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.

反向形状补偿广泛用于增材制造中，以抵消由各种来源（例如体积收缩，热冷却等）引起的位移变形。此外，反向形状补偿还是用于四维（4D）打印技术的有效工具，形状记忆聚合物（SMP）或3D自组装结构，以在环境刺激下（如电，温度，重力等）获得所需的几何形状。在本文中，提出了一种基于梯度的运动粒子优化方法，用于反向形状补偿在给定的刺激下获得所需的几何形状。几何形状由离散粒子描述，其中半径基核函数用于实现从粒子到密度场的映射，有限元分析用于计算外部刺激下的变形。详细阐述了优化问题，并实现了MMA优化器，以根据敏感度信息更新离散粒子的位置。在这项工作中，由于重力作用在线性弹性结构上的自重被认为是变形的来源。问题的目的是找到初始形状，以使重力下的变形形状接近所需的几何形状。提出了一种基于人工神经网络的形状插值方法，以重建精确的几何原型。数值算例表明了所提出的反向形状补偿方法的有效性。