Four-dimensional (4D) printing is a new category of printing that expands the fabrication process to include time as the forth dimension, and its process planning and simulation have to take time into consideration as well. The common tool to estimating the behavior of a deformable object is the finite element method (FEM). Although FEM is powerful, there are various sources of deformation from hardware, environment, and process, just to name a few, which are too complex to model by FEM. This paper introduces Geometry-Driven Finite Element (GDFE) as a solution to this problem. Based on the study on geometry changes, the deformation principles can be drawn to predict the relationship between the 4D-printing process and the shape transformation. Similar to FEM, the design domain is subdivided into a set of GDFEs, and the principles are applied on each GDFE, which are then assembled to a larger system that describes the overall shape. The proposed method converts the complex sources of deformation to a geometric optimization problem, which is intuitive and effective. The usages and applications of the GDFE framework have also been presented in this paper, including freeform design, reserve design, and design validation.

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