Narrow Results

This paper presents a simple yet efficient method for the topology optimization of continuum structures considering interval uncertainties in loading directions. Interval mathematics is employed to equivalently transform the uncertain topology optimization problem into a deterministic one with multiple load cases. An efficient soft-kill bi-directional evolutionary structural optimization (BESO) method is proposed to solve the problem, which only requires two finite element analyses per iteration for each external load with directional uncertainty regardless of the number of the multiple load cases. The presented algorithm leads to significant computational savings when compared with Monte Carlo-based optimization (MCBO) algorithms. A series of numerical examples including symmetric and nonsymmetric loading variations demonstrate the considerable improvement of computational efficiency of the proposed approach as well as the significance of including uncertainties in topology optimization when to design a structure. Optimums obtained from the proposed algorithm are verified by MCBO method.

Composites with various layings of unidirectional plies in the conditions of a plane stress state are considered. Using the criteria of maximum stresses and Tsai–Wu, their tensile and shear strength is investigated. The dependences of the failure stresses on the direction of loading in polar coordinates are constructed. For comparison, the results of calculations by the finite element method using the ANSYS Mechanical APDL 2020 R2 program are presented.