally graded microbeams
based on a modified couple stress theory. Compos. Struct. 93, 342–350 (2011)
135. Volmir, A.S.: Nonlinear Dynamics Plates and Shells. Science, Moscow (1972) (in Russian)
136. Gao, X.L., Zhang, G.Y.: A microstructure- and surface energy-dependent third-order shear
deformation beam model. Z. Angew. Math. Phys. 66, 1871–1894 (2015)
137. Ghayesh, M.H., Farokhi, H., Amabili, M.: Coupled nonlinear size-dependent behaviour of
microbeams. Appl. Phys. A 112, 329–338 (2013)
138. Fedoseyev, V.I.: On the method of finding solution to the non-linear stability problems of
deformable systems. Appl. Math. Mech. 27(2), 265–274 (1963) (in Russian)
139. Awrejcewicz, J., Krysko, V.A., Dobriyan, V., Papkova, I.V., Krysko, A.V.: On the Lyapunov
exponents computation of coupled non-linear Euler-Bernoulli beams. In: Proceedings of
the Fourteenth International Conference on Civil, Structural and Environmental Engineering Computing. Civil-Comp Press, Stirlingshire, UK, Paper 53 (2013)
140. Krysko, A.V., Awrejcewicz, J., Kutepov, I.E., Krysko, V.A.: Stability of curvilinear EulerBernoulli beams in temperature fields. Int. J. Non-linear Mech. 94, 207–215 (2017)
141. Vaz, M.A., Solano, R.F.: Post-buckling analysis of slender elastic rods subjected to uniform
thermal loads. J. Therm. Stress. 26, 847–860 (2003)
142. Li, S.R., Cheng, C.J., Zhou, Y.H.: Thermal post-buckling of elastic beams subjected to a
transversely non-uniform temperature rising. Appl. Math. Mech. 24(5), 514–520 (2003)
143. Li, S.R., Cheng, C.J., Zhou, Y.H.: Thermal post-buckling analysis of heated elastic rods. Appl.
Math. Mech. 21(2), 133–140 (2000)
144. Li, S.R., Zhou, Y.H., Zheng, X.J.: Thermal post-buckling of heated elastic rods with pinnedfixed ends. J. Therm. Stress. 25, 45–56 (2002)
145. Li, S.R., Zhou, Y.H.: Geometrically nonlinear analysis of Timoshenko beams under thermomechanical loadings. J. Therm. Stress. 26, 861–872 (2003)
146. Dinzart, F., Molinari, A., Herbach, R.: Thermomechanical response of a viscoelastic beam
under cyclic bending; self-heating and thermal failure. Arch. Mech. 60(1), 59–85 (2008)
147. Abbasi, M., Sabbaghian, M., Eslami, M.R.: Exact closed-form solution of the dynamic coupled
thermoelastic response of a functionally graded Timoshenko beam. J. Mech. Mater. Struct.
5(1), 79–94 (2010)
148. Ma, L.S., Lee, D.W.: A further discussion of nonlinear mechanical behavior for FGM beams
under in-plane thermal loading. Compos. Struct. 93(2), 831–842 (2011)