The change in the value of the breaking energy is discussed here for selected steel grades used in building structures after subjecting the samples made of them to episodes of heating in the steady-state heating regime and then cooling in simulated fire conditions. These changes were recorded based on the instrumented Charpy impact tests, in relation to the material initial state. The S355J2+N, 1H18N9T steels and also X2CrNiMoN22-5-3 duplex steel were selected for detailed analysis. The fire conditions were modelled experimentally by heating the samples and then keeping them for a specified time at a constant temperature of: 600 °C (first series) and 800 °C (second series), respectively. Two alternative cooling variants were investigated in the experiment: slow cooling of the samples in the furnace, simulating the natural fire progress, without any external extinguishing action and cooling in water mist simulating an extinguishing action by a fire brigade. The temperature of the tested samples was set at the level of −20 °C and alternatively at the level of +20 °C. The conducted analysis is aimed at assessing the risk of sudden, catastrophic fracture of load-bearing structure made of steel degraded as a result of a fire that occurred previously with different development scenarios.
Solution time of nonlinear constrained optimization problem depends on the number of constraints, decision variables and conditioning of decision variables space. While the numbers of constraints and decision variables are external to the optimization procedure itself, one may try to affect the conditioning of the decision variables space within the self contained optimization module. This will directly affect the ratio of convergence of an iterative, gradient based optimization routine. Another opportunity for speedup of the solution process in case of quadratic objective function lies in the chance to eliminate the decision variables least affecting the objective function, and thus decrease the optimization problem size. Elimination of decision variables is based on the singular value decomposition of the objective function. Singular values showing up as a result of such procedure indicate that certain linear combinations of original decision variables do not affect the objective function, and thus may be eliminated from further deliberations. Also if near singular values are encountered as well, even deeper reduction of the optimization problem size is still possible, but at a cost in terms of final solution quality. An idea how to improve the conditioning of decision variables space, and limit the number of decision variables in case of quadratic objective function using singular value decomposition is presented in this paper. Results of computer tests performed during minimization of quadratic objective function and subject to quadratic constraints are enclosed and discussed.
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