Investigation of the possible numerical treatments of a compliance-function-shape-oriented robust truss sizing model with uncertain loading directions. (November 2020) - Csébfalvi, Anikó; Lógó, János
Highlights: The total-compliance-variation is introduced for the robust truss-sizing problem with directionally uncertain loads as a new robustness measure. A one-step asymptotically optimal and a two-steps metaheuristic algorithm are developed for the weight-constrained-total-compliance-variation-minimization . The one-step algorithm is working on the usual search space spanned by the design variables with two alternative objectives. The two-steps algorithm firstly defines a lower dimensional search space, and then uses a hybrid metaheuristic search strategy. The two algorithms are benchmarked on the classical ten-bar truss sizing problem with one, two, and four directionally uncertain loads. Abstract: In this paper, the possible numerical treatments of a new compliance-function-shape-oriented robust truss sizing model with directionally uncertain loads have been analyzed. The applied robustness measure is the total-compliance-variation; the corresponding model is a total-compliance-variation minimization model. The model, according to the number of uncertain loads, can be classified as a curve-length, surface-area, volume, and generalized volume minimization problem where the objective is integral and the weight increase is constrained. The numerical treatment of the model is a challenging problem. In this paper, for the numerical treatment a one-step asymptotically optimal algorithm and a two-steps heuristic algorithm are presented. The central element of the one-step algorithm is a mesh with mesh-point-specific displacements, stress constraints, and compliance values. The algorithm can be formulated as a sample-based iterative process using one of the two alternative objectives. The one-step algorithm is computationally expensive but able to find an optimal solution with appropriate maximum running time and mesh-size settings. The two-steps algorithm firstly defines a lower dimensional searching space without displacements and stress constraints and uses it as the searching space in the second step. The hybrid metaheuristic search method is a modified ANGEL algorithm, which is a hybridization of the ant-colony ( AN ), the genetic ( GE ) and a local search ( L ) algorithms. The two-steps algorithm is faster but its result is not necessary optimal. To illustrate the efficiency of the solution possibilities the popular ten-bar truss sizing problem will be used with one, two, and four directionally uncertain point loads as the benchmark problem.