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Extra info for (0, 1, 2, 4) Interpolation by G -splines
This algorithm starts with the calculation of Ψ for a number of random combinations of B and H, chosen within their bounds, locating the combination corresponding to the lowest value of Ψ. Starting from this combination, used now as an initial anchor, a random search is executed within a specified radius from the anchor point. Whenever a lower value of Ψ is found, the anchor is moved to the corresponding combination of design variables and the process is repeated. The sequence is stopped when all values of Ψ within the search radius are larger than the corresponding value at the anchor.
Consider the problem shown in Figure 1, a timber beam with cross-sectional dimensions B and H and a span L, carrying loads P and Q. Both are uniformly distributed but have different statistical properties: P is a dead load, with low variability, Q is a live load with higher variability. The bending strength of the beam is f and the modulus of elasticity is E. Two performance requirements are specified under normal service conditions: (a) the beam must carry the loads without bending failure and (b) the maximum deflection should not exceed 1/180 of the span.
In Table 2 the optimum designs obtained and the corresponding structural weights are shown together with the CPU times required by each procedure. It can be seen that the NDP procedures give the most economic designs, in terms of the material weight, while the MmRS procedure lead to the most expensive solution. Furthermore, comparing the dynamic procedures with natural and artificial records it can be seen that natural records lead to less material weight. The LDP procedures compared to the MmRS procedure achieved a volume reduction of 12% and 4% for the natural records (NAT) and the artificial records (AR) case, respectively, while the corresponding reduction of the NDP procedures is 60% and 57%, respectively.
(0, 1, 2, 4) Interpolation by G -splines