This paper presents a novel space–time isogeometric topology optimization (ITO) framework for additive manufacturing, enabling concurrent optimization of structural shape and fabrication sequence with accurate geometric representation. The method integrates a density distribution function with a pseudo-time function to optimize build sequences for complex structures, with an objective function that minimizes compliance under external loads and accounts for self-weight effects during fabrication. Density values and virtual heat conduction coefficients are defined at B-spline control points to serve as design variables. A heat conduction-based formulation is employed to generate the pseudo-time function so that prevents the generation of isolated or floating material regions. A layer thickness constraint, defined by the pseudo-time gradient, further enhances manufacturability. The approach has been validated in 2D and 3D examples, demonstrating its effectiveness in managing objectives of entire structure's stiffness and self-weight of intermediate structures.

The Geometry-Independent Field approximaTion (GIFT) technique, an extension of isogeometric analysis (IGA), allows for separate spaces to parameterize the computational domain and approximate solution field. Based on the GIFT approach, this paper proposes a novel IGA methodology that incorporates toric surface patches for multi-sided geometry representation, while utilizing B-spline or truncated hierarchical B-spline (THB-spline) basis for analysis. By creating an appropriate bijection between the parametric domains of distinct bases for modeling and approximation, our method ensures smoothness within the computational domain and combines the compact support of B-splines or the local refinement potential of THB-splines, resulting in more efficient and precise solutions. To enhance the quality of parameterization and consequently boost the accuracy of downstream analysis, we suggest optimizing the composite toric parameterization. Numerical examples validate the effectiveness and superiority of our suggested approach.