Kucherenko O. Nonlinear topology optimization of truss-like structures under deterministic and random loads

The thesis is devoted to the study, development and justification of a new approach to the optimal design of truss-like structures functioning in a stochastic environment under deterministic and random loads. In this paper it is proposed to use the Monte Carlo method to generate load samples. Then a modified semidefinite optimization problem is solved for each sample. To check design requirements for the truss (e.g., buckling) an algorithm for piecewise linear approximation of moments of inertia has been developed. Also an algorithm for the optimal shape selection of a cross-section has been developed. It is proposed to use statistical bootstrapping to convolve the set of solutions for each sample to a single generalized solution. This approach allows us to estimate a confidence interval for each parameter of any member of the truss (e.g., for 0.9-quantile of a cross-section area). The algorithm described in the thesis provides effective solutions for planar and space high-dimensional problems. The proposed approach can be used to solve truss topology optimization problems and for further study of optimization and statistical methods in computational mechanics.