Wyboczenie trójwarstwowej płyty kołowej poza zakresem sprężystym

When considering an ideal sandwich plate (the Kirchhoff hypothesis of normal segment is valid for the whole plate cross-section, in external layers act the membrane stresses), the integration of the basic set of Eqs. (2.15) is possible. The exact solution (2.17) is of the same form as in elastic plates but its coefficients depend both on the type of process and yielding of the zones of the plate considered. Results obtained on the base of the hypothesis of constant loads and increasing loads are analyzed. These solutions are valid both for the deformation theory and for the plastic flow theory, depending on the form of the stiffness matrix E_jr, according to (2.11). In the case of increasing loads the formula (3.14) for the slope at the bifurcation point is derived. An approximate solution for the constant load hypothesis is obtained, applying the Iliyushin method of neclecting the membrane forces variation. The exact solution leads to characteristic equations which result from satisfying the continuity relations and the appropriate boundary conditions. Eq. (4.7) for the simply supported plate is obtained, and for the clamped one the set of Eqs. (4.14) or (4.16), depending on the number of zones of different types of processes. A special case of ideally elastic-plastic material is also considered. Numerical computations for the theory of plastic flow and Poisson's ratio v=0.3 are performed. The results are presented in tables for different values of the tangent modulus. The obtained solutions are generalized on the case of the real sandwich cross-section with a determable core. The formula (7.3) has been derived to caleulate the buckling load according to the Bijlaard method of split ridigities.