### Abstract

The emphasis of this paper is on the derivation of finite displacement fields in which warping displacement is fully examined. The resulting displacement fields are considered to be accurate in the sense that all the second-order terms with respect to displacements are taken into account. The principle of virtual work is used to derive equilibrium equations and associated boundary conditions. The validity of the governing equilibrium equations is verified by comparison with currently accepted equilibrium equations for typical cases. Numerical analysis is restricted primarily to procedures embodying the finite element method, where nonlinear problems can be formulated using Hellinger-Reissner's Principle with the help of mixed finite elements. Governing nonlinear equations are solved by Newton-Raphson's method. The validity of the formulation is illustrated through numerical solutions for nonlinear behavior of a curved and twisted thin-walled beam, and a comparison of these solutions with experimental results.

Original language | English |
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Title of host publication | Memoirs of the School of Science and Engineering, Waseda University |

Pages | 277-294 |

Number of pages | 18 |

Edition | 46 |

Publication status | Published - 1982 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Engineering(all)

### Cite this

*Memoirs of the School of Science and Engineering, Waseda University*(46 ed., pp. 277-294)

**FINITE DISPLACEMENT THEORY OF CURVED AND TWISTED THIN-WALLED BEAMS.** / Hirashima, Masaharu; Yoda, Teruhiko.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*Memoirs of the School of Science and Engineering, Waseda University.*46 edn, pp. 277-294.

}

TY - CHAP

T1 - FINITE DISPLACEMENT THEORY OF CURVED AND TWISTED THIN-WALLED BEAMS.

AU - Hirashima, Masaharu

AU - Yoda, Teruhiko

PY - 1982

Y1 - 1982

N2 - The emphasis of this paper is on the derivation of finite displacement fields in which warping displacement is fully examined. The resulting displacement fields are considered to be accurate in the sense that all the second-order terms with respect to displacements are taken into account. The principle of virtual work is used to derive equilibrium equations and associated boundary conditions. The validity of the governing equilibrium equations is verified by comparison with currently accepted equilibrium equations for typical cases. Numerical analysis is restricted primarily to procedures embodying the finite element method, where nonlinear problems can be formulated using Hellinger-Reissner's Principle with the help of mixed finite elements. Governing nonlinear equations are solved by Newton-Raphson's method. The validity of the formulation is illustrated through numerical solutions for nonlinear behavior of a curved and twisted thin-walled beam, and a comparison of these solutions with experimental results.

AB - The emphasis of this paper is on the derivation of finite displacement fields in which warping displacement is fully examined. The resulting displacement fields are considered to be accurate in the sense that all the second-order terms with respect to displacements are taken into account. The principle of virtual work is used to derive equilibrium equations and associated boundary conditions. The validity of the governing equilibrium equations is verified by comparison with currently accepted equilibrium equations for typical cases. Numerical analysis is restricted primarily to procedures embodying the finite element method, where nonlinear problems can be formulated using Hellinger-Reissner's Principle with the help of mixed finite elements. Governing nonlinear equations are solved by Newton-Raphson's method. The validity of the formulation is illustrated through numerical solutions for nonlinear behavior of a curved and twisted thin-walled beam, and a comparison of these solutions with experimental results.

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UR - http://www.scopus.com/inward/citedby.url?scp=0020340935&partnerID=8YFLogxK

M3 - Chapter

AN - SCOPUS:0020340935

SP - 277

EP - 294

BT - Memoirs of the School of Science and Engineering, Waseda University

ER -