Bi-directional evolutionary topology optimization of continuum structures subjected to inertial loads

This paper proposes to investigate topology optimization of continuum structures with density-dependent inertial loads which including self-weight, centrifugal forces, the magnitude and direction of the acceleration of inertial loads in order to make topology optimization more realistic. By using an extended bi-directional evolutionary structural optimization (BESO) method, this work presents an extension of this procedure to deal with maximum stiffness (minimum compliance) topology optimization of continuum structures when different combinations of inertial loads and fixed forces are applied. Notably, the magnitude and direction of the acceleration of inertial loads are considered. The computation of the element sensitivity numbers is deduced in detail in order to achieve the optimum design. MATLAB programming of proposed mathematical approach is done and compared with the conventional structural optimization problems with fixed external force. The procedure has been tested in several 2D and 3D benchmark examples to illustrate and validate the approach. The inertial loads have great influence on the topological structure, especially when the fixed external force is relatively small. The inertial loads change the magnitude and variation trend of objective function. The iterative curves converge to constant values stably, and the convergence rate is fast.

Automated summary

This study proposes a method for topology optimization of continuum structures with density-dependent inertial loads, including self-weight, centrifugal forces, and acceleration of inertial loads, using an extended bi-directional evolutionary structural optimization method. The approach considers different combinations of inertial loads and fixed forces to achieve maximum stiffness, with detailed computation of element sensitivity numbers for optimum design. MATLAB programming and testing on benchmark examples show that inertial loads significantly impact topological structure, especially when external forces are small, resulting in changes to the objective function and fast convergence rates.