Topology optimization (TO) has become a core computational paradigm for structural design by defining optimality through physics-based objectives and constraints. However, practical engineering design often involves incomplete and imperfect physical modeling due to multi-physics coupling, manufacturing uncertainty, and computational constraints, leaving critical design factors insufficiently captured in purely physics-driven formulations. In parallel, data-driven and generative methods have enabled rapid topology generation and intent-aware design exploration, yet often weaken explicit optimality guarantees. This review argues that these seemingly divergent developments can be organized under a unified information–physics perspective. We term this emerging field Topology Optimization Informatics (TOI): optimal structural design is obtained through the joint modeling and optimization of physical laws and design-relevant information. We first summarize the integration of artificial intelligence (AI) and TO into two major paradigms: AI-based one-shot TO, which learns mappings or distributions of near-optimal designs from data and prioritizes fast generation and diversity, and AI-enhanced iterative TO, which embeds learning-based modules into the classical solver-in-the-loop pipeline while keeping the underlying governing equations unchanged. Finally, we show that traditionally separate tasks—design control, computational acceleration, and fidelity enhancement—can be interpreted as different manifestations of information–physics co-modeling within a single optimization framework, thereby clarifying their connections and design implications and outlining opportunities for semantic- and data-enabled next-generation structural design.

Isogeometric analysis uses computer splines such as non-uniform rational B-splines as the basis functions. When the order of the basis function is 2 or greater, the control points do not coincide with the element nodes and the support domain of the basis function spans multiple elements, which makes it difficult to impose local fixed constraints precisely in isogeometric analysis. To solve this problem, this paper uses a step function to modify the displacement interpolation function of isogeometric analysis. The step function takes a value of 0 in the locally fixed constraint region and 1 in the other region, so that the displacement value in the fixed constraint region is forced to be 0, and the displacement interpolation function in other region is revert to the original form. In order to minimize the influence of step function on the analysis domain, the rising interval of the step function is set to be small. Meanwhile, the hierarchical spline is used to subdivide the elements in the rising interval locally, therefore, the Gaussian points of the subdivided elements fall into the rising interval of the step function as well as the step function has an effect on the stiffness matrix. In addition, the element subdivision also effectively improves the solution accuracy in the local constraint region where large strains are present. Finally, the method mentioned above is compared with analytical solution and the finite element method to verify its accuracy, flexibility and reliability, finding that the results of calculation coincide with the analytical solution. Finally, by considering the situations with different fixed constrains that vary in shape, area and location., the finite element method with coarse mesh and fine mesh are used to calculate the examples, finding that the displacement and stress obtained by the proposed method are closer to those obtained by the fine mesh finite element method, which illustrates that the solution accuracy can be achieved with fewer elements; and that the proposed method is of good accuracy, flexibility and reliability.