2001 , Volume 6, № 5, p.39-59

The algorithm for numerical solution of quasistatic problems on axisymmetric deformation of shells of revolution, which are made from elastoplastic material, is suggested taking into account geometric nonlinearity. The determination of equilibrium configurations is reduced to the solution of Cauchy problem for a system of nonlinear ordinary differential equations due to finite-difference approximation of differential equations with respect to meridional coordinate. The special attention is given to determination of these configurations in neighborhoods of singular points of integral curve, namely, bifurcation and return points, where the matrix of system of equations degenerates. The auxiliary generalized problem on determination of eigenvalues and appropriate eigenvectors is suggested to be solved for continuation of the solution through singular points. The developed algorithm of solving problems in vicinities of singular points is applied to the problem on deformation of the longitudinally compressed simply supported circular cylindrical shell. The new solutions are obtained, which are verified by comparison with known experimental data. The singular points of both types (return and bifurcation) are obtained in the solutions of these problems. The singular points being simultaneously return and bifurcation points are also obtained.

*74C05 Small-strain, rate-independent theories (including rigid-plastic and elasto-plastic materials)

74S20 Finite difference methods

74K25 Shells