Analytical thermoelastic solutions for additive manufacturing processes

Abstract

This work is motivated by the need to determine residual thermo-structural fields in a computationally efficient manner relative to the finite element method for solving the balance of energy and momentum partial differential equations. The present paper describes an analytical model that computes the time-dependent three-dimensional distributions of the thermo-mechanical fields for heat deposition problems in general, and additive manufacturing problems in particular. This corresponds to the determination of the displacement, strain, and stress fields generated by a moving heat flux in thermally conducting and mechanically deforming structures. The problem is solved by a one-way coupled approach where temperature fields determined analytically by the solution of the heat transfer problem are used as inputs for solving the analytical solution of the solid mechanics problem. The heat transfer problem is solved first using the recently developed Enriched Analytical Solution Method (EASM) for evaluating the spatio-temporal distribution of temperature fields generated during additive manufacturing (AM) processes. Because the EASM provides the temperature over the entire domain at any time, a non-uniform thermal eigenstrain field can be used in conjunction with Green’s function for the half-space to determine the corresponding elastic fields. The analytical predictions of the elastic fields are compared with those obtained by the finite element analysis for the case of a single track laser powder bed fusion application. The results indicate that the proposed analytical model accurately matches the finite element calculated structural response.