6th World Congresses of Structural and Multidisciplinary Optimization

1. Abstract In the engineering practice it is very common that during the analysis and design process the designers should take into consideration time dependent loading and/or the state variables are time dependent, as well. The inelastic structural behaviour with a given load history can be solved by step-by-step methods what are connected to time integration techniques and a variety of space discretization methods. Unfortunately, each of them has significant difficulties during the time stepping analysis due to the lack of information in the load history, constitutive equation problems of describing inelastic behaviour of the structures, high computational cost. In this paper a new approach is presented for the design of structures where the solution of the boundary value problem is approximated by an infinite function series of the state variables in time. 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 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. The objective function contains the elastic strain energy and dissipative energy, as well. The equilibrium of the structure, the boundary and initial conditions are given in form of equality constraints. The yield condition of state-change, the yield condition of load carrying capacity for every member and the bounds of the unknowns are expressed by the inequalities, respectively. The design variables are the dimensions of the cross-sectional areas.