A sequential linear programming approach for truss optimization based on the uncertainty analysis-based data-driven computational mechanics (UA-DDCM)

Based on the sequential linear programming approach for the data-driven computational mechanics considering uncertainty, a novel approach for truss optimization with displacement and stress constraints is introduced. The proposed approach still capitalizes on the merits of data-driven computational mechanics, enabling optimization across various constitutive relationships by a mere replacement of the dataset. Moreover, in order to obtain the singular global optimal solution, the approach integrates the Simultaneous Analysis and Design framework, incorporating displacement as a design variable and establishing conservation law and kinematic relationship as equality constraints. In actuality, the data-driven approach is not only applicable to handling constitutive models but can also be employed to transform complex nonlinear relationships into linear combinations of data points. Consequently, the original nonlinear problem is transformed into a sequential linear programming problem. Numerical examples demonstrate that for stress-constrained truss optimization problem with the lower bound of cross-sectional area as 0, the proposed algorithm can directly yield a global optimum solution rather than a local optimal solution. In scenarios featuring linear constitutive behavior and incorporating stress and displacement constraints, both the results and efficiency yielded by this methodology closely align with traditional algorithms. Additionally, within the realm of a nonlinear constitutive model, the computational time is close to that of the linear constitutive model. In a word, the aforementioned results thoroughly demonstrate the effectiveness of the data-driven approach, providing a novel approach to solve nonlinear problems by sequential linear programming.