Interlaminar shear stress continuity and transient stress constrained topology optimization of piezoelectric structures under active vibration control

Piezoelectric materials are widely used in active vibration control due to their high sensitivity and self-sensing capability. However, despite these advantages, piezoelectric materials remain at risk of failure in practical engineering applications because of their brittle nature, whether under combined mechanical–electrical loads or either type of load alone. To address this issue, this paper proposes a topology optimization method for active vibration control of piezoelectric structures with stress constraints. Self-sensing piezoelectric materials are employed to avoid numerical problems caused by the asymmetry of the equivalent damping matrix in active control. Meanwhile, considering that the conventional equivalent single-layer approach leads to interlayer shear stress discontinuity, a finite element model that inherently satisfies stress continuity is adopted in this work. Moreover, a stress relaxation parameter is introduced and adjusted to ensure stress continuity throughout the optimization process. In the optimization problem, the nested p-norm method is employed to approximate the maximum stress, while the sum of squared displacements at discrete target points over each time interval serves as the objective function. An adjoint-variable sensitivity analysis scheme is developed to compute sensitivity analysis of both the objective function and the constraints. Finally, numerical examples are presented to investigate the influence of various parameters on the optimization results. The results demonstrate that stress constraints are crucial for the design of piezoelectric composite structures, and this approach effectively reduces the risk of excessive stress and fracture. • The layered linear displacement assumption was incorporated into the topology optimization framework. • Interlaminar stress continuity was accounted during the optimization and computation process. • The transient stresses of self-sensing piezoelectric materials were aggregated using the nested p-norm method. • A discrete adjoint variable method is employed for sensitivity analysis of the objective and constraint functions.