In this paper, the problem of the elasto-viscoplastic dynamic behaviour of geometrically non-linear plates and shells is studied under the assumption of small strains and moderate rotations. The Chaboche and Bodner-Partom models were chosen among several types of constitutive laws. To avoid the calculation of the stiffness matrix, an effective procedure using the central difference method of solving the equations of motion was applied. The trapezoidal method was used to integrate the constitutive viscoplastic laws. A nine-node isoparametric shell element was utilised for the finite element algorithm.

Dynamics of elasto-viscoplastic plates and shells

A review of the works devoted to stability of Bingham flows with respect to perturbations of various kinds is presented. Both hydrodynamic aspects and bifurcation approaches to stability are affected. Much attention is given to Il’yushin’ articles in the late 1930s and the early 1940s of the twentieth century which had been pioneer in these subjects.

Stability of Bingham flows: from the earliest works of A.A. Il'yushin to the present

Variational bounds and integral relations method in problems of stability

In this paper, the problem of the elasto‐viscoplastic dynamic and thermal behaviour of geometrically non‐linear plates and shells is studied under the assumption of small strains and large rotations. The first‐order shear deformation shell theory and the Chaboche constitutive viscoplastic model taking the temperature fields into account are used for computations. An effective procedure using the central difference method of solving the equations of motion is applied. The trapezoidal method is used to integrate the constitutive viscoplastic law. A nine node isoparametric shell element has been utilised for the finite element algorithm. Finally, some examples are presented and compared with the results obtained by moderate rotation theory.

W. Wojewódzki

Papers

Dynamic buckling of viscoplastic spherical shell