In this work, the particle finite element method (PFEM) is extended to simulate additive manufacturing processes in a variety of different complicated geometries. A three-dimensional α-shape approach is used to carry out the material addition procedure. It overcomes the limitation of merely employing the traditional element birth and death technique and reduces the degrees-of-freedom compared to this technique. Furthermore, numerical examples are used to evaluate and demonstrate the applicability of the PFEM method for additive manufacturing within the framework of a weakly coupled thermoelasticity formulation. During additive manufacturing operations, deflections, stresses, and temperature are computed using a user-defined implementation in FEniCS.