Application of the R-Function Theory and Least Square Method for Torsion Problem with H-Shaped Cross-Section

Abstract:

The R-function theory and least square method are employed to solve the torsion problem of the bar with H-shaped cross-section. When the least square method is used to solve the elastic torsion problem alone, the stress function can be set to meet the boundary condition, only with the simple cross-section such as the rectangle and ellipse. For the H-shaped cross-section, it is hard to find a stress function to meet the boundary condition. The R-function theory can solve the problem, and it can be used to describe H-shaped cross-section by implicit function form. Introducing the R-function theory can be easy to construct the stress function that satisfied the boundary of H-shaped cross-section. A numerical example demonstrates the feasibility and efficiency of the present method.

• Periodical: Applied Mechanics and Materials (Volumes 217-219)
• Pages: 2313-2316
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.217-219.2313
• Online since: November 2012
• Authors: Ping Ping Li, Hong Yuan, Shan Qing Li
• Keywords: Bar with H-Shaped Cross-Section, Least-Square Method (LSM), R-Function Theory, Torsion Problem

References

[1] W.C. Chien: The Theory of Elastic Cylinder to Reverse (Science Press, Beijing 1956) (In Chinese).

[2] W.C. Chien, K.Y. Ye: Elasticity Mechanics (Science Press, Beijing 1960) (In Chinese).

[3] Z.L. Xu: Elasticity Mechanics (Higher Education Press, Beijing 1979) (In Chinese).

[4] C.D. Xu: Solid Mechanics Weighted Residual Method (Mechanics in Engineering), Vol.4(1960) (In Chinese).

[5] Y.X. Xia: The vt least squares (Theory and applied mechanics),Vol.2,1991 (In Chinese).

[6] Timoshenko, Goodier, Z.L. Xu, Y.Z.Wu: Theory of Elastic (People's Education Press, Beijing1964) (In Chinese).

[7] H. Yuan, S.Q. Li and R.H. Liu: Applied Mathematics and Mechanics (English Edtion), Vol.28 (2007), p.847

[8] S.Q. Li and H. Yuan: Applied Mathematics and Mechanics (English Edtion), Vol.32 (2011), p.276

[9] S.Q. Li and H. Yuan: Applied Mathematics and Mechanics (English Edtion), Vol.31 (2010), p.635

[10] S.Q. Li and H. Yuan: Acta Mechanica Solida Sinica, Vol.23 (2010), p.370

[11] S.Q. Li, H. Yuan and X.W. Xue: Chinese Journal of Computational Mechanics, Vol.28 (2011), p.270 (In Chinese)

[12] S.Q. Li and H. Yuan: Acta Mechanica Solida Sinica, Vol.25 (2012), p.37

[13] S.Q. Li and H. Yuan: Applied Mechanics and Materials, Vol.117-119 (2012), p.456

[14] S.Q. Li and H. Yuan: Applied Mechanics and Materials, Vol.138-139 (2012), p.705

[15] S.Q. Li and H. Yuan: Advanced Materials Research, Vol.446-449 (2012), p.3582

[16] S.Q. Li and H. Yuan: Advanced Materials Research, Vol.468-471 (2012), p.8

[17] V.L. Rvachev: Theory of R-function and Some of its Application (Nauk Dumka Press, Ukraine 1982) (In Russian).