Powder bed fusion (PBF) is a widely used metal additive manufacturing method where a part is built with almost no limitation on its geometrical layout. However, parts built by PBF typically suffer from distortions and residual stresses which depend on the PBF processing conditions and the geometrical layout of the part. In order to investigate this relation, a new computational tool is presented. The unique property of our methodology is to keep the total number of degrees of freedom constant by utilising a moving grid to represent a growing part with time. Thermal transients are calculated and are coupled to a mechanical boundary value problem to evaluate the evolution of temperature history and residual stresses. The significant gain in the computational efficiency of the moving grid technique is demonstrated in comparison to the state of the art models available in the literature.