On an optimal control problem for the shape of thin inclusions in elastic bodies
Tóm tắt
Từ khóa
Tài liệu tham khảo
N. F. Morozov,Mathematical Questions of Crack Theory (Nauka, Moscow, 1984) [in Russian].
A. M. Khludnev and V. A. Kovtunenko, Analysis of Cracks in Solids (WIT Press, Southampton, Boston, 2000).
A.M. Khludnev, Elasticity Theory Problems in Nonsmooth Domains (Fizmatlit, Moscow, 2010) [in Russian].
G. P. Cherepanov, Mechanics of Brittle Fracture (Nauka, Moscow, 1974; McGraw-Hill, New York, 1979).
E. M. Rudoi, “Differentiation of Energy Functionals in Two-Dimensional Elasticity Theory for Solids With Curvilinear Cracks,” Zh. Priklk. Mekh. Tekhn. Fiz. 45(6), 83–94 (2004) [J. Appl.Mech. Tech. Phys. 45 (6), 843–852 (2004)].
E. M. Rudoi, “Differentiation of Energy Functionals in a Problem on Curvilinear Crack With Possible Contact of the Faces,” Mekh. Tverd. Tela No. 6, 113–127 (2007).
N. V. Banichuk, Optimization of Elastic Body Forms (Nauka, Moscow, 1980) [in Russian].
N. V. Banichuk, Optimization of Structure Components of Composites (Mashinostroenie, Moscow, 1988) [in Russian].
V. G. Litvinov, Optimization in Elliptic Boundary Value Problems With Application to Mechanics (Nauka, Moscow, 1987) [in Russian].
J. Haslinger and P. Neittaanmäki, Finite Element Approximation for Optimal Shape Design: Theory and Applications (Wiley, New York, 1988; Mir, Moscow, 1992).
K. A. Lur’e, Optimal Control in Problems of Mathematical Physics (Nauka, Moscow, 1975) [in Russian].
A. M. Khludnev and J. Sokolowski, Modelling and Control in SolidMechanics (Birkhauser, Basel, 1997).
A. M. Khludnev and G. Leugering, “Optimal Control of Cracks in Elastic Bodies With Thin Rigid Inclusions,” Z. Angew.Math.Mech. 91(2), 125–137 (2011).
A. M. Khludnev, “Optimal Control of Crack Growth in Elastic Body With Inclusions,” Europ. J. Mech. A/Solids 29(3), 392–399 (2010).
A. Khludnev, G. Leugering, and M. Specovius-Neugebauer, “Optimal Control of Inclusion and Crack Shapes in Elastic Bodies,” J. Optim. Theory Appl. 155(1), 54–78 (2012).
A. M. Khludnev and M. Negri, “Optimal Rigid Inclusion Shapes in Elastic Bodies With Cracks,” Z. Angew. Math. Phys. 64(1), 179–191 (2012).
G. Leugering and A. M. Khludnev, “On the Equilibriumof Elastic Bodies Containing Thin Rigid Inclusions,” Dokl. Akad. Nauk 430(1), 47–50 (2010) [Dokl. Phys. 55 (1), 18–22 (2010)].