Problemy optymalnego kształtowania wspornikowej belki lepkopłastycznej przy obciążeniu quasi-statycznym

The paper is devoted to the shape optimization of cantilever I beam under proportional external loading P(X,T)=P_1(X)P_2(T) where P_1(X) denotes arbitrary function of spatial variable, P_2(T) – power function of time. Under the assumption of constant volume and criterion of minimum residual deflection of the free end or minimum of total dissipated energy, the function of cross section A=A_ap(X) is sought. The analytical solution is given for linear and nonlinear law of elastic viscoplastic material; the influence of the form of quasi-static loading program P_2(T) on the optimal function A_opt is described.