Reverse shape compensation via a gradient-based moving particle optimization method

Abstract

Reverse shape compensation is widely used in additive manufacturing to offset the displacement distortion caused by various sources, such as volumetric shrinkage, thermal cooling, etc. Also, reverse shape compensation is also an effective tool for the four-dimensional (4D) printing techniques, shape memory polymers (SMPs), or 3D self-assemble structures to achieve a desired geometry shape under environmental stimuli such as electricity, temperature, gravity etc. In this paper, a gradient-based moving particle optimization method for reverse shape compensation is proposed to achieve a desired geometry shape under a given stimulus. The geometry is described by discrete particles, where the radius basis kernel function is used to realize a mapping from particle to density field, and finite element analysis is used to compute the deformation under the external stimulus. The optimization problem is formulated in detail, and MMA optimizer is implemented to update the location of discrete particles based on sensitivity information. In this work, self-weight due to gravity imposed on linear elastic structures is considered as the source of deformation. The objective of the problem is then to find the initial shape so that the deformed shape under gravity is close to desired geometry shape. A shape interpolation method based on Artificial Neural Network is proposed to reconstruct the accurate geometric prototype. Several numerical examples are demonstrated to verify the effectiveness of proposed method for reverse shape compensation. The computational framework for reverse shape compensation described in this paper has the potential to be extended to consider linear and non-linear deformation induced by other external stimuli.