Research on application of Spline Functions to Structural Analysis

1. Antes, H.:Die Spline-Interpolation zur Losung von Integralgleichungen und ihr Anwndung bei der Berechnung von Spannungen in krummlinig berandeten Scheiben. Dissertation, Aachen Inst. Tech., Aachen, 1970.

2. Antes, H.:Fundamental-splinefunktionen bei einer variationsverfahren zur Balken berechnung. Wissenschaftliche Zeitschrift der Hochschule fur Architektur und Bauwesen Weimar, vol. 19, pp. 131-134, 1972.

3. Antes, H.:Plattenberechnung mit fundamental-splinefunktionen. ZAMM, vol. 54, pp. 182-183, 1974.

4. Antes, H.:Bicubic fundamental splines in plate bending. Int. J. Num. Meth. Eng., vol. 8, pp. 503-511, 1974.

5. Antes, H.:Splinefunktionen bei der Plattenberechnung mittels Spannungs-funktionen. Wissenschaftliche Zeitschrift der Hochschule fur Architektur und Bauwesen Weimar, vol. 22, pp. 135-137, 1975.

6. Au, F.T.K. and Cheung, Y.K.: Isoparametric spline finite strip for plane structures. Comput. Struct., Vol. 48, pp. 23-32, 1993.

7. Au, F.T.K. and Cheung, Y.K.: Static and free vibration analysis of variable-depth bridges of arbitrary alignments using the isoparametric spline finite strip method. Thin-Walled Structures, Vol. 24, pp. 19-51, 1996.

8. Au, F.T.K. and Cheung, Y.K.: Free vibration and stability of shells by the isoparametric spline finite strip method. Thin-Walled Structures, Vol. 24, pp. 53-82, 1996.

9. Bert, C.W. and Sheu, Y.: Static analysis of beams and plates by spline collocation method. J. Eng. Mech.(ASCE), Vol. 122, No. 4, pp. 375-378, 1996.

10. Boyer, J.C. and Trompette, P.:An improvement of the stree calculations in plane elasticity by use of spline functions. J. Appl. Mech., vol. 48, pp. 972-974, 1981.

11. Chen, C.J.: The unequally spaced cubic B-spline compound strip method. Ph. D. Thesis, Colorado State Univ., Fort Collins, CO., 1989.

12. Chen, C.J., Gutkowski, R.M. and Puckett, J.A.: B-spline compound strip analysis of stiffened plates under transverse loading. Comput. Struct., vol. 34(2), pp. 337-347, 1990.

13. Chen, C.J., Gutkowski, R.M. and Puckett, J.A.: Spline compound strip analysis of folded plate structures with intermediate supports.

Comput. Struct., vol. 39, pp. 369-379, 1991.

14. Chen, C.J., Gutkowski, R.M. and Puckett, J.A.: B-spline compound strip formulation for braced thin-walled structures. Journal of Structural Engineering, ASCE, vol. 117(5), pp. 1303-1316, 1991.

15. Chen, J.L.:Modified finite strip method with spline functions. Ph. D. Thesis, University of Wyoming, 1985.

16. Cheung, M.S. and Li, W.: Analysis of haunched, continuous bridges by spline finite strips. Comput. and Struct., vol. 36, pp. 297-300, 1990.

17. Cheung, Y.K. and Fan, S.C.:Static analysis of right box girder bridges by spline finite strip method. Proc. Instn Civil Engrs, part 2, vol. 75, pp. 311-323, 1983.

18. Cheung, Y.K., Tham, L.G. and Li, W.Y.:Application of spline-finite-strip method in the analysis of curved slab bridges, Proc. Instn Civil Engrs, part2, vol. 81, pp. 111-124, 1986.

19. Cheung, Y.K. and Dashan, Z.:Large deflection analysis of arbitrary shaped thin plates. Computers & structures, vol. 26, pp. 811-814, 1987.

20. Cheung, Y.K., Tham, L.G. and Li, W.Y.: Free vibration and static analysis of general plate by spline finite strip. Computational Mechanics, vol. 3, pp. 187-197, 1988.

21. Cheung, Y.K., Li. W.Y. and Tham, L.G.:Free vibration analysis of singly curved shell by spline finite strip method. Journal of Sound and Vibration, vol. 128, pp. 411-422, 1989.

22. Cheung, Y.K. and Zhu, D.S.: Postbuckling analysis of circular cylinderical shells under external pressure. Thin-Walled Structures, vol. 7, pp. 239-256, 1989.

23. Cheung, Y.K. and Kong, J.: Approximate three-dimensional analysis of rectangular thick laminated plates-bending,vibration and buckling. Computers and Structures, Vol. 47, pp. 193-199, 1993.

24. Cheung, Y.K. and Kong, J.: Linaer elastic stability analysis of shear-deformable plates using a modified spline finite strip method. Comput. Struct., Vol. 47, pp. 189-193, 1993.

25. Chong, K.P. and Chen, J.L.: Buckling of irregular plates by splined finite strips. AIAA Journal, vol. 24, pp. 534-536, 1986.

26. Chungtze, S.:On spline finite element method(in Chinese). Mathematics Numericas Sinica, vol. 1, pp. 50-72, 1979.

27. Cida, X.:The dynamic response of plates and shells by the spline collocation method(in Chinese). The Computational Mechanics of Structures and its Applications, vol. 2(1), 1985.

28. Dawe, D.J. and Wang, S.: Vibration of shear-deformable beams using a spline-function approarch. Int. J. Num. Meth. Eng., vol. 33, pp. 819-844, 1992.

29. Dawe, D.J. and Wang, S.: Free vibration of generally-laminated, shear-deformable, composite rectangular plates using a spline Rayleigh-Ritz method. Composite Structures, Vol. 25, pp. 77-87, 1993.

30. Dawe, D.J. and Wang, S.: Spline finite strip analysis of the buckling and vibration of rectangular composite laminated plates. Int. J. Mech. Sci., Vol. 37(6), pp. 645-667, 1995.

31. Dade, H.: Analysis of laminated plates and shells by using spline Gauss collocation method. Comput. Struct., vol. 38(4), pp. 469-473, 1991.

32. Fan, S.C.:Spline finite strip in structural analysis. Ph. D. Thesis, Department of Civil Engineering, Univ. of Hong Kong, Hong Kong, 1982.

33. Fan, S.C. and Cheung, Y.K.:Analysis of shallow shells by spline finite strip method. Engineering Structures, vol. 5, pp. 255-262, 1982.

34. Fan, S.C. and Cheung, Y.K.:Flexural free vibrations of rectangular plates with complex support conditions. J. Sound and Vibration, vol. 93, pp. 81-94, 1984.

35. Fan, S.C. and Luah, M.H.: Spline finite element for axisymmetric free vibrations of shells of revolution. J. Sound and Vibration, vol. 131(1), pp. 61-72, 1989.

36. Fan, S.C. and Luah, M.H.: New spline finite element for analysis of shells of revolution J. Engineering Mechanics, ASCE, vol. 116, pp. 709-725(1990).

37. Fan, S.C. and Luah, M.H.: New spline finite element for plate bending. J. Engng Mech., ASCE, vol. 118, pp. 1065-1089, 1992.

38. Fan, S.C. and Luah, M.H.: A nine-node spline element for free vibration analysis of general plates. J. Sound and Vib., vol. 165, pp. 85-100, 1993.

39. Fan, S.C. and Luah, M.: Free vibration analysis of arbitrary thin shell structures by using spline finite element. J. Sound and Vibr., Vol. 179(5), pp. 763-776, 1995.

40. Fujii, F.:Spline-Functionen mit mehrfachen Knoten in der gemischten Platten berechnung. Ingenieur-Archiv, vol. 50, pp. 365-375, 1981.

41. Fujii, F.:Discrete and non-discrete mixed methods for plate bending analysis. Int. J. Num. Meth. Eng., vol. 17, pp. 1843-1859, 1981.

42. Fujii, F. and Hoshino, T.:Discrete and non-discrete mixed methods applied to eigenvalue problems of plates. J. Sound and Vibration, vol. 87, pp. 525-535,1983.

43. Fujii, F.:A simple mixed formulation for elastica problems. Computers & Structures, vol. 17, pp. 79-88, 1983.

44. Fujii, F.:Functions spline aux noeuds multiples en analyse numerique des plaques- Flexion Flambement et Vibration. Theories et Meth. de Calcul Annales de linstitut Tech. du Batiment et des Travaux Publics, No. 403 ,pp. 91-102, 1983.

45. Geannakakes, G.N. and Wang, P.C.: Moving load analysis of arbitrarily shaped plates using B3-spline finite strip method. J. Sound and Vib., vol. 141, pp. 127-142(1990).

46. Geannakakes, G.N. and Wang, P.C.: Vibration analysis of arbitrary-shaped shell panels using B3-spline finite strips. Comput. Struct., vol. 39(5), pp. 489-492, 1991.

47. Gu, D.: Calculation in the unsymmetrical bending problem of thin plates by spline boundary layer method. Comput. Struct., vol. 34, pp. 663-668, 1990.

48. Gu, D.: Application of B-spline approximation to symmetric buckling problems of truncated shallow spherical shells subjected to line loads. Int. J. Num. Meth. Eng., vol. 31, pp. 895-907, 1991.

49. Guo, Y.L.: Nonlinear analysis of thin shells by spline finite strip method. J. Xian Inst. Metallurgy and Construction Engng, vol. 22, pp. 366-373, 1990.

50. Guo, Y.L. and Lindner, J.: Analysis of elasto-plastic interaction buckling of stiffened panaels by spline finite strip method. Comput. Struct., vol. 46(3), pp. 529-536, 1993.

51. Gupta, A., Kiusalaas, J. and Saraph, M.: Cubic B-spline for finite element analysis of axisymmetric shells. Comput. Struct., vol. 38(4), pp. 463-468(1991).

52. Gupta, U.S. and Lal, R.:Transverse vibrations of a non-uniform rectangular plates on an elastic foundation. J. Sound and Vibration, Vol. 61, pp. 127-133, 1978.

53. Gupta, U.S. and Lal, R.:Axisymmetric vibrations of linearly tapered annular plates resting on elastic foundation:by spline method. The Journal of the Aeronautical Society of India, vol. 31, pp. 97-102, 1979.

54. Gupta, U.S., Lal, R. and Verma, C.P.:Effect of an elastic foundation on axisymmetric vibrations of polar orthotropic annular plates of variable thickness. J. Sound and Vibration vol. 103, pp. 159-169, 1985.

55. Gupta, U.S., Lal, R. and Verma, C.P.:Buckling and vibrations of polar orthotropic annular plates of variable thickness. J. Sound and Vibration, vol. 104, pp. 357-369, 1986.

56. Gupta, U.S., Lal, R. and Verma, C.P.:Buckling and vibrations of polar orthotropic annular plates on elastic foundation subjected to hydrostatic peripheral loading. J. Sound and Vibration, vol. 109, pp. 423-434, 1986.

57. Gutkowski, R.M., Chen, C.J. and Puckett, J.A.: Plate bending analysis by unequally spaced splines. Thin-Walled Structures, vol. 11, pp. 409-430, 1991.

58. Hadid, H.A. and Bashir, M.H.M.: Free vibration of beams and oblique panels by spline-integral method. J. Sound and Vibr., Vol. 189(1), pp. 3-12, 1996.

59. Hinrichsen, R.L.:The nonlinear analysis of thick composite plates using a cubic spline function. Ph. D. Thesis, Air Force Institute of Technology, Wright-Patterson AFB, 1984.

60. Hinrichsen, R.L. and Palazotto, A.N.:Nonlinear finite element analysis of thick composite plates using cubic spline functions. AIAA Journal vol. 24, pp. 1836-1842, 1986.

61. 入江 敏博、山田 元:相似だ円孔を有する直交異方性だ円板の自由振動.    日本機械学会論文集(c編), 45巻390号、pp. 171-178, 1979.

62. 入江 敏博、山田 元:スプライン関数を用いた変厚有孔円板の自由振動解析.    日本機械学会論文集(C編), 45巻394号、pp. 681-688, 1979.

63. Irie, T., Yamada, G. and Kanda, R.:Free vibration of rotating non-uniform disc:spline interpolation technique calculations. J. Sound and Vibration, vol. 66, pp. 13-23, 1979. 64. Irie, T., Yamada, G. and Takahashi, I.:Determination of the steady state response of a Timoshenko beam of varying cross-section by use of the spline interpolation technique. J. Sound and Vibration, vol. 63, pp. 287-295, 1979.

65. Irie, T., Yamada, G. and Ito, F.: Vibration of polar-orthotropic sector plates. J. Sound and Vibration, vol. 67, pp. 89-100, 1979.

66. Jianqiao, Y.: Non-linear bending analysis of plates and shells by using a mixed spline boundary element and finite element method. Int. J. Num. Meth. Eng., vol. 31, pp. 1283-1294, 1991.

67. Kao, R.:Approximate solutions by utilizing Hill functions. Computers & Structures, vol. 3, pp. 397-412, 1973. 68. Kao, R.:Application of Hill functions to circular plate problems. Quart. Appl. Math., vol. 28, pp. 63-72, 1975.

69. Kao, R.:Application of Hill functions to two-dimensional plate problems. Int. J. Solids and Structures, vol. 11, pp. 21-31, 1975.

70. Kilberth, K. and Weidner, P.:Berechnung dunner Rechteck- und Parallelogrammplatten mittels Splines. Ingenieur-Archiv, vol. 43, pp. 247-254, 1974.

71. Kim, J.:B-spline finite element analysis of arbitrary loaded shells of revolution. Ph. D. Thesis, Cornell University, 1983.

72. Kong, J. and Cheung, Y.K.: Application of the spline finite strip to the analysis of shear-deformable plates. Comput. Struct., vol. 46(6), pp. 985-988, 1993.

73. Kong, J. and Cheung, Y.K.: A generalized spline finite strip for the analysis of plates. Thin-Walled Structures, Vol. 22, pp. 181-202, 1995.

74. Lal, R.:Vibrations of elastic plates of variable thickness. Ph. D. Thesis, Univ. of Roorkee, India, 1979.

5. Lau, S.C.W. and Hancock, G.J.:Buckling of thin flat-walled structures by a spline finite strip method. Thin-Walled Structures, vol. 4, pp. 269-294, 1986.

76. Lau, S.C.W.: Distortional buckling of thin-walled columns. Ph. D. Thesis, Univ. of Sydney, Sydney, Australia, 1988.

77. Lau, S.C.W. and Hancock, G.J.: Inelastic buckling analyses of beams, columns and plates using spline finite strip method. Thin-Walled Structures, vol. 7, pp. 213-238(1989).

78. Leung, A.Y.T. and Au, F.T.K.: Spline finite elements for beam and plate. Comput. and Struct., vol. 37(5), pp. 717-729(1990)

79. Li, W.Y., Cheung, Y.K. and Tham, L.G.:Spline finite strip analysis of general plates.    Journal of Eng. Div., ASCE, vol. 112, pp. 43-54, 1986.

80. Li, W.Y., Tham, L.G. and Cheung, Y.K.: Curved box girder bridges. J. Struct. Eng., ASCE, vol. 114, pp. 1324-1338(1988).

81. Li, W.Y., Tham, L.G. and Cheung, Y.K.: Free vibration analysis of doubly curved shells by spline finite strip method. J. Sound and Vibration, vol. 140, pp. 39-53(1990).

82. Loo, Y.C., Tam, W.S. and Byun, Y.J.: Higher order spline finite strip method. International Journal of Structures, vol. 5(1), pp. 45-69(1985)

83. Luah, M.H. and Fan, S.C.: General free vibration analysis of shells of revolution using the spline element method. Comput. Struct., vol. 33, pp. 1153-1162(1989).

84. Luah, M.H. and Fan, S.C.: Analysis of complicated plates by a nine-node spline plate element. Comput. Strct., vol. 45(2), pp. 243-252, 1992.

85. Luah, M. and Fan, S.C.: Spline finite element for curved thin shells of arbitrary geometry. J. of Eng. Mech., ASCE, Vol. , pp. , 1995.

86. Mickley, K.:Berechnung von Platten unter Verwendung von bikubischen spline functionen. Diplomarbeit von Archen Tech. Univ., Aachen, 1973.

87. 水澤富作、梶田建夫、成岡昌夫: B-spline関数を用いた斜板の自由振動解析について. 土木学会論文報告集、第272, pp. 131-134, 1978.

88. Mizusawa, T., Kajita, T. and Naruoka, M.:Vibration of skew plates by using B-spline functions. J. Sound and Vibration, vol. 62, pp. 301-308, 1979.

89. Mizusawa, T., Kajita, T. and Naruoka, M.:Vibration of stiffened skew plates by using B-spline functions. Computers and Structures, vol. 10, pp. 821-826, 1979.

90. Mizusawa, T., Kajita, T. and Naruoka, M.:Buckling of skew plate structures using B-spline functions. Int. J. Num. Meth. Eng., vol. 15, pp. 87-96, 1980.

91. Mizusawa, T., Kajita, T. and Naruoka, M.:Analysis of skew plate problems with various constraints. J. Sound and Vibration, vol. 73, pp. 575-584, 1980.

92. Mizusawa, T., Kajita, T. and Naruoka, M.:Vibration and buckling of plates of abruptly varying stiffnesses. Computers and Structures, vol. 12, pp. 689-693, 1980.

93. Mizusawa, T. and Kajita, T.:Application of point least squares method with B-splines in solid mechanics problems. Int. J. Num. Meth. Eng., vol. 16, pp. 897-907, 1982.

94. Mizusawa, T. and Fujii, F.:Spline functions for plate and shell analysis. Finite Element News, No. 3, pp. 18-19, 1982.

95. Mizusawa, T. and Kajita, T.:Elastic limit loads of skew plates. Computers and Structures, vol. 16, pp. 597-602, 1983.

96. 水澤富作: 斜板構造の力学的挙動に関する数値解析学的研究.  名古屋大学学位論文、1983.

97. Mizusawa, T. and Kajita, T.:Vibration of continous skew plates. Earthquake Eng. Structural Dynamics, vol. 12, pp. 847-850, 1984.

98. 水澤富作、 梶田建夫: Spline帯板法を用いた斜板の曲げと自由振動解析. 土木学会論文報告集、第341, pp. 201-208, 1984.

99. Mizusawa, T.:Natural frequencies of rectangular plates with free edges. J. Sound and Vibration, vol. 105, pp. 451-459, 1986.

100. Mizusawa, T.:Comments on Natural frequencies of rectangular plates with free edges :Author replay. J. sound and Vibration, vol. 111, pp. 171-172, 1986.

101. Mizusawa, T. and Kajita, T.:Vibration and buckling of skew plates with edges elastically restrained in rotation. Computers and Structures, vol. 22, pp. 987-994, 1986.

102. Mizusawa, T. and Kajita, T.:Vibration and buckling of rectangular plates with nonuniform elastic constraints in rotation. Int. J. Solids and Structures, vol. 23, pp. 45-55, 1987.

103. Mizusawa, T. and Kajita, T.:Vibration of skew plates resting on point supports. J. Sound and Vibration, vol. 115, pp. 243-251, 1987.

104. Mizusawa, T.:Vibration of skew plates carrying a concentrated mass. J. Sound and Vibration, vol. 116, pp.561-572, 1987.

105.Mizusawa, T.:Application of spline strip method to analyse vibration of open cylindrical shells. Int. J. Num. Method Eng., vol. 26, pp. 663-676, 1988.

106.Mizusawa, T. and Leonard, J.D.:Vibration and buckling of plates with mixed boundary conditions. Eng. Struct., vol. 12(4), pp. 285-290, 1990.

107.Mizusawa, T.: Application of the spline element method to vibration of annular sector plates. J. Sound and Vibration, vol. 149(3), pp. 461-470, 1991.

108.Mizusawa, T.: Vibration of stepped annular sector plates using the spline element method. Compt. and Struct., vol. 41(2), pp. 377-383, 1991.

109.Mizusawa, T. : Vibration of stiffened annular sector plates by spline element method. Ing.-Archiv., vol 62, pp.62-71, 1992.

110.Mizusawa, T. and Takami, T.: Vibration of tapered thickness annular sector plates by spline element method. Journal of Sound and Vibration, vol. 154(1), pp. 147-160, 1992.

111.Mizusawa, T. and Kajita, T.: Vibration of annular sector plates using spline strip method. Comm. Applied Num. Meth., vol. 8, no. 8, pp. 537-546, 1992.

112.Mizusawa, T.: Vibration of rectangular Mindlin plates with tapered thickness by the spline strip method. Computers & Structers, Vol. 46(3), pp. 451-463, 1993.

113.水澤富作、高木信治: Spline Prism法を用いた長方形厚板の振動解析について 構造工学論文集, vol. 39A, pp. 1-12, 1993.

114.Mizusawa, T.: Buckling of rectangular Mindlin plates with variable thickness by the spline strip method. Int. J. Solids and Structures, Vol. 30, pp. 1663-1677, 1993.

115. Mizusawa, T.: Vibration of rectangular Mindlin plates by spline strip method. Journal of Sound and Vibration, Vol. 163, pp. 193-205, 1993.

116. Mizusawa, T.: Application of the spline element method to analyse bending of skew plates. Computers & Structers, Vol. 53, No. 2, pp. 439-448, 1994.

117. Mizusawa, T., Kito, H. and Kajita, T.: Vibration of annular sector Mindlin plates using the spline strip method. Computers & Structers, Vol. 53, No. 5, pp. 1205-1215, 1994.

118. 高木信治,水澤富作: Spline Prism法を用いた扇形厚板の三次元解析について 構造工学論文集, Vol. 40A, pp. 1-12, 1994.

119. 水澤富作、鬼頭博史: 高次せん断変形理論に基づくスプライン帯板法を用いた積層複合板の 振動解析について 構造工学論文集, Vol. 40A, pp. 71-83, 1994.

120. 水澤富作、高木信治: Spline Prism法を用いた長方形厚板の三次元曲げ解析について 土木学会論文集, 第489号/I-27, pp. 101-110, 1994.

121. Mizusawa, T. and Takagi, S.: Application of the spline prism method to analyse vibration of thick rectangular plates. Comm. Appl. Numer. Meth., Vol. 11, No. 1, pp. 1-11, 1995.

122. Mizusawa, T. and Kito, H.: Vibration of antisymmetric angle-ply laminated cylindrical panels by the spline strip method. Computers & Structers, Vol. 56(4), pp. 589-604, 1995.

123. Mizusawa, T. and Kito, H.: Vibration of cross-ply laminated cylindrical panels by the spline strip method. Computers & Structers, Vol. 57(2), pp. 253-265, 1995.

124. 水澤富作、加藤年宏: Spline Prism法を用いた厚肉円筒パネルの振動解析について, 構造工学論文集, Vol. 41A, pp. 65-71, 1995.

125. Mizusawa, T. and Kato, T.: Application of the spline prism method to analyze vibration of thick circular cylindrical panels. International Journal of Solids and Stuctures, Vol. 33, No.7, pp.967-976,1996.

126. Mizusawa, T. and Ushijima, H.: Vibration of annular sector Mindlin plates with intermediate arc supports by the spline strip method. Comput. Struct.( to be published, June 5, '95, accepted Jan. 18, '96)

127. Mizusawa, T.: Vibration of thick laminated cylindrical panels by the spline strip method. Comput. Struct.( to be published, June 6 ,'95, accepted Jan. 18, '96)

128. Narita, Y.: Vibration of a non-uniform cantilever beam partially immersed in an ideal liquid. J. Sound and Vibration, vol. 81, pp. 583-586, 1982.

129. Navaneethakrishnan, R.V.:Buckling of nonuniform plates - spline method. J. of Eng. Mech. Div., ASCE, vol. 114, pp. 893-898, 1988.

130. Ng, S.F. and Chen, X.: Analysis of arbitrary Mindlin plates or bridge decks by spline finite strip method. Comput. Struct., Vol. 54(1), pp. 111-118, 1995.

131. Patlashenko, I. and Weller, T.: Cubic B-spline collocation method for nonlinear static analysis of panels under mechanical and thermal loading. Comput. Struct., Vol. 49, pp. 89-96, 1993.

132. Patlashenko, I. and Weller, T.: Two-dimensional spline collocation method for nonlinear analysis of laminated panels. Comput. Struct., Vol. 57(1), pp. 131-139, 1995.

133. Raggett, G.F., Stone, J.A.R. and Wilson, P.D.:On the use of cubic splines to solve certain circular plate Problems. Computer Methods in Applied Mechanics and Engineering,vol. 4, pp.39-45, 1974.

134. Rogalevich, V.V.:Solution of a nonlinear problem of bending of a plate using cubic splines (in Russian). Stroitelnaya Mekhanika i Raschet Sooruzhenii, no. 5, pp. 29-34, 1977.

135. Rong, Q.:Spline finite-point method. Journal on Numerical Methods and Computer Applications(in Chinese), vol. 2, pp. 68-81,1981.136. Rong, Q.:The method of spline functions for structural mechanics(in Chinese). Guangxi   Peoples Publishing House, 1987.

137. Sheikh, A.H. : linear and nonlinear analysis of stiffened plates under static and dynamic loading by the spline finite strip method. Ph. D. thesis, Indian Institute of Technology, Kharagpur, 1992.

138. Sheikh, A.H. and Mukhopadhyay, M.: Analysis of stiffened plate with arbitrary planform by the general spline finite strip method. Comput. Struct., vol. 42(1), pp. 53-67, 1992.

139. Sheikh, A.H. and Mukhopadhyay, M.: Transverse vibration of plate structures with elastically restrained edges by the spline/finite strip method. J. of Vibration and Acoustics,ASME, Vol. 115, pp. 295-302, 1993.

140. Shen, P.C. and Wan, J.G.:Solution of governing differential equations of vibrating cylindrical shells using B-spline functions. Int. J. Numerical Method for Partial Differential Equations, vol. 2, pp. 173-185, 1986.

141. Shen, P.C. and Wan, J.G.:Vibration analysis of flat shells by using B-spline functions. Computers and Structures, vol. 25, pp. 1-10, 1987.

142. Shen, P.C. and Wan, J.G.:Static analysis of cylindrical shells by using B-spline functions Computers and Structures, vol. 25, pp. 809-816, 1987.

143. Shen, P.C., Huang, D. and Wang, Z.:Static, vibration and stability analysis of stiffened plates using B-spline functions. Comput. & Struct., vol. 27, pp. 73-78, 1987.

144. Shen, P.C. and Wan, J.G.:A semianalytical method for static analysis of shallow shells. Computers & Structures, Vol. 31, pp. 82-831, 1989. 145. Shen, P.C. and Dade, C.: Dynamic analysis of stiffened plates and shells using spline Gauss collocation method. Comput. and Struct., vol. 36(4), pp. 623-629(1990).

146. Shen P.C. and Kan H.B.: Multivariable spline element analysis for plate bending problems. Comput. Struct., vol. 40(6), pp. 1343-1349, 1991.

147. Shen, P.C., He, P.X. and Le, Y.: Vibration analysis of plates using the multivariable splaine element method. Int. J. Solids and Struct., vol. 29(24), pp. 3289-3295, 1992.

148. Shen Pengcheng and He Peixiang: Bending analysis of rectangular moderately thick plates using spline finite element method. Comput. Struct., Vol. 54, pp. 1023-1029, 1995.

149. Sheng-Nian, Q.:An application of spline interpolation to the finite element method.   Acta Mech. Solids Sin., 1981, No. 3, pp. 384-394.

150. Soni, S.R.:Vibrations of elastic plates and shells of variable thickness. Ph. D. Thesis, Univ. of Roorkee, India, 1972.

151. Soni, S.R. and Rao, K.S.:Vibrations of non-uniform rectangular plates: a spline technique method of solution. J. Sound and Vibration, 1974, vol. 35, pp. 35-45.

152. Soni, S.R.:Quintic splines in vibrations of nonuniform annular plates. Computers & Structures 1974, vol. 4, pp. 1269-1279.

153. Soni, S.R.:Vibration of beams mode of variable thickness layers. J. Sound and Vib., vol. 65, pp. 75-84, 1979.

154. Tawfik, M.S.: Analysis of pipelines under large soli deformations. Ph. D. Thesis, Cornell University, U.S.A., 1986.

155. Tham, L.G., Li, W.Y., Cheung, Y.K. and Chen, M.J.:Bending of skew plates by spline finite strip method. Computers and structures, 1986, vol. 22, pp. 31-38.

156. Tham, L.G. and Szeto, H.Y.: Buckling analysis of arbitrarily shaped plates by spline finite strip method. Comput. Struct., vol. 36(4), pp. 729-735(1990).

157. Tham, L.G.: Application of spline finite strip method in the analysis of space structures. Thin-Walled Structures, vol. 10, pp. 235-246, 1990.

158. Van Erp, G.M. and Menken, C.M.: The spline finite-strip method in the buckling analysis of thin-walled structures. Communications in Applied Numerical Methods, vol. 6, pp. 477-484, 1990.

159. Van Erp, G.M. and Menken, C.M.: Initial post-buckling analysis with the spline finite-strip method. Comput. Struct., vol. 40(5), pp. 1193-1201, 1991.

160. Van Erp, G.M.: Advanced buckling analyses of beams with arbitrary cross sections. Ph. D. thesis, Eindhoven University of Technology, The Netherlands, 1989.

161. Gang Wang and Cheng-Tzu Thomas Hsu: Static and dynamic analysis of arbitrary quadrilateral flexural plates by B3-spline functions. Int. J. Solids and Strcutures, Vol. 31(5), pp. 657-667, 1994.

162. Wang, S. and Dawe, D.J.: Vibration of shear-deformable rectangular plates using a spline-function Rayleigh-Ritz approach. Int. J. Num. Meth. Eng., Vol. 36, pp. 695-711, 1993. 

163. Wang, S. : The use of spline functions in the analysis of composite laminated plates. Ph. D. Thesis, The University of Birmingham, 1990.

164. Wu, C.Q., Cheung, Y.K. and Fan, S.C.:Spline Finite Strip Method in Structural Analysis(in Chinese). Guangdong Scientific and Technology Press, 1986.

165. Yang, H.Y. and Chong, K.P.: Finite strip method with X-spline functions. Computers and Structures, vol. 18, pp. 127-132, 1984.

166. Yuan, S.:Spline elements in stress analysis(in Chinese). Ph. D. Thesis, Department of Civil Engineering, Tsinghua Univ., 1984.

167. Yuan, S.:Spline rectangular thick/thin plate elements(in Chinese). Acta Mechanica Sinica, vol. 16, pp. 401-407, 1984.

168. Yuan, S.:Spline rectangular elements(in Chinese). Computational Structural Mechanics and Application, vol. 1, pp. 41-47, 1984.

169. Zhang, Y.C. and He, X.:Analysis of free vibration and buckling problems of beams and plates by discrete least-squares method using B5-spline as trial function. Comput. and Struct., vol. 31, pp. 115-119(1989).

170. Zhenghua, L.:The least square method of bending analysis of thin plates by quintic    B-spline. Journal of Changsha Railway Institute, No. 1, 1981.

171. Zhu, D.S. and Cheung, Y.K.: Postbuckling analysis of shells by spline finite strip method. Comput. Struct., vol. 31, pp. 357-364(1989).

172. Zhou, H.B. and Li, G.Y.: Free vibration analysis of sandwich plates with laminated faces using spline finite point method. Comput. Struct., Vol. 59, pp. 257-263, 1996.

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