NEW ASPECT OF THE ANALYSIS OF ELASTO-PLASTIC STRUCTURES WITH TIME-DEPENDENT LOADING
Abstract
In case of time-dependent loading the state variables of a structure depend on space and time and in a significant part of calculations time is the independent parameter. By use of the Hamiltonian principle one can overcome the difficulties if the time is an independent parameter. In this paper a new approach is presented where the solution of the boundary value problem is approximated by an infinite function series of the state variables in time and is obtained by mathematical programming. The space of the structure is discretized at the usual way (finite domain), but the state variables, ordered to the nodes, are continuous functions of time. The problem is solved by mathematical programming in the function space \ell 2 and in spite of direct solution technique of the mathematical programming, the time-dependent structural response for the time-dependent loading can be followed and the energy dissipation is considered. A comparison of the regular and the new method is discussed, as well. Finally, a numerical example is presented.
