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401
111. Passos, A.G., Luersen, M.A.: Multiobjective optimization of laminated composite parts with
curvilinear fibers using Kriging-based approaches. J. Struct. Multidisci. Optim. 57(3), 1115–
1127 (2018)
112. Bakhvalov, N.S., Panasenko, G.: Homogenisation: Averaging Processes in Periodic Media.
Springer, Netherlands (1989)
113. Andrianov, I.V., Awrejcewicz, J., Danishevs’kyy, V.V., Ivankov, A.O.: Asymptotic Methods
in the Theory of Plates with Mixed Boundary Conditions. Wiley, New York (2014)
114. Pareto, V.: Manual of Political Economy. Macmillan, New York (1971)
115. Krysko, A.V., Awrejcewicz, J., Pavlov, S.P., Bodyagina, K.S., Zhigalov, M.V., Krysko, V.A.:
Non-linear dynamics of size-dependent Euler-Bernoulli beams with topologically optimized
microstructure and subjected to temperature field. Int. J. Non-Lin. Mech. 104, 75–86 (2018)
116. Ozdemir, O., Kaya, M.O.: Flapwise bending vibration analysis of a rotating tapered cantilever
Bernoulli-Euler beam by differential transform method. J. Sound Vib. 289(1–2), 413–420
(2006)
117. Mindlin, R.D., Tiersten, H.F.: Effects of couple-stresses in linear elasticity. Arch. Ration.
Mech. Anal. 11, 415–448 (1962)
118. Yang, F., Chong, M., Lam, D.C.C., Tong, P.: Couple stress based strain gradient theory for
elasticity. Int. J. Solids Struct. 39, 2731–2743 (2002)
119. Farokhi, H., Ghayesh, M.H., Amabili, M.: Nonlinear dynamics of a geometrically imperfect
microbeam based on the modified couple stress theory. Int. J. Eng. Sci. 68, 11–23 (2013)
120. Ghayesh, M.H., Amabili, M., Farokhi, H.: Nonlinear forced vibrations of a microbeam based
on the strain gradient elasticity theory. Int. J. Eng. Sci. 63, 52–60 (2013)
121. Krysko, A.V., Awrejcewicz, J., Zhigalov, M.V., Pavlov, S.P., Krysko, V.A.: Nonlinear
behaviour of different flexible size-dependent beams models based on the modified couple
stress theory. Part 2. Chaotic dynamics of flexible beams. Int. J. Non-Lin. Mech. 93, 106–121
(2017)
122. Krysko, A.V., Awrejcewicz, J., Zhigalov, M.V., Pavlov, S.P., Krysko, V.A.: Nonlinear
behaviour of different flexible size-dependent beams models based on the modified couple stress theory. Part 1. Governing equations and static analysis of flexible beams. Int. J.
Non-Lin. Mech. 93, 96–105 (2017)
123. Krysko, A.V., Awrejcewicz, J., Pavlov, S.P., Zhigalov, M.V., Krysko, V.A.: Mathematical
model of a three-layer micro- and nano-beams based on the hypotheses of the GrigolyukChulkov and the modified couple stress theory. Int. J. Sol. Struct. 117, 39–50 (2017)
124. Awrejcewicz, J., Krysko, V.A., Sopenko, A.A., Zhigalov, M.V., Kirichenko, A.V., Krysko,
A.V.: Mathematical modelling of physically/geometrically non-linear micro-shells with
account of coupling of temperature and deformation fields. Chaos Sol. Fract. 104, 635–654
(2017)
125. Duhamel, J.M.C.: Second memoire sur les phenomenes thermoomecaniques. de l’Ecole Polytechnique, 15 (1837)
126. Deaton, J.D., Grandhi, R.V.: Stress-based topology optimization of thermal structures. In:
10th World Congress on Structural and Multidisciplinary Optimization, May 19–24, Orlando
(2013)
127. Choa, S., Choib, J.-Y.: Efficient topology optimization of thermo-elasticity problems using
coupled field adjoint sensitivity analysis method. Fin. Elem. Anal. Des. 41, 1481–1499 (2005)
128. Rodrigues, H., Fernandes, P.: Topology optimal design of thermoelastic structures using a
homogenization method. Control Cyber. 23(3), 553–563 (1994)
129. Asghari, M., Rahaeifard, M., Kahrobaiyan, M.H., Ahmadian, M.T.: The modified couple
stress functionally graded Timoshenko beam formulation. Mater. Des. 32, 1435–1443 (2011)
130. Wolf, A., Swift, J.B., Swinney, H.L., Vastano, J.A.: Determining Lyapunov exponents from
a time series. Phys. D 16, 285–317 (1985)
131. 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)
132. Kantz, H.: A robust method to estimate the maximal Lyapunov exponent of a time series.
Phys. Lett. A 185, 77–87 (1994)