A general material perturbation method using fixed mesh for stress sensitivity analysis and structural shape optimization

• A material perturbation method using fixed mesh is developed for shape optimization.
• The method has the advantage of avoiding sophisticated velocity field calculation.
• Material properties are related to the shape perturbation via the domain function.
• Stress corrections are carried out for sensible elements in local coordinate systems.
• It is shown that stress corrections have a remarkable effect on the stress accuracy.

Stress sensitivity analysis constitutes an essential problem in gradient-based structural shape optimization. Unlike the traditional grid perturbation method (GPM), a general material perturbation method (MPM) using a fixed mesh is originally developed to simplify the sensitivity analysis scheme in this work. A domain function is introduced to characterize the boundary perturbation, whose effect is considered by correcting simultaneously stiffness matrices and stresses of elements attaching the perturbed boundary. Implementations of the MPM on shape optimization of plane stress, axisymmetric, 3D and thin-walled curved shell problems show that the proposed method has the advantage of efficient and explicit computing of stress sensitivities.