1. 创新型结构优化设计

面向诸如高超飞行器、运载火箭、轨道空间站和核聚变装置等国家重大装备，以及民用领域如车辆、船舶、飞行器等零部件的轻量化、多功能化、创新型结构构型优化设计。

2. 超材料设计、材料结构一体化设计

面向力学、光学、声学、电磁学等多学科交叉领域的超材料设计，以及多物理场作用下的宏微观结构一体化设计。

3. 多物耦合多尺度计算方法

针对多场耦合下非均质材料与结构力学行为问题，发展高精度高效率的多尺度计算方法。

4. 复合材料计算力学

针对连续/不连续纤维增强复合材料(热塑性复合材料、纤维混凝土等)的宏观等效力学性质，发展高精度的数值预测模型。

2024年：

王林军, 李家豪, 张正伟, 吴振雨, 魏悠贵, 刘辉*. 基于可靠性指标法的连续体结构可靠性拓扑优化. 计算力学学报, 2024, https://link.cnki.net/urlid/21.1373.o3.20240227.1807.026.

X. Chen, H. Liu*, P. Wei*. Extended multiscale FEM-based concurrent optimization of three-dimensional graded lattice structures with multiple microstructure configurations. Composite Structures, 2024, 341: 118186.

Y. Lu, X. Chang, Z. Zhang, H. Liu*, Y. Zhou, H. Li*. A body-fitted adaptive mesh and Helmholtz-type filter based parameterized level-set method for structural topology optimization. Acta Mechanica Sinica, 2024, doi: 10.1007/s10409-024-24119-x.

J. Wu, J. Zhu, J. Gao*, L. Gao, H. Liu*. A CAD-oriented parallel-computing design framework for shape and topology optimization of arbitrary structures using parametric level set. Computer Methods in Applied Mechanics and Engineering, 2024, 431: 117292.

Y. Xia, X. Zhou, H. Niu, H. Liu*, C. Wu*. Electric-Mechanical coupling analysis of two-dimensional piezoelectric heterogeneous materials in flexible electric devices with extended multiscale isogeometric analysis. European Journal of Mechanics / A Solids, 2025, 109: 105430. 

专利：

[1] 刘辉, 陈炼雄, 姜宏毅, 段苏航, 罗淞元. 梯度复合晶格结构的设计方法, 发明专利, 专利号：ZL 2022 1 0293708.5, 授权：2024年07月12日;

[2] 刘辉, 陈炼雄, 江忆, 朱德洲, 周宇发. 梯度随机点阵/多孔结构多尺度优化设计方法, 发明专利, 专利号：ZL 2021 1 1575942.9, 授权：2024年06月25日;

[3] 刘辉, 亓艺童, 陈炼雄. 一种基于多微结构原型和多尺度有限元的多孔结构设计方法, 发明专利, 专利号：ZL 2022 1 0544212.0, 授权：2024年9月24日;

软著：

[1] 梯度功能多孔结构优化设计软件, 登记号：2024SR0812784; 

2023年：

S. Huo, B. Du*, Y. Zhao, H. Liu*, Y. Shi, X. Chen. Thermal design of functionally graded cellular structures with multiple microstructure configurations through topology optimization. Composite Structures, 2023, doi: 10.1016/j.compstruct.2023.116922. 

L. Chen, Y. Fan, R. Zhang, X. Chu, H. Liu*. Scale-separated VCUT level set method for designing the graded stochastic Voronoi cellular structure. Structural and Multidisciplinary Optimization, 2023, 66: 54. 

L. Chen, Y. Pan, X. Chu, H. Liu*, X. Wang*. Multiscale design and experimental verification of Voronoi graded stochastic lattice structures for the natural frequency maximization problem. Acta Mechanica Sinica, 2023, doi: 10.1007/s10409-023-22445-x. 

L. Chen, R. Zhang, X. Chu, H. Liu*. Multiscale design of graded stochastic cellular structures for the heat transfer problem. Applied Sciences, 2023, 13(7): 4409.

Y. Xia, H. Niu, Z. Zhang, H. Liu*, C. Wu*. Extended multiscale isogeometric analysis for mechanical simulation of two-dimensional periodic heterogeneous materials. Composite Structures, 2023, 315: 116988.

H. Liu*, Y. Qi, L. Chen, Y. Li, W. Xiao. An efficient data-driven optimization framework for designing graded cellular structures. Applied Mathematical Modelling, 2024, 125: 574-598. 

软件著作权：

[1] 非均质结构多层级阶谱有限元方法静动力学分析软件. 登记号: 2023SR0767193.

[2] 基于PETSc并行的参数化水平集结构拓扑优化设计软件. 登记号: 2023SR1522166.

[3] 非均质材料的扩展多尺度有限元分析软件. 登记号: 2023SR1401994.

[4] 维诺型梯度随机多孔结构优化设计软件. 登记号: 2023SR1519451.

2022年：

H. Lin, H. Liu*, P. Wei*. A parallel parameterized level set topology optimization framework for large-scale structures with unstructured meshes. Computer Methods in Applied Mechanics and Engineering, 2022, 397, 115112. 

H. Liu, L. Chen, T. Shi, Q. Xia*. M-VCUT level set method for the layout and shape optimization of stiffeners in plate. Composite Structures, 2022, 293, 115614.

H. Liu*, L. Chen, H. Bian. Data-driven M-VCUT topology optimization method for heat conduction problem of cellular structure with multiple microstructure prototypes. International Journal of Heat and Mass Transfer, 2022, 198, 123421. 

H. Liu*, L. Chen, H. Jiang, S. Duan, S. Luo, X. Wang*. Data-driven design of graded composite lattice structures with multiple microstructure prototypes and materials. Composite Structures, 2023, 305, 116485. 

H. Liu*, L. Chen, Y. Jiang, D. Zhu, Y. Zhou, X. Wang*. Multiscale optimization of additively manufactured graded non-stochastic and stochastic lattice structures. Composite Structures, 2023, 305, 116546. 

陈炼雄, 肖奥宇, 刘辉*. 基于计算均匀化方法的梯度多孔结构优化设计. 应用力学学报, 2022, 39(6): 1055-1064.

专利：

刘辉, 陈炼雄, 楚锡华, 史铁林, 夏奇. 一种平板加筋的布局及形状优化方法和装置（发明专利：ZL202111192985.9）.

2021年：

H. Liu, P. Wei, M. Y. Wang. CPU parallel based adaptive parameterized level set method for large-scale structural topology optimization. Structural and Multidisciplinary Optimization, 2021, accepted (in press).

H. Liu*, D. Yang, J. Wu, Y. Zheng, H. Zhang. An open-source MATLAB implementation for elastic analysis of heterogeneous materials using the Extended Multiscale Finite Element Method. International Journal for Multiscale Computational Engineering, 2021, 19(6), 19-43.

L. Chen, H. Liu*, X. Chu, J. Wang. Functionally Graded Cellular Structure Design Using the Subdomain Level Set Method with Local Volume Constraints. CMES-Computer Modeling in Engineering & Sciences, 2021, 128(3), 1197–1218. 

2020年：

L. Chen, J. Wan, X. Chu, H. Liu*. Parameterized level set method for structural topology optimization based on the Cosserat elasticity. Acta Mechanica Sinica, 2020, online. 

Q. Xia, H. Zong, T.L. Shi, H. Liu*. Optimizing cellular structures through the M-VCUT level set method with microstructure mapping and high order cutting, Composite Structures, 2020, online, 113298. 

X. Cai, H. Liu, J. Yang. Natural granular pile as electromagnetic ground cloak, Applied Physics Letters, 2020, 117, 163701. 

H. Liu, H. Zong, T.L. Shi, Q. Xia. M-VCUT level set method for optimizing cellular structures, Computer Methods in Applied Mechanics and Engineering, 2020, 367: 113154. 

2019年：

H. Liu, H. Zong, Y. Tian, Q. Ma, M. Y. Wang. A novel subdomain level set method for structural topology optimization and its application in graded cellular structure design, Structural and Multidisciplinary Optimization, 2019, 60: 2221-2247. 

H. Liu, Y. Tian, H. Zong, Q. Ma, M. Y. Wang, L. Zhang. Fully parallel level set method for large-scale structural topology optimization, Computers & Structures, 2019, 221: 13-27. 

H. Zong, H. Liu, Q. Ma, Y. Tian, M. Zhou, M. Y. Wang. VCUT level set method for topology optimization of functionally graded cellular structures, Computer Methods in Applied Mechanics and Engineering, 2019, 354: 487-505. 

J. Wan, Z. Chen, X. Chu*, H. Liu, An improved method for zero-energy modes suppression in peridynamic correspondence model, Acta Mechanica Sinica, 2019, 35(5): 1021-1032. 

J. Wang, X. Chu*, J. Zhang, H. Liu, The effects of microstructure on wave velocity and wavefront in granular assemblies with binary-sized particles, International Journal of Solids and Structures, 2019, 159: 156-162. 

Z. Chen, J. Wan, X. Chu*, H. Liu, Two Cosserat peridynamic models and numerical simulation of crack propagation, Engineering Fracture Mechanics, 2019, 211: 341-361. 

X.Y. Sun, H. Liu, S. Ju, Dependence of wrinkling geometric patterns on the chirality of monolayer graphene under shear deformation, Physica E: Low-dimensional Systems and Nanostructures, 2019, 105: 62-67. 

2018年：

H. Liu*, Y. Wang, H. Zong, M.Y. Wang, Efficient Structure Topology Optimization by using the Multiscale Finite Element Method, Structural and Multidisciplinary Optimization, 2018, 58: 1411-1430. 

P. Fu, H. Liu*, X. Chu, W. Qu, Multiscale finite element method for a highly-efficient coupling analysis of heterogeneous magneto-electro-elastic media, International Journal for Multiscale Computational Engineering, 2018, 16(1): 77-100. 

