Summary This paper will propose a more effective and efficient topology optimization method based on isogeometric analysis, termed as isogeometric topology optimization (ITO), for continuum structures using an enhanced density distribution function (DDF). The construction of the DDF involves two steps. (1) Smoothness: the Shepard function is firstly utilized to improve the overall smoothness of nodal densities. Each nodal density is assigned to a control point of the geometry. (2) Continuity: the high‐order NURBS basis functions are linearly combined with the smoothed nodal densities to construct the DDF for the design domain. The nonnegativity, partition of unity, and restricted bounds [0, 1] of both the Shepard function and NURBS basis functions can guarantee the physical meaning of material densities in the design. A topology optimization formulation to minimize the structural mean compliance is developed based on the DDF and isogeometric analysis to solve structural responses. An integration of the geometry parameterization and numerical analysis can offer the unique benefits for the optimization. Several 2D and 3D numerical examples are performed to demonstrate the effectiveness and efficiency of the proposed ITO method, and the optimized 3D designs are prototyped using the Selective Laser Sintering technique.

Jie Gao

Liang Gao

Zhen Luo

Peigen Li

International Journal for Numerical Methods in Engineering

《国际工程数值方法杂志》发表了原创论文，描述了适用于工程问题的数值方法的重大、新颖的发展。该杂志以欢迎在计算工程广泛领域的贡献而闻名，包括模型简化中的计算问题，不确定性量化、验证和确认、逆分析和随机方法、优化、元素技术、求解技术和并行计算、损伤和断裂、微观和纳米尺度力学、低速流体动力学、流固耦合、电磁学、耦合扩散现象，以及误差估计和网格生成。需要强调的是，这绝不是一份详尽的清单，尤其欢迎有关多尺度、多物理或多学科问题以及新兴主题的论文。

The International Journal for Numerical Methods in Engineering publishes original papers that describe significant and novel developments in numerical methods applicable to engineering problems. The journal is known for welcoming contributions across a wide range of computational engineering fields, including computational issues in model simplification, uncertainty quantification, validation and verification, inverse analysis and stochastic methods, optimization, element techniques, solution techniques and parallel computing, damage and fracture, micromechanics and nanomechanics, low-speed fluid dynamics, fluid-structure interaction, electromagnetics, coupled diffusion phenomena, as well as error estimation and mesh generation. It is important to emphasize that this is by no means an exhaustive list, and papers on multiscale, multiphysics, or interdisciplinary issues, as well as emerging topics, are especially encouraged.

《International Journal for Numerical Methods in Engineering》发表原创论文，介绍适用于工程问题的数值方法的重大和新颖发展。该杂志以欢迎计算工程广泛领域的贡献而闻名，包括模型简化中的计算问题、不确定性量化、验证与确认、逆分析和随机方法、优化、元素技术、求解技术与并行计算、损伤与断裂、微观和纳米尺度力学、低速流体动力学、流固耦合、电磁学、耦合扩散现象，以及误差估计和网格生成。需要强调的是，这并不是一份详尽的清单，尤其欢迎有关多尺度、多物理或多学科问题以及新兴主题的论文。

Isogeometric topology optimization for continuum structures using density distribution function

Several 2D and 3D numerical examples are performed to demonstrate the effectiveness and efficiency of the proposed ITO method, and the optimized 3D designs are prototyped using the Selective Laser Sintering technique.

Category	Quartile
工程技术	3
工程技术, 工程综合	3
工程技术, 数学跨学科应用	3

Isogeometric topology optimization for continuum structures using density distribution function

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Category	Quartile
MATHEMATICS, INTERDISCIPLINARY APPLICATIONS	1