Fail-safe topology optimization of continuum structures with fundamental frequency constraints based on the ICM method

Abstract

It is an important topic to improve the redundancy of optimized configuration to resist the local failure in topology optimization of continuum structures. Such a fail-safe topology optimization problem has been solved effectively in the field of statics. In this paper, the fail-safe topology optimization problem is extended to the field of frequency topology optimization. Based on the independent continuous mapping (ICM) method, the model of fail-safe topology optimization is established with the objective of minimal weight integrating with the discrete condition of topological variables and the constraint of the fundamental frequency. The fail-safe optimization model established above is substituted by a sequence of subproblems in the form of the quadratic program with exact second-order information and solved efficiently by the dual sequence quadratic programming (DSQP) algorithm. The numerical result reveals that the optimized fail-safe structure has more complex configuration and preserved materials than the structure obtained from the traditional frequency topology optimization, which means that the optimized fail-safe structure has higher redundancy. Moreover, the optimized fail-safe structure guarantees that the natural frequency meets the constraint of fundamental frequency when the local failure occurs, which can avoid the structural frequency to be sensitive to local failure. The fail-safe optimization topology model is proved effective and feasible by four numerical examples.