Challenges and solutions to arc-length controlled structural shape design problems

Abstract

This paper presents a general and reliable shape optimization scheme for snap-through structures to match a target load-deflection curve. The simulation of the snap-through structures typically requires the Arc Length Control (ALC) method. The adaptive stepping in ALC creates unavoidable discontinuities in the objective function. A discontinuous objective function is often handled by zero-order methods. However, we opt to solve the optimization problems using gradient-only optimization. Numerical examples demonstrate that function value based methods can misinterpret discontinuities as minima and terminate prematurely. In contrast, gradient-only algorithms are demonstrated to be insensitive to numerical discontinuities, and locate the correct solutions reliably.

Keywords:

• Shape sensitivity
• arc length control
• optimization
• discontinuities
• gradient-only

Disclosure statement

The authors declare that they have no conflict of interest.

Replication of results

All necessary algorithms and problem parameters for possible replication of all results presented in this work have been detailed and referenced.