No abstract

The advance in computational science and engineering allows people to simulate the additive manufacturing (AM) process at high fidelity, which has turned out to be a valid way to model, predict, and even design the AM processes. In this paper, we propose a new method to simulate the melting process of metal powder-based AM. The governing physics is described using partial differential equations for heat transfer and Laminar flow. Level set methods are applied to track the free surface motion of the molten metal flow. Some fundamental issues in the metal-based AM process, including free surface evolution, phase transitions, and velocity field calculation, are explored, which help us gain insight into the metal-based AM process. The convergence problem is also examined to improve the efficiency in solving this multiphysics problem.

In this paper, we propose a new method to approach the problem of structural shape and topology optimization on manifold (or free-form surfaces). A manifold is conformally mapped onto a 2D rectangle domain, where the level set functions are defined. With conformal mapping, the corresponding covariant derivatives on a manifold can be represented by the Euclidean differential operators multiplied by a scalar. Therefore, the topology optimization problem on a free-form surface can be formulated as a 2D problem in the Euclidean space. To evolve the boundaries on a free-form surface, we propose a modified Hamilton-Jacobi equation and solve it on a 2D plane following the conformal geometry theory. In this way, we can fully utilize the conventional level-set-based computational framework. Compared with other established approaches which need to project the Euclidean differential operators to the manifold, the computational difficulty of our method is highly reduced while all the advantages of conventional level set methods are well preserved. We hope the proposed computational framework can provide a timely solution to increasing applications involving innovative structural designs on free-form surfaces in different engineering fields.