Optimization of process parameters in additive manufacturing based on the finite element method

TL;DR

The paper addresses optimizing additive manufacturing process parameters by coupling a fully discretized thermomechanical finite element model with PDE-constrained optimization. It develops a gradient-based method that uses analytically derived sensitivities and a gradient-free pair (local variations and Bayesian optimization with Gaussian processes) to handle non-differentiable parameters. Through two 2D AM test cases, the study demonstrates how process variables like convection, layer thickness, and printing speed influence shape error, and compares the effectiveness and trade-offs of each optimization approach. The findings suggest a flexible framework that can extend to more parameters and fidelity levels, balancing accuracy, computational cost, and practical industrial constraints.

Abstract

A design optimization framework for process parameters of additive manufacturing based on finite element simulation is proposed. The finite element method uses a coupled thermomechanical model developed for fused deposition modeling from the authors' previous work. Both gradient-based and gradient-free optimization methods are proposed. The gradient-based approach, which solves a PDE-constrained optimization problem, requires sensitivities computed from the fully discretized finite element model. We show the derivation of the sensitivities and apply them in a projected gradient descent algorithm. For the gradient-free approach, we propose two distinct algorithms: a local search algorithm called the method of local variations and a Bayesian optimization algorithm using Gaussian processes. To illustrate the effectiveness and differences of the methods, we provide two-dimensional design optimization examples using all three proposed algorithms.

Figures (15)

• Figure 1: Schematic of the distance functions $d$ and $\bar{d}$
• Figure 2: Measurement of shape error for two-dimensional wall with deformation magnified five times for visual clarity (the reference edges in black have zero shape error, while the deformed ones in blue deviate from the designed height due to the thermomechanical response of the material)
• Figure 3: Two-dimensional wall: Optimization of convection coefficient
• Figure 4: Two-dimensional wall optimization path in the optimization space with method of local variations
• Figure 5: Two-dimensional wall Bayesian optimization, expected improvement and mean value contour, iteration 1. The axes $x_1$ and $x_2$ are the number of layers ($10/\Delta y$) and temporal step size $\delta t$, respectively, as in \ref{['eq:bounds1']}.