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.

Recent years have seen a growing interest in topology optimization of functionally graded microstructures, characterized by an array of microstructures with varying volume fractions. However, microstructures optimized at slightly different volume fractions do not necessarily connect well when placed adjacently. Furthermore, optimization is commonly performed on a finite set of volume fractions, limiting the number of microstructure configurations. In this paper, we introduce the concept of differentiable microstructures, which are parameterized microstructures that exhibit continuous variations in both geometry and mechanical properties. To construct such microstructures, we propose a novel formulation for topology optimization. In this approach, a series of 2-dimensional microstructures is represented using a height field, and the objective is to maximize the bulk modulus of the entire series. Through this optimization process, an initial microstructure with a small volume fraction undergoes non-uniform transformations, generating a series of microstructures with progressively increasing volume fractions. Notably, when compared to traditional uniform morphing methods, our proposed optimization approach yields a series of microstructures with bulk moduli that closely approach the theoretical limit.

Offsetting-based hollowing is a solid modeling operation widely used in 3D printing, which can change the model's physical properties and reduce the weight by generating voids inside a model. However, a hollowing operation can lead to additional supporting structures for fabrication in interior voids, which cannot be removed. As a consequence, the result of a hollowing operation is affected by these additional supporting structures when applying the operation to optimize physical properties of different models. This paper proposes a support-free hollowing framework to overcome the difficulty of fabricating voids inside a solid. The challenge of computing a support-free hollowing is decomposed into a sequence of shape optimization steps, which are repeatedly applied to interior mesh surfaces. The optimization of physical properties in different applications can be easily integrated into our framework. Comparing to prior approaches that can generate support-free inner structures, our hollowing operation can reduce more volume of material and thus provide a larger solution space for physical optimization. Experimental tests are taken on a number of 3D models to demonstrate the effectiveness of this framework.

Recently, 3D printing has become a powerful tool for personal fabrication. However, the price of some materials is still high which limits its applications in home users. To optimize the volume of the model, while not largely affecting the strength of the objects, researchers propose algorithms to divide the model with different kinds of lightweight structures, such as frame structure, honeycomb cell structure, truss structure, medial axis tree. However, these algorithms are not suitable for the model whose internal space needs to be reused. In addition, the structural strength and static stability of the models, obtained with modern 3D model acquirement methods, are not guaranteed. In consequence, some models are too fragile to print and cannot be survived in daily usage, handling, and transportation or cannot stand in a stable. To handle the mentioned problems, an algorithm system is proposed based on cross sections in this work. The structural weak cross sections are enhanced, and structural strong cross sections are adaptively hollowed to meet a given structural strength, static stability, printability, etc., while the material usage is minimized. The proposed algorithm system has been tested on several typical 3D models. The experimental results demonstrate the effectiveness and practicability of our system.