caa a22 4500 475775570 CHVBK 20180406123630.0 cr unu---uuuuu 170329e20000101xx s 000 0 eng 10.1007/BF02465246 doi (NATIONALLICENCE)springer-10.1007/BF02465246 Bondar' V. aut Complex-potential method in the nonlinear theory of elasticity [Elektronische Daten] [V. Bondar'] For materials characterized by a linear relation between Almansi strains and Cauchy stresses, relations between stresses and complex potentials are obtained and the plane static problem of the theory of elasticity is thus reduced to a boundary-value problem for the potentials. The resulting relations are nonlinear in the potentials; they generalize well-known Kolosov's formulas of linear elasticity. A condition under which the results of the linear theory of elasticity follow from the nonlinear theory considered is established. An approximate solution of the nonlinear problem for the potentials is obtained by the small-parameter method, which reduces the problem to a sequence of linear problems of the same type, in which the zeroth approximation corresponds to the problem of linear elasticity. The method is used to obtain both exact and approximate solutions for the problem of the extension of a plate with an elliptic hole. In these solutions, the behavior of stresses on the hole contour is illustrated by graphs. Kluwer Academic/Plenum Publishers, 2000 Journal of Applied Mechanics and Technical Physics Kluwer Academic Publishers-Plenum Publishers 41/1(2000-01-01), 120-130 0021-8944 41:1<120 2000 41 10808 https://doi.org/10.1007/BF02465246 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02465246 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Bondar' V. aut NATIONALLICENCE 773 0- Journal of Applied Mechanics and Technical Physics Kluwer Academic Publishers-Plenum Publishers 41/1(2000-01-01), 120-130 0021-8944 41:1<120 2000 41 10808 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer