二步法方型三维编织复合材料细观结构及其有效弹性性能预测
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摘要
本文全面系统地研究了二步法方型三维编织复合材料的细观结构，并采用细观力学分析方法对其有效弹性性能进行了分析预测。
二步法三维编织复合材料的组分材料和增强体的细观结构对其宏观力学性能起着重要的作用。本文对其细观结构作了准确的单胞划分，定义了三种细观结构的单胞模型。即大单胞模型，亚单胞模型和子单胞模型。基于子单胞模型，通过计算轴纱内纱线填充因子，考虑了轴纱受编织纱挤压产生的变形，进而，建立了复合材料编织结构参数之间的关系，准确地计算了复合材料的纤维体积含量。同时，给出了二步法三维编织工艺的设计步骤，并由纱线挤紧状态确定出编织工艺的设计范围。
本文基于内部子单胞模型，提出了类似层合板结构的单胞力学模型，应用经典层合板理论实现由纤维和基体的性能、单胞力学模型的几何参数以及单层板的纤维体积含量分析并计算了二步法方型三维编织复合材料的有效弹性性能。
本文基于大单胞模型，提出了对二步法方型三维编织复合材料进行细观结构离散的思想，并建立有限元分析模型。其中，轴纱、编织纱和基体均被视为两端铰接的空间杆单元，复合材料用离散的杆单元组成的桁架结构代替。利用有限元分析软件包MARC实现单轴拉伸静载实验的模拟，分析了二步法三维编织复合材料的弹性性能，同时，预测了轴向拉伸模量随轴纱与编织纱线密度之比和节距长度变化的趋势。
本文设计并完成了单轴拉伸性能实验，在获得二步法三维编织复合材料宏观拉伸模量和泊松比的同时，对两种理论分析模型的预测结果进行了验证。预测结果与实验结果的比较显示了细观力学的两种分析模型都可以较为有效地分析二步法三维编织复合材料的力学性能。
In this thesis, the yarn architecture of the two-step rectangular three-dimensional braided composites was studied comprehensively and the effective elastic properties have been analyzed by means of two kinds of micro mechanical method.
The properties of components and the microstructure play an important role in the mechanical properties of two-step three-dimensional braided composites. Analyzing the microstructure of composites truly, three kinds of unit cell structures have been identified, i.e. large unit cells, sub unit cells and micro unit cells. The deformations of axial yarns packed by braider yarns have been calculated through the changes of fiber packing fractions of axial yarns. The relations between the braiding parameters of the composites were derived and the fiber volume fraction of the composites was computed exactly. The process of designing a two-step 3-D braided composite was given. The window of braiding process was given with the yarn jamming condition.
The model of the analogous laminar unit cell has been proposed based on the micro unit cells. The classical laminated plate theory was utilized to analyze the mechanical properties of two-step 3-D composite materials. In this methodology, the effective elastic properties were predicted through the properties of fiber and resin, the geometry of the laminated plate model and the fiber volume fraction.
Furthermore, the finite element model has been established on the basis of the large unit cells of the composites. The composite material was considered as an assemblage of a finite number of unit cells. In this model, axial yarns, braider yarns and resin were treated as spatial beam elements. Each unit cell is then treaded as space truss. Three-dimensional finite element method can be employed for the mechanic analysis. Utilizing the finite element software MARC, the monotonic tension tests of the beam samples were simulated. Parametric study showed the range of variability in the elastic modulus of the composites.
The parameters include the linear density ratio of axial yarn to braider yarn and the braiding pitch length.
The two model predictions were found to be in good agreement with the results of monotonic tensional tests performed in this study. The resolution method and the numerical method can be used to analyze the mechanical properties of two-step three-dimensional braided composites effectively.
二步法三维编织复合材料的组分材料和增强体的细观结构对其宏观力学性能起着重要的作用。本文对其细观结构作了准确的单胞划分，定义了三种细观结构的单胞模型。即大单胞模型，亚单胞模型和子单胞模型。基于子单胞模型，通过计算轴纱内纱线填充因子，考虑了轴纱受编织纱挤压产生的变形，进而，建立了复合材料编织结构参数之间的关系，准确地计算了复合材料的纤维体积含量。同时，给出了二步法三维编织工艺的设计步骤，并由纱线挤紧状态确定出编织工艺的设计范围。
本文基于内部子单胞模型，提出了类似层合板结构的单胞力学模型，应用经典层合板理论实现由纤维和基体的性能、单胞力学模型的几何参数以及单层板的纤维体积含量分析并计算了二步法方型三维编织复合材料的有效弹性性能。
本文基于大单胞模型，提出了对二步法方型三维编织复合材料进行细观结构离散的思想，并建立有限元分析模型。其中，轴纱、编织纱和基体均被视为两端铰接的空间杆单元，复合材料用离散的杆单元组成的桁架结构代替。利用有限元分析软件包MARC实现单轴拉伸静载实验的模拟，分析了二步法三维编织复合材料的弹性性能，同时，预测了轴向拉伸模量随轴纱与编织纱线密度之比和节距长度变化的趋势。
本文设计并完成了单轴拉伸性能实验，在获得二步法三维编织复合材料宏观拉伸模量和泊松比的同时，对两种理论分析模型的预测结果进行了验证。预测结果与实验结果的比较显示了细观力学的两种分析模型都可以较为有效地分析二步法三维编织复合材料的力学性能。
In this thesis, the yarn architecture of the two-step rectangular three-dimensional braided composites was studied comprehensively and the effective elastic properties have been analyzed by means of two kinds of micro mechanical method.
The properties of components and the microstructure play an important role in the mechanical properties of two-step three-dimensional braided composites. Analyzing the microstructure of composites truly, three kinds of unit cell structures have been identified, i.e. large unit cells, sub unit cells and micro unit cells. The deformations of axial yarns packed by braider yarns have been calculated through the changes of fiber packing fractions of axial yarns. The relations between the braiding parameters of the composites were derived and the fiber volume fraction of the composites was computed exactly. The process of designing a two-step 3-D braided composite was given. The window of braiding process was given with the yarn jamming condition.
The model of the analogous laminar unit cell has been proposed based on the micro unit cells. The classical laminated plate theory was utilized to analyze the mechanical properties of two-step 3-D composite materials. In this methodology, the effective elastic properties were predicted through the properties of fiber and resin, the geometry of the laminated plate model and the fiber volume fraction.
Furthermore, the finite element model has been established on the basis of the large unit cells of the composites. The composite material was considered as an assemblage of a finite number of unit cells. In this model, axial yarns, braider yarns and resin were treated as spatial beam elements. Each unit cell is then treaded as space truss. Three-dimensional finite element method can be employed for the mechanic analysis. Utilizing the finite element software MARC, the monotonic tension tests of the beam samples were simulated. Parametric study showed the range of variability in the elastic modulus of the composites.
The parameters include the linear density ratio of axial yarn to braider yarn and the braiding pitch length.
The two model predictions were found to be in good agreement with the results of monotonic tensional tests performed in this study. The resolution method and the numerical method can be used to analyze the mechanical properties of two-step three-dimensional braided composites effectively.
引文
1. 李嘉禄，孙颖．二步法方型三维编织复合材料的细观结构．复合材料学报，2000：20(4)：7—10．
2. 黄故．现代纺织复合材料．北京：中国纺织出版社，2000．1，p6．
3. Y. M. Tarnopolskii, A. V. Roze &. G. G. Portnov. Some Negative Characteristics of Fiber Reinforced Materials. Polymer Mechanics, Vol. 5, No. 1, 1969: 115-123.
4. Ko, F.K.. Three-dimensional Fabrics for Composites--An Introduction to the Magnaweave Structure. Proc. ICCM-4, Japan Soc. Composite Material, Tokyo, Japan, 1982, 1609.
5. Tsu-Wei Chou and Frank K.Ko. Textile Structural Composites. Elsevier Science Publishers, 1989, 129-171.
6. 李嘉禄，刘谦．三维编织复合材料中纤维束走向的研究．纺织学报，1999；20(4)： 7—10．
7. Ko, F.K, C.M. Pastore, A.A. Head. Handbook of Industrial Braiding, Atkins & Pearce, Inc.
8. McConnell R. & Popper P.. Complex Shaped Braided Structures. U.S. Patent No. 4,719,837, Jan. 19,1988.
9. Brown, R.T.. Design and Manufacture of 3-D Braided Preforms. 5~(th) Textile Structural Composites Symposium. Philadelphia, PA, Dec.5, 1991.
10. 李嘉禄．立体多向编织结构对复合材料性能的影响．复合材料学报，1996，13(3)，71-75．
11. 肖丽华，李嘉禄．制作复合材料的三维编织技术．天津纺织工学院学报，1993，12(3)，5-10．
12. 钟明辉．编织复合材料．纤维复合材料，1992，(2)，42-48，59．
13. 周光明，刘文宁．三维编织复合材料编织工艺研究(B)．复合材料进展，航空工业出版社，1994，174-176．
14. 肖丽华，李嘉禄．三维编织结构复合材料的编织设计．宇航材料工艺，1994，24(2)，22-25．
15. 杨桂．编织结构复合材料及其工艺的研究(B)．复合材料进展，航空工业出版社，1994，225-229．
16. 陈利．三维编织复合材料的细观结构及其弹性性能分析．天津纺织工学院博士研
究生论文，1998年9月．
17. Chou, T-W.. Microstructural Design of Fiber Composites. Cambridge University Press, Cambridge, England, 1991.
18. 修英殊．四步法三维编织复合材料力学性能的有限元分析．天津工业大学硕士论文，2001，1．
19. 刘谦．三维编织复合材料卫星桁架接头的研制和性能分析．天津工业大学博士论文，2001，1．
20. Brian N. Cox, Gerry Flanagan. NASA CR 4750, Contact NAS1-19243,1997,3.
21. 孙颖．二步法方型三维编织复合材料的细观结构及其力学性能分析．天津纺织工学院硕士研究生论文，2000年2月．
22. P. Popper, R. F. McConnell. U.S. Patent 4719837, January 1988.
23. Frank K. Ko.. Three-Dimensional Fabrics for Composites. Textile Structural Composites, 1989: 129-171.
24. Ro M. Bluck. High Speed Bias Weaving and Braiding. U.S. Patent 3426804, 11, Feb., 1969.
25. E. R. Stover, W. C. Mark, I. Marfowitz and W. Mueller.Preparation of an Omniweave Reinforced Carbon-Carbon Cylinder as a Candidate for Evaluation in the Advanced Heat Shield Screening Program. AFML-TR-70-283, Mar. 1971.
26. M. A. Maistre. Construction of a Three Dimensional Structure. F. R. D. Pantent P2301696.8, 1973.
27. R. A. Florentine. Apparatus for Weaving a Three Dimensional Article. U. S. Patent 4,312,261, January 26,1982.
28. Chang-Long Ma, Jenn-Ming Yang, and Tsu-Wei Chou. Elastic Stiffness of Three-dimensional Braided Textile Structural Composites. Composite Materials: Testing and Design, Seventh Conference, 1984, 404-421.
29. J.M. Yang, C. L. Ma, T-W. Chou. Fibre Inclination Model of Three Dimensional textile Structural Composite. J. Composite Materials, 1986 20:472-483.
30. Jianhua Han and S. V. Hoa. A Three-dimensional Multilayer Composite Finite Element for Stress Analysis of Composite Laminates. International Journal for Numerical Methods in Engineering. Vol. 36, 1993, 3903-3914.
31. D.L. Wu. Three-cell Model and 5D Braided Structural Composites. Composites Science and Technology 56 (1996) 225-233.
32. D. W. Whyte. Ph.D. Thesis, Drexel University, June 1986.
33. Amos Alexander, Jerome T. Tzeng. Three dimensional effective properties of composite materials for element applications. Journal of composite materials. 1997,5 vol.31.
34. Charles Lei, Yun-Jia Cai & Frank Ko. Finite element analysis of 3D braided composites. Advances in Engineering. Software 14 (1992) 187-194.
35. Chen Li, Tao Xiaoming and Choy Choy-loong. Mechanical Analysis of 3-D Braided Composites By Finite Multiphase Element Method. Posters of Fiber Society International Meeting, Asheville, North Carolina, USA, July, 1998.
36. Surya R. Kalidindi and Abdel Abusafieh. Longitudinal and Transverse Moduli and Strengths of Low Angle 3-D Braided Composites. J. Compos. Mater., Vol. 30, No. 8(1996), 885-905.
37. Howard A. Hardee, Keith Black, Rona Reid and Aly EI-Shiekh. Flexural Properties of 2-D and 3-D Braided Carbon/Epoxy Composites. 4~(th) International SAMPE Symposium, May, 1995, 821-830.
38. Nagain K, Yokoyama A, Maekawa Z, Hamada H, Noguchi Y. The Study of Analytical Method for Three Dimensional Composite Materials. Transactions of the Japan Society of Mechanical Engineers, 1994, 60(2): 514-519.
39. Jian Li, Pusheng Chen and Aly El-Shiekh. Construction and Geometry of 6-Step Braided Preforms for Composites. 39~(th) International SAMPE Symposium, April, 1994,826-833.
40. Charles S.C.Lei, M.A.El-Sherif and Frank K.Ko. Analysis of Stresses Around Embedded optical Fibers in 3-D Braided Composites. The Second International Symposium on Composite Materials and Structures, 1992, 922-927.
41. A. Abusafieh, S.R. Kalidindi and E. Franco. An Experimental and Numerical Study of Response of 3-D Braided Structural Textile Composites. Proceedings of the American Society for Composites Ninth Technical Conference: Composite Materials, Mechanics and Processing, 1994, 1118-1125.
42. Pusheng Chen, Rona Reid, Keith Black and Aly Elshiekh. Compressive and Flexural Properties of Carbon/Epoxy Composites. 39~(th) International SAMPE Symposium, April, 1994, 834-843.
43. Charles S.C. Lei and Frank K. Ko. A Strength Theory for Failure of 3-D Braided Composites. 41~(st) International SAMPE Symposium, March, 1996, 443-449.
44. Hui-Yu Sun and Xin Qiao. Prediction of The Mechanical Properties of Three-Dimensionally Braided Composites. Composites Science and Technology, 57(1997), 623-629.
45. Yasser A. Gowayed, Christopher M. Pastore and Carl S. Howarth. An Integrated Approach to The Geometrical and Mechanical Modeling of Textile Reinforced Composites. 39~(th) International SAMPE Symposium, April, 1994, 2841-2855.
46. F. K. Ko, H.B. Soebroto and C. Lei. Proceedings of 33~(rd) International SAMPE Symposium, 1988, p.912.
47. G. W. Du, P. Popper & T-W. Chou. Analysis of 3-D Textile Preforms for Multidirectional Reinforcement of Composites. J. Mater. Sci., 26(1991), 3438-3448.
48. W. Li, M. Hammad, & A. El-Shiekh. Structural Analysis of 3-D Braided Preforms for Composites. Part Ⅱ :The two-step preforms., J. Text. Inst., 1990, 81, No.4, 515-537.
49. J. -H. Byun, T.J. Whitney, G. W. Du & T-W. Chou. Analytical Characterization of 2-step Braided Composites. J. Comp. Mater., 25(1991) 1599-1618.
50. J. -H. Byun, & T-W. Chou. Process-Microstructure Relationships of 2-step and 4-step Braided Composites. Composites Science and Technology, 56(1996), 235-251.
51. 孙颖．二步法方型三维编织复合材料细观结构及其力学性能分析．2000，2．
52. Ishikawa, T.. Anti-symmetric Elastic Properties of Composite Plates of Satin Weave Cloth. Fiber Science and Technology, vol. 15, pp.127-145.
53. T. Ishikawa, T. W. Chou. Elastic Behavior of Woven Hybird Composites. Journal of Composite Materials, Vol. 16, 1982, 2.
54. Yang, J.M., Ma, C. L. and Chou T. W. Elastic Stiffness of Biaxial and Triaxial Woven Fabric Composites. Proceeding of the 29~(th) SAMPE National Symposium, Reno(1984).
55. 刘锡礼，王秉权．复合材料力学基础．北京：中国建筑工业出版社，1984，3，p39．
56. 杜善义，王彪．复合材料细观力学．北京：科学出版社，1998，3．p5．
57. Y.H. Zhao and G.J. Weng. Effective Elastic Moduli of Ribbon-Reinforced Composites,.J. Appl. Mech.. 1990,57:158-167.
58. F. Scardino, F. Ko. Triaxial Woven Fabrics. Textile Research Journal, Vol. 51, No. 2, 1981,80.
59. Rm. Jones. Mechanics of Composite Materials. Scripta Book Company: Washington, D.C., 1975.
60. Kuno K.U. Stellbrink. Micromechanics of Composites. Hanser Publishers,
Munich Vienna New York, 1996.
61. 田宗若．复合材料中的边界元法．西安：西北工业大学1992，p．589．
62. 龚尧南．结构力学．北京：北京航空航天大学，2002，3，p．45．
63. ASTM D3039/D3039M—95, Standard Test Method for Tensile Properties of Polymer Matrix Composite Materials.
64. 国家标准局，GB1447—83，玻璃纤维增强塑料拉伸性能试验方法．
65. 国家标准局，GB1446—83，纤维增强塑料性能试验方法总则．
66. Engineered Materials Handbook, Ohio: ASM International, Vol. 1, 1989.
67. 杨连贺．三维机织复合材料有效弹性性能预测．天津纺织工学院博士论文，1999，3．
2. 黄故．现代纺织复合材料．北京：中国纺织出版社，2000．1，p6．
3. Y. M. Tarnopolskii, A. V. Roze &. G. G. Portnov. Some Negative Characteristics of Fiber Reinforced Materials. Polymer Mechanics, Vol. 5, No. 1, 1969: 115-123.
4. Ko, F.K.. Three-dimensional Fabrics for Composites--An Introduction to the Magnaweave Structure. Proc. ICCM-4, Japan Soc. Composite Material, Tokyo, Japan, 1982, 1609.
5. Tsu-Wei Chou and Frank K.Ko. Textile Structural Composites. Elsevier Science Publishers, 1989, 129-171.
6. 李嘉禄，刘谦．三维编织复合材料中纤维束走向的研究．纺织学报，1999；20(4)： 7—10．
7. Ko, F.K, C.M. Pastore, A.A. Head. Handbook of Industrial Braiding, Atkins & Pearce, Inc.
8. McConnell R. & Popper P.. Complex Shaped Braided Structures. U.S. Patent No. 4,719,837, Jan. 19,1988.
9. Brown, R.T.. Design and Manufacture of 3-D Braided Preforms. 5~(th) Textile Structural Composites Symposium. Philadelphia, PA, Dec.5, 1991.
10. 李嘉禄．立体多向编织结构对复合材料性能的影响．复合材料学报，1996，13(3)，71-75．
11. 肖丽华，李嘉禄．制作复合材料的三维编织技术．天津纺织工学院学报，1993，12(3)，5-10．
12. 钟明辉．编织复合材料．纤维复合材料，1992，(2)，42-48，59．
13. 周光明，刘文宁．三维编织复合材料编织工艺研究(B)．复合材料进展，航空工业出版社，1994，174-176．
14. 肖丽华，李嘉禄．三维编织结构复合材料的编织设计．宇航材料工艺，1994，24(2)，22-25．
15. 杨桂．编织结构复合材料及其工艺的研究(B)．复合材料进展，航空工业出版社，1994，225-229．
16. 陈利．三维编织复合材料的细观结构及其弹性性能分析．天津纺织工学院博士研
究生论文，1998年9月．
17. Chou, T-W.. Microstructural Design of Fiber Composites. Cambridge University Press, Cambridge, England, 1991.
18. 修英殊．四步法三维编织复合材料力学性能的有限元分析．天津工业大学硕士论文，2001，1．
19. 刘谦．三维编织复合材料卫星桁架接头的研制和性能分析．天津工业大学博士论文，2001，1．
20. Brian N. Cox, Gerry Flanagan. NASA CR 4750, Contact NAS1-19243,1997,3.
21. 孙颖．二步法方型三维编织复合材料的细观结构及其力学性能分析．天津纺织工学院硕士研究生论文，2000年2月．
22. P. Popper, R. F. McConnell. U.S. Patent 4719837, January 1988.
23. Frank K. Ko.. Three-Dimensional Fabrics for Composites. Textile Structural Composites, 1989: 129-171.
24. Ro M. Bluck. High Speed Bias Weaving and Braiding. U.S. Patent 3426804, 11, Feb., 1969.
25. E. R. Stover, W. C. Mark, I. Marfowitz and W. Mueller.Preparation of an Omniweave Reinforced Carbon-Carbon Cylinder as a Candidate for Evaluation in the Advanced Heat Shield Screening Program. AFML-TR-70-283, Mar. 1971.
26. M. A. Maistre. Construction of a Three Dimensional Structure. F. R. D. Pantent P2301696.8, 1973.
27. R. A. Florentine. Apparatus for Weaving a Three Dimensional Article. U. S. Patent 4,312,261, January 26,1982.
28. Chang-Long Ma, Jenn-Ming Yang, and Tsu-Wei Chou. Elastic Stiffness of Three-dimensional Braided Textile Structural Composites. Composite Materials: Testing and Design, Seventh Conference, 1984, 404-421.
29. J.M. Yang, C. L. Ma, T-W. Chou. Fibre Inclination Model of Three Dimensional textile Structural Composite. J. Composite Materials, 1986 20:472-483.
30. Jianhua Han and S. V. Hoa. A Three-dimensional Multilayer Composite Finite Element for Stress Analysis of Composite Laminates. International Journal for Numerical Methods in Engineering. Vol. 36, 1993, 3903-3914.
31. D.L. Wu. Three-cell Model and 5D Braided Structural Composites. Composites Science and Technology 56 (1996) 225-233.
32. D. W. Whyte. Ph.D. Thesis, Drexel University, June 1986.
33. Amos Alexander, Jerome T. Tzeng. Three dimensional effective properties of composite materials for element applications. Journal of composite materials. 1997,5 vol.31.
34. Charles Lei, Yun-Jia Cai & Frank Ko. Finite element analysis of 3D braided composites. Advances in Engineering. Software 14 (1992) 187-194.
35. Chen Li, Tao Xiaoming and Choy Choy-loong. Mechanical Analysis of 3-D Braided Composites By Finite Multiphase Element Method. Posters of Fiber Society International Meeting, Asheville, North Carolina, USA, July, 1998.
36. Surya R. Kalidindi and Abdel Abusafieh. Longitudinal and Transverse Moduli and Strengths of Low Angle 3-D Braided Composites. J. Compos. Mater., Vol. 30, No. 8(1996), 885-905.
37. Howard A. Hardee, Keith Black, Rona Reid and Aly EI-Shiekh. Flexural Properties of 2-D and 3-D Braided Carbon/Epoxy Composites. 4~(th) International SAMPE Symposium, May, 1995, 821-830.
38. Nagain K, Yokoyama A, Maekawa Z, Hamada H, Noguchi Y. The Study of Analytical Method for Three Dimensional Composite Materials. Transactions of the Japan Society of Mechanical Engineers, 1994, 60(2): 514-519.
39. Jian Li, Pusheng Chen and Aly El-Shiekh. Construction and Geometry of 6-Step Braided Preforms for Composites. 39~(th) International SAMPE Symposium, April, 1994,826-833.
40. Charles S.C.Lei, M.A.El-Sherif and Frank K.Ko. Analysis of Stresses Around Embedded optical Fibers in 3-D Braided Composites. The Second International Symposium on Composite Materials and Structures, 1992, 922-927.
41. A. Abusafieh, S.R. Kalidindi and E. Franco. An Experimental and Numerical Study of Response of 3-D Braided Structural Textile Composites. Proceedings of the American Society for Composites Ninth Technical Conference: Composite Materials, Mechanics and Processing, 1994, 1118-1125.
42. Pusheng Chen, Rona Reid, Keith Black and Aly Elshiekh. Compressive and Flexural Properties of Carbon/Epoxy Composites. 39~(th) International SAMPE Symposium, April, 1994, 834-843.
43. Charles S.C. Lei and Frank K. Ko. A Strength Theory for Failure of 3-D Braided Composites. 41~(st) International SAMPE Symposium, March, 1996, 443-449.
44. Hui-Yu Sun and Xin Qiao. Prediction of The Mechanical Properties of Three-Dimensionally Braided Composites. Composites Science and Technology, 57(1997), 623-629.
45. Yasser A. Gowayed, Christopher M. Pastore and Carl S. Howarth. An Integrated Approach to The Geometrical and Mechanical Modeling of Textile Reinforced Composites. 39~(th) International SAMPE Symposium, April, 1994, 2841-2855.
46. F. K. Ko, H.B. Soebroto and C. Lei. Proceedings of 33~(rd) International SAMPE Symposium, 1988, p.912.
47. G. W. Du, P. Popper & T-W. Chou. Analysis of 3-D Textile Preforms for Multidirectional Reinforcement of Composites. J. Mater. Sci., 26(1991), 3438-3448.
48. W. Li, M. Hammad, & A. El-Shiekh. Structural Analysis of 3-D Braided Preforms for Composites. Part Ⅱ :The two-step preforms., J. Text. Inst., 1990, 81, No.4, 515-537.
49. J. -H. Byun, T.J. Whitney, G. W. Du & T-W. Chou. Analytical Characterization of 2-step Braided Composites. J. Comp. Mater., 25(1991) 1599-1618.
50. J. -H. Byun, & T-W. Chou. Process-Microstructure Relationships of 2-step and 4-step Braided Composites. Composites Science and Technology, 56(1996), 235-251.
51. 孙颖．二步法方型三维编织复合材料细观结构及其力学性能分析．2000，2．
52. Ishikawa, T.. Anti-symmetric Elastic Properties of Composite Plates of Satin Weave Cloth. Fiber Science and Technology, vol. 15, pp.127-145.
53. T. Ishikawa, T. W. Chou. Elastic Behavior of Woven Hybird Composites. Journal of Composite Materials, Vol. 16, 1982, 2.
54. Yang, J.M., Ma, C. L. and Chou T. W. Elastic Stiffness of Biaxial and Triaxial Woven Fabric Composites. Proceeding of the 29~(th) SAMPE National Symposium, Reno(1984).
55. 刘锡礼，王秉权．复合材料力学基础．北京：中国建筑工业出版社，1984，3，p39．
56. 杜善义，王彪．复合材料细观力学．北京：科学出版社，1998，3．p5．
57. Y.H. Zhao and G.J. Weng. Effective Elastic Moduli of Ribbon-Reinforced Composites,.J. Appl. Mech.. 1990,57:158-167.
58. F. Scardino, F. Ko. Triaxial Woven Fabrics. Textile Research Journal, Vol. 51, No. 2, 1981,80.
59. Rm. Jones. Mechanics of Composite Materials. Scripta Book Company: Washington, D.C., 1975.
60. Kuno K.U. Stellbrink. Micromechanics of Composites. Hanser Publishers,
Munich Vienna New York, 1996.
61. 田宗若．复合材料中的边界元法．西安：西北工业大学1992，p．589．
62. 龚尧南．结构力学．北京：北京航空航天大学，2002，3，p．45．
63. ASTM D3039/D3039M—95, Standard Test Method for Tensile Properties of Polymer Matrix Composite Materials.
64. 国家标准局，GB1447—83，玻璃纤维增强塑料拉伸性能试验方法．
65. 国家标准局，GB1446—83，纤维增强塑料性能试验方法总则．
66. Engineered Materials Handbook, Ohio: ASM International, Vol. 1, 1989.
67. 杨连贺．三维机织复合材料有效弹性性能预测．天津纺织工学院博士论文，1999，3．