Stress, displacement and weight minimization by multicriteria optimization and game theory approach

Structural design problems, which usually involve multiple conflicting criteria to be considered simultaneously, often occur. In this paper, three objective functions are considered, i.e. weight, displacements and von Mises criterion, in application to sizing optimization of bending (beam) and 2-D (plane stress state) structures. Design variables are represented by thickness parameters, and the constraints deal directly with displacements and/or stresses. Then various multicriteria problems are formulated. A scalarization method based on the game theory is applied. Linear programming techniques are employed to find the weighting coefficients, and they generate Pareto-optimal solutions of multicriteria optimization problems. To solve the involved optimization problems a sensitivity analysis based on the scaling of the internal forces (continuum approach) is developed and interfaced with ABAQUS code.