By W. Gutkowski (eds.)
The engineering layout of buildings and machines is composed frequently to find the easiest answer between a finite variety of possible judgements. This quantity includes difficulties and resolution tools for discrete structural optimization. specific, approximate and heuristic equipment are awarded employing deterministic and stochastic approaches.
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Additional resources for Discrete Structural Optimization
Step 1. Solve the problem as a continuous one omitting constraints imposed on integrity of x. If obtained values of design variables x< 0 > are all integer then it is an optimum solution for the problem in question. In other case go to step 2. Step 2. Divided one of the obtained non integer variables say xi0 > into integral [xi0 >J and fractional parts. Step 3. Branch the initial problem in the two following subproblems f(x) (1) minimize subject to h(x) g(x) ~ 0; x~e ~ [x~0 )] g(x) ~ 0; Xk f(x) (2) minimize subject to = 0; h(x) = 0; ~ [xi0 >] + 1 and solve them as continuous problems.
W·c <- wmax . dfo-l,t dfo-l,t (28) Store vortices of each subgraph (fo - 1, i) for which wdfo,i- w; =min Step f +2 (29) Successively verify if structures related to these combinations do not violate any of constraints. First structure fulfilling this condition is the solution of discrete minimum weight solution. If no one of these combinations fulfils constraint conditions go back to Step 2 replacing combination wd. 4. Preselection of List of Available Member Sizes by Constraint Variation. There are practical cases with which z, is the same for several structural elements.
Finally coming to the span r = 3 (Fig. 24) we find that the smallest value of the maximum moment can be found equal to M2 = 80. 6 and moment distribution shown on Fig. 25. -120 Fig. 24. Moments along third span. -80 Fig. 25. Moments distribution for three span beam. = 80. 35 Design Problems and Exact Solution Methods Example of a statically determined truss The dynamic programming procedure case be also applied to minimum weight design of statically determined trusses. The statement of such a problem can be formulated as follows.