Fu Bao-lian. On Equivalents of the Reciprocal Theorem to Superposition Principles[J]. Applied Mathematics and Mechanics, 1985, 6(9): 813-818.
Citation:
Fu Bao-lian. On Equivalents of the Reciprocal Theorem to Superposition Principles[J]. Applied Mathematics and Mechanics, 1985, 6(9): 813-818.
Fu Bao-lian. On Equivalents of the Reciprocal Theorem to Superposition Principles[J]. Applied Mathematics and Mechanics, 1985, 6(9): 813-818.
Citation:
Fu Bao-lian. On Equivalents of the Reciprocal Theorem to Superposition Principles[J]. Applied Mathematics and Mechanics, 1985, 6(9): 813-818.
On Equivalents of the Reciprocal Theorem to Superposition Principles
Received Date: 1982-08-21Publish Date:
1985-09-15
Abstract
In this paper in the terms of theory we have proved that the reciprocal theorem is equivalent to the superposition principle of displacements and is equivalent to the superposition principle of reactive forces. These equivalents have important theoretical values and practical values. At the same time we also point out that Castigliano's displacement equation can be applied to solve the interior displacement of the region of the deformable body too.
References
[1]
钱伟长、叶开沅,弹性力学,科学出版社,(1980).
[2]
龙驭球、包世华,结构力学(上册),人民教育出版社.
[3]
付宝连,求解位移方程的能量原理,应用数学和力学,2. 6(1981).
[4]
付宝连,应用功的互等定理求解具有复杂边界条件的矩形板的挠曲面方程,应用数学和力学,3,3(1982).
Relative Articles
[1] FU Baolian. On Discussion of Discussion on the Modified Reciprocal Theorem of Works [J]. Applied Mathematics and Mechanics, 2024, 45(12): 1589-1592.
[2] XU Xiao-ming, YANG Di-xiong. Discussion on the Modified Reciprocal Theorem of Works [J]. Applied Mathematics and Mechanics, 2016, 37(9): 993-998. doi: 10.21656/1000-0887.370021
[3] FU Bao-lian. Corrected Reciprocal Theorem for 3D Linear Elasticity and Its Application [J]. Applied Mathematics and Mechanics, 2015, 36(5): 523-538. doi: 10.3879/j.issn.1000-0887.2015.05.008
[4] FU Bao-lian. The Reciprocal Theorem for the Finite Displacement Theory and Its Applications [J]. Applied Mathematics and Mechanics, 2015, 36(10): 1019-1034. doi: 10.3879/j.issn.1000-0887.2015.10.002
[5] FU Bao-lian. Corrected Reciprocal Theorem of Works for Bending Thin Plates and Its Application [J]. Applied Mathematics and Mechanics, 2014, 35(11): 1197-1209. doi: 10.3879/j.issn.1000-0887.2014.11.003
[6] ZHAO Bao-sheng, WANG Min-zhong. Equivalence of the Refined Theory and the Decomposed Theorem of an Elastic Plate [J]. Applied Mathematics and Mechanics, 2005, 26(4): 447-455.
[7] ZHANG Guo-qing, YU Jian-xing. Study of the Equivalent Theorem of Generalized Variational Principles in Elasticity [J]. Applied Mathematics and Mechanics, 2004, 25(3): 313-322.
[8] He Jihuan. Further Study of the Equivalent Theorem of Hellinger- Reissner and Hu-Washizu Variational Principles [J]. Applied Mathematics and Mechanics, 1999, 20(5): 515-524.
[9] Li Huijian, Fu Baolian, Tan Wenfeng. Reciprocal Theorem Method for the Forced Vibration of Elastic Thick Rectangular Plates [J]. Applied Mathematics and Mechanics, 1998, 19(2): 175-188.
[10] Fu Bao-lian, Tan Wen-feng. Reciprocal Theorem Method for Solving the Problems of Bending of Thick Rectangular Plates [J]. Applied Mathematics and Mechanics, 1995, 16(4): 367-379.
[11] Li Nong. A Method Using the Reciprocal Theorem to Solve the Bending of Thin Elastic Semicircular Plates [J]. Applied Mathematics and Mechanics, 1992, 13(12): 1081-1085.
[12] Fu Bao-lian, Li Nong. The Method of the Reciprocal Theorem of Forced Vibration for the Elastic Thin Rectangular Plates(Ⅲ)—Cantilever Rectangular Plates [J]. Applied Mathematics and Mechanics, 1991, 12(7): 621-638.
[13] Fu Bao-lian, Li Nong. The Method of the Reciprocal Theorem of Force Vibration for the Elastic Thin Rectangular Plates (Ⅱ)——Rectangular Plates with Two Adjacent Clamped Edges [J]. Applied Mathematics and Mechanics, 1990, 11(11): 977-988.
[14] Fu Bao-lian. Application of the Method of the Reciprocal Theorem to Finding Displacement Solutions of Cubes [J]. Applied Mathematics and Mechanics, 1989, 10(4): 297-308.
[15] Fu Bao-lian, Li Nong. The Method of the Reciprocal Theorem of Forced Vibration for the Elastic Thin Rectangular Plates(Ⅰ)——Rectangular Plates with Four Clamped Edges and with Three Clamped Edges [J]. Applied Mathematics and Mechanics, 1989, 10(8): 693-714.
[16] Fu Bao-lian. On the Method of Reciprocal Theorem to Find Solutions of the Plane Problems of Elasticity [J]. Applied Mathematics and Mechanics, 1989, 10(5): 437-446.
[17] Fu Bao-lian. The Reciprocal Theorem and Linear Elastic Variational Principles [J]. Applied Mathematics and Mechanics, 1989, 10(3): 253-258.
[18] Li Nong, Fu Bao-lian. Application of Reciprocal Theorem for Caculating the Transverse Displacement Equations of the Thin Elastic Circular Plates [J]. Applied Mathematics and Mechanics, 1988, 9(9): 835-842.
[19] Fu Bao-lian. Application of the Reciprocal Theorem for Calculating the Natural Frequencies of Rectangular Elastic Thin Plates [J]. Applied Mathematics and Mechanics, 1985, 6(11): 985-997.
[20] Fu Bao-lian. Applications of the Reciprocal Theorem to Solving the Equations of the Deflection Surface of the Rectangular Plates with Various Edge Conditions [J]. Applied Mathematics and Mechanics, 1982, 3(3): 315-325.
Proportional views
DownLoad: