1 Jirousek J, Leon N. A powerful finite element for plate bending. Computer Methods in Applied Mechanics and Engineering, 1977, 12(1):77-96
2 Qin QH. The Trefftz Finite and Boundary Element Method. Southampton:WIT Press, 2000
3 Qin QH, Wang H. MATLAB and C Programming for Trefftz Finite Element Methods. Boca Raton:CRC Press, 2008
4 徐鹏, 金吾根, 万远富. 流形 Trefftz 直接法. 计算力学学报, 2008, 25 (2):260-264
5 Li ZC, Lu TT, Hu HY, et al. Trefftz and Collocation Methods. Southampton:WIT Press, 2008
6 Kolodziej JA, Zielinski AP. Boundary Collocation Techniques and Their Application in Engineering. Southampton:WIT Press, 2009
7 司马玉洲, 朱宏平, 苗雨. 双重互易杂交边界点方法在势问题中 的应用. 力学与实践, 2007, 29 (6):37-40
8 Weißer S. Arbitrary order Trefftz-like basis functions on polygonal meshes and realization in BEM-based FEM. Computers & Mathematics with Applications, 2014, 67(7):1390-1406
9 Wang H, Han MY, Yuan F, et al. Fundamental-solutionbased hybrid element model for nonlinear heat conduction problems with temperature-dependent material properties. Mathematical Problems in Engineering, 2013, 2013(3):831-842
10 王克用, 李培超, 张敏良. 正交各向异性位势问题的 Trefftz 有 限元法. 力学季刊, 2012, 33(3):499-506
11 Choo YS, Choi N, Lee BC. A new hybrid-Trefftz triangular and quadrilateral plate elements. Applied Mathematical Modelling, 2010, 1(1):14-23
12 Wang KY, Zhang LQ, Li PC. A four-node hybrid-Trefftz annular element for analysis of axisymmetric potential problems. Finite Elements in Analysis & Design, 2012, 60:49-56
13 Wang H, Qin QH, Liang XP. Solving the nonlinear Poisson-type problems with F-Trefftz hybrid finite element model. Engineering Analysis with Boundary Elements, 2012, 36(1):39-46
14 Dong L, Atluri SN. T-Trefftz Voronoi cell finite elements with elastic/rigid inclusions or voids for micromechanical analysis of composite and porous materials. Computer Modeling in Engineering & Sciences, 2012, 83:183-219
15 Dong L, Atluri SN. Development of 3D T-Trefftz Voronoi cell finite elements with/without spherical voids and/or elastic/rigid inclusions for micromechanical modeling of heterogeneous materials. CMC -Computers Materials and Continua, 2012, 29:169-211
16 Dong L, Atluri SN. Development of 3D Trefftz Voronoi cells with ellipsoidal voids and/or elastic/rigid inclusions for micromechanical modeling of heterogeneous materials. CMC -Computers Materials and Continua, 2012, 30:39-81
17 秦庆华. Hybrid-Trefftz 有限元简介和展望. 力学与实践, 1993, 15(3):22-24
18 Silva CM, Castro LMSS. Hybrid-displacement (Trefftz) formulation for softening materials. Computers & Structures, 2007, 85(17-18):1331-1342
19 Zhang ZW, Wang H, Qin QH. Method of fundamental solutions for nonlinear skin bioheat model. Journal of Mechanics in Medicine & Biology, 2014, 14(4):1450060
20 Moldovan ID, Cao TD, Teixeira DFJA. Hybrid-Trefftz finite elements for biphasic elastostatics. Finite Elements in Analysis & Design, 2013, 66(66):68-82
21 Freitas JATD, Toma M. Hybrid-Trefftz stress and displacement elements for axisymmetric incompressible biphasic media. Computer Methods in Applied Mechanics & Engineering, 2009, 198(30-32):2368-2390
22 Moldovan ID, Freitas JATD. Hybrid-Trefftz displacement and stress elements for bounded poroelasticity problems. Computers & Geotechnics, 2012, 42(3):129-144
23 Herrera I. General variational principles applicable to the hybrid element method. National Academy of Sciences, USA, 1977
24 Herrera I. Boundary methods:a criterion for completeness. National Academy of Sciences, USA, 1980
25 Herrera I, Ewing RE, Celia MA, et al. Eulerian-Lagrangian localized adjoint method:the theoretical framework. Numerical Methods for Partial Differential Equations, 1993, 9(4):431-457
26 Herrera I, Sabina FJ. Connectivity as an alternative to boundary integral equations:construction of bases. National Academy of Sciences, USA, 1978
27 Rezaiee-Pajand M, Karkon M. Two higher order hybridTrefftz elements for thin plate bending analysis. Finite Elements in Analysis & Design, 2014, 85(8):73-86
28 Wang H, Qin QH. Hybrid FEM with fundamental solutions as trial functions for heat conduction simulation. Acta Mechanica Solida Sinica, 2009, 22(5):487-498
29 Wang H, Qin QH. Fundamental-solution-based finite element model for plane orthotropic elastic bodies. European Journal of Mechanics-A/Solids, 2010, 29(5):801-809
30 Cao C, Qin QH, Yu A. Hybrid fundamental-solution-based FEM for piezoelectric materials. Computational Mechanics, 2012, 50(4):3 97-412
31 Wang H, Qin QH. Some problems with the method of fundamental solution using radial basis functions. Acta Mechanica Solida Sinica, 2007, 20(1):21-29
32 Wang H, Qin QH. Hybrid fundamental solution based finite element method:theory and applications. Advances in Mathematical Physics, 2015, 2015:1-38
33 Wang H, Qin QH, Arounsavat D. Application of hybrid Trefftz finite element method to nonlinear problems of minimal surface. International Journal for Numerical Methods in Engineering, 2007, 69(6):1262-1277
34 王克用. 一种 Trefftz 孔洞单元及其在接触问题中的应用. 力学 季刊, 2011, 32(3):460-465
35 Wang H, Qin QH. FE approach with Green's function as internal trial function for simulating bioheat transfer in the human eye. Archives of Mechanics, 2010, 62(6):493-510
36 Cao LL, Wang H, Qin QH. Fundamental solution based graded element model for steady-state heat transfer in FGM. Acta Mechanica Solida Sinica, 2012, 25(4):377-392
37 Fu ZJ, Qin QH, Chen W. Hybrid-Trefftz finite element method for heat conduction in nonlinear functionally graded materials. Engineering Computations:International Journal for Computer-Aided Engineering and Software, 2011, 28(5):578-599
38 Wang KY, Li PC, Wang DZ. Trefftz-type FEM for solving orthotropic potential problems. Latin American Journal of Solids & Structures, 2014, 11(14):2537-2554
39 刘博, 王克用, 王明红. 轴对称 Poisson 方程的 Trefftz 有限元 解法. 应用数学和力学, 2015, 36(2):140-148
40 Moldovan ID. A new approach to non-homogeneous hyperbolic boundary value problems using hybrid-Trefftz stress finite elements. Engineering Analysis with Boundary Elements, 2016, 69:57-71
41 Liu RF, Yeih WC, Kuo SR, et al. Indirect T-Trefftz and F-Trefftz methods for solving boundary value problem of Poisson equation. Journal of the Chinese Institute of Engineers, 2006, 29(6):989-1006
42 Liu CS. Optimally scaled vector regularization method to solve ill-posed linear problems. Applied Mathematics and Computation, 2012, 218(21):10602-10616
43 Jirousek J, Venkatesh A. Hybrid Trefftz plane elasticity elements with p-method capabilities. International Journal for Numerical Methods in Engineering, 1992, 35(7):1443-1472
44 Wang H, Qin QH. Numerical implementation of local effects due to two-dimensional discontinuous loads using special elements based on boundary integrals. Engineering Analysis with Boundary Elements, 2012, 36(12):1733-1745
45 Piltner P. Special finite elements with holes and internal cracks. International Journal for Numerical Methods in Engineering, 1985, 21(8):1471-1485
46 Leconte N, Langrand B, Markiewicz E. On some features of a plate hybrid-Trefftz displacement element containing a hole. Finite Elements in Analysis & Design, 2010, 46(10):819-828
47 Wang H, Qin QH. Fundamental-solution-based hybrid FEM for plane elasticity with special elements. Computational Mechanics, 2011, 48(5):515-528
48 Zhang J. A hybrid finite element method for heterogeneous materials with randomly dispersed rigid inclusions. International Journal for Numerical Methods in Engineering, 1995, 38(10):1635-1653
49 Zhang J, Katsube N. A hybrid finite element method for heterogeneous materials with randomly dispersed elastic inclusions. Finite Elements in Analysis & Design, 1995, 19(1):45-55
50 Zhang J, Katsube N. A polygonal element approach to random heterogeneous media with rigid ellipses or elliptical voids. Computer Methods in Applied Mechanics & Engineering, 1997, 148(3-4):225-234
51 张洪武, 王辉. 基于参数变分原理的含夹杂 Voronoi 单元法及 非均质材料弹塑性计算. 复合材料学报, 2007, 24(4):145-153
52 Dong L, Atluri SN. Development of T-Trefftz four-node quadrilateral and Voronoi cell finite elements for macro-& micromechanical modeling of solids. CMES:Computer Modeling in Engineering & Sciences, 2011, 81(1):69-118
53 Ghosh S, Mallett RL. Voronoi cell finite element. Computers & Structures, 1994, 50(1):33-46
54 Wang H, Qin QH, Xiao Y. Special n-sided Voronoi fiber/matrix elements for clustering thermal effect in natural-hemp-fiber-filled cement composites. International Journal of Heat & Mass Transfer, 2016, 92:228-235
55 Cao C, Yu A, Qin QH. A new hybrid finite element approach for plane piezoelectricity with defects. Acta Mechanica, 2013, 224(1):41-61
56 Wang H, Qin QH. Fundamental-solution-based hybrid FEM for plane elasticity with special elements. Computational Mechanics, 2011, 48(5):515-528
57 Qin QH, Wang H. Special circular hole elements for thermal analysis in cellular solids with multiple circular holes. International Journal of Computational Methods, 2013, 10(4):683-728
58 王辉, 赵新娟, 白杨等. 基于基本解的杂交有限元法及特殊孔洞 单元的构造理论. 第十四届北方七省市区力学学会学术会议, 中 国威海, 2012
59 Bishay PL, Atluri SN. Trefftz-Lekhnitskii Grains (TLGs) for efficient direct numerical simulation (DNS) of the micro/meso mechanics of porous piezoelectric materials. Computational Materials Science, 2014, 83(2):235-249
60 Hennuyer C, Leconte N, Langrand B, et al. Interpolation functions of a hybrid-Trefftz perforated super-element featuring nodes on the hole boundary. Finite Elements in Analysis & Design, 2014, 91(91):40-47
61 Kunter K, Heubrandtner T, Suhr B, et al. A hybrid crack tip element containing a strip-yield crack-tip plasticity model. Engineering Fracture Mechanics, 2014, 129:3-13
62 Chen MC, Ping XC, Liu WH, et al. A novel hybrid finite element analysis of two polygonal holes in an infinite elastic plate. Engineering Fracture Mechanics, 2012, 83:26-39
63 Bussamra FLS, Neto EL, Jr DSR. Hybrid quasi-Trefftz 3D finite elements for laminated composite plates. Computers & Structures, 2012, s92-93(3):185-192
64 Cao C, Yu A, Qin QH. A novel hybrid finite element model for modeling anisotropic composites. Finite Elements in Analysis & Design, 2013, 64(2):36-47
65 Karkon M. Hybrid-Trefftz formulation for analysis of anisotropic and symmetric laminated plates. Composite Structures, 2015, 134:460-474
66 Karkon M, Rezaiee-Pajand M. Hybrid-Trefftz formulation for analysis of thick orthotropic plates. Aerospace Science & Technology, 2016, 50:234-244
67 赵新娟, 赵吉义. 位势问题的杂交有限元算法研究. 中原工学院 学报, 2011, 22(1):59-61
68 Wang H, Qin QH. Boundary integral based graded element for elastic analysis of 2D functionally graded plates. European Journal of Mechanics-A/Solids, 2012, 33(3):12-23
69 Petrolito J. Vibration and stability analysis of thick orthotropic plates using hybrid-Trefftz elements. Applied Mathematical Modelling, 2014, 38(24):5858-5869
70 Petrolito J. Vibration and stability of plates using hybridTrefftz elements. International Journal of Structural Stability & Dynamics, 2011, 4(4):559-578 |