Methods for Enhancing the Speed of Numerical Calculations for the Prediction of the Mechanical Behavior of Parts Made Using Additive Manufacturing

Finite element modeling (FEM) is one of the most common methods for predicting the thermo-mechanical properties of 3D structures. Since FEM was developed primarily to analyze and optimize structures that would then be mass-produced, the time for modeling was small compared to the time required to produce the components. With the advent of Additive Manufacturing (AM) it is now possible to produce and test complex parts more quickly than FEM methods can predict their mechanical performance. As such, an enhanced numerical method for quickly solving for the mechanical behavior of components is needed to fully take advantage of the speed and versatility of this new manufacturing paradigm. In order to enhance the computational efficiency of FEM, a novel method was developed to adapt FEM for prediction of fundamental deformation responses of AM-produced parts. A general FEM strategy comprised of constructing the stiffness and external stimuli (such as laser power or pressure) as matrices and vectors respectively has been formulated. Thermo-mechanical response is calculated by obtaining the compliance matrix from the stiffness matrix and then multiplying the corresponding values of the compliance matrix with the external stimulus vector. Obtaining the compliance matrix from the stiffness matrix is accomplished, in most cases, using a well-known Cholesky algorithm which starts by transforming the stiffness matrix into a lower triangular matrix with zeros above its diagonal [1]. In this study, the Cholesky algorithm has been improved by identification of discrete sparse bands and by eliminating many zero multiplications in the lower triangular matrix to obtain the thermo-mechanical response much faster than currently available algorithms. In addition, the vector based storage strategy of the above-mentioned discrete sparse bands and multipliers have been used to save computer storage space, including free cache memory, resulting in faster computations. An example showing the time advantage of this new framework over previously used algorithms to obtain the deformation response of an additively manufactured axial beam is provided along with its theoretical background.