2017年：

P. Fu, H. Liu*, X.H. Chu, An Efficient Multiscale Computational Formulation for Geometric Nonlinear Analysis of Heterogeneous Piezoelectric Composite, Composite Structures, 2017, 167: 191-206. 

H. Liu, J. Lv, An equivalent continuum multiscale formulation for 2D geometrical nonlinear analysis of lattice truss structure,Composite Structures, 2017, 160: 335-348. 

2016年：

P. Fu, H. Liu, X.H. Chu, Y.J. Xu, A Multiscale Computational Formulation for Gradient Elasticity Problems of Heterogeneous Structures, International Journal of Computational Methods, 2016, 13, 1650030. 

H. Liu, D. Zeng, Y. Li, L.Y. Jiang, Development of RVE-embedded solid elements model for predicting effective elastic constants of discontinuous fiber reinforced composites, Mechanics of Materials, 2016, 93: 109-123. 

2015年：

H. Liu, X.Y. Sun, Y.J. Xu, X.H. Chu, A hierarchical multilevel finite element method for mechanical analyses of periodical composite structures, Composite Structures, 2015, 131: 115-127. 

H. Liu, X.Y. Sun, Y.J. Xu, X.H. Chu, A new adaptive multiscale method based on the estimate of residual forces for static analysis of heterogeneous materials, Finite Elements in Analysis and Design, 2015, 101: 34-45. 

J. Lv, H. Liu, H.W. Zhang, L. Liu, Multiscale Method for Geometrical Nonlinear Analysis of Fluid Actuated Cellular Structures with Polygonal Microstructures, Journal of Aerospace Engineering, 2015, Accepted. 

X.X. Zhuo, H. Liu, X.H. Chu, Y.J. Xu. A generalized multiscale finite element method for dynamic analysis of heterogeneous material. Chinese Journal of Theoretical and Applied Mechanics, 2015, accepted. (In Chinese)

2014年：

H. Liu, H.W. Zhang. An equivalent multiscale method for 2D static and dynamic analyses of lattice truss materials. Advances in Engineering Software, 2014, 75: 14-29. 

H. Liu, H.W. Zhang. An Efficient Multiscale Computational Method for 2D Dynamic Analysis of the Coupling System of Fluid and Heterogeneous Structure. Finite Elements Analysis and Design, 2014, 85: 59-72. (Q1/3区)

H. Liu, L. Zhang, D.S. Yang, H.W. Zhang. An efficient multiscale method for 2D large displacement – small strain analysis of heterogeneous materials, Computational Materials Science, 2014, 83: 443-456. 

J. Lv, H. Liu, H.W. Zhang. A multiscale co-rotational method for geometrically nonlinear shape morphing of 2D fluid actuated cellular structures. Mechanics of Materials, 2014, 79: 1-14. 

H.W. Zhang, H. Liu. A Multiscale Computational Method for 2D Elasto-Plastic Dynamic Analysis of Heterogeneous Materials, International Journal for Multiscale Computational Engineering, 2014, 12: 127-154. 

2013年：

H. Liu, H.W. Zhang. A Uniform Multiscale Method for 3D Static and Dynamic Analyses of Heterogeneous Materials, Computational Materials Science, 2013, 79: 159-173. 

H. Liu, H.W. Zhang. A p-adaptive multi-node extended multiscale finite element method for 2D elastostatic analysis of heterogeneous materials, Computational Materials Science, 2013, 73: 79-92. 

H.W. Zhang, H. Liu, J.K. Wu. A Uniform Multiscale Method for 2D Static and Dynamic Analyses of Heterogeneous Materials. International Journal for Numerical Methods in Engineering, 2013, 94: 714-746. 

H.W. Zhang, Y.G. Zheng, J.K. Wu, H. Liu, Z.D. Fu. Generalized Four-Node Plane Rectangular and Quadrilateral Elements and their Applications in the Multiscale Analysis of Heterogeneous Structures. International Journal for Multiscale Computational Engineering, 2013, 11(1): 71-91. 

H. Liu, H.W. Zhang. Multi-node extended multiscale finite element method. Chinese Journal of Solid Mechanics, 2013, 33: 50-56. (In Chinese)

2012年：

H. Liu, J.J. Ma, F.F. Ji, et al. Numerical simulation and optimization design for high speed train body. Computer Aided Engineering, 2012, 21(4): 12-15. (In Chinese)

2010年：

H.W. Zhang, H. Liu, J.K. Wu, Y.G. Zheng. Plane 4 node generalized isoparametric element. Chinese Journal of Computational Mechanics, 2010, 27(3): 397-402. (In Chinese)

H.W. Zhang, J.K. Wu, H. Liu, Y.G. Zheng, Z.D. Fu. Generalized plane and space rectangular elements. Chinese Journal of Computational Mechanics, 2010, 27(3): 391-396. (In Chinese)

H.W. Zhang, J.K. Wu, H. Liu, Z.D. Fu. Basic theory of extended multiscale finite element method. Computer Aided Engineering, 2010, 19(2): 3-9. (In Chinese)