### Abstract

The static deflection of a general elastically end restrained non-uniform beam resting on a non-linear elastic foundation subjected to axial and transverse forces, governed by a non-linear fourth order non-homogeneous ordinary differential equation with variable coefficients, is examined. By using the method of perturbation, the governing differential equation is transformed into a set of self-adjoint linear fourth order ordinary differential equations with variable coefficients. It is shown that the deflection of the beam can be expressed in terms of the fundamental solutions of these linear ordinary differential equations. Especially if the coefficients of the linear fourth order ordinary differential equations are in an arbitrarily polynomial form, then the exact solution for the static deflection of the beam can be obtained.

Original language | English |
---|---|

Pages (from-to) | 513-519 |

Number of pages | 7 |

Journal | Computers and Structures |

Volume | 51 |

Issue number | 5 |

DOIs | |

Publication status | Published - 1994 Jun 3 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Civil and Structural Engineering
- Modelling and Simulation
- Materials Science(all)
- Mechanical Engineering
- Computer Science Applications

### Cite this

*Computers and Structures*,

*51*(5), 513-519. https://doi.org/10.1016/0045-7949(94)90058-2

}

*Computers and Structures*, vol. 51, no. 5, pp. 513-519. https://doi.org/10.1016/0045-7949(94)90058-2

**Deflection of nonuniform beams resting on a nonlinear elastic foundation.** / Kuo, Y. H.; Lee, Sen-Yung.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Deflection of nonuniform beams resting on a nonlinear elastic foundation

AU - Kuo, Y. H.

AU - Lee, Sen-Yung

PY - 1994/6/3

Y1 - 1994/6/3

N2 - The static deflection of a general elastically end restrained non-uniform beam resting on a non-linear elastic foundation subjected to axial and transverse forces, governed by a non-linear fourth order non-homogeneous ordinary differential equation with variable coefficients, is examined. By using the method of perturbation, the governing differential equation is transformed into a set of self-adjoint linear fourth order ordinary differential equations with variable coefficients. It is shown that the deflection of the beam can be expressed in terms of the fundamental solutions of these linear ordinary differential equations. Especially if the coefficients of the linear fourth order ordinary differential equations are in an arbitrarily polynomial form, then the exact solution for the static deflection of the beam can be obtained.

AB - The static deflection of a general elastically end restrained non-uniform beam resting on a non-linear elastic foundation subjected to axial and transverse forces, governed by a non-linear fourth order non-homogeneous ordinary differential equation with variable coefficients, is examined. By using the method of perturbation, the governing differential equation is transformed into a set of self-adjoint linear fourth order ordinary differential equations with variable coefficients. It is shown that the deflection of the beam can be expressed in terms of the fundamental solutions of these linear ordinary differential equations. Especially if the coefficients of the linear fourth order ordinary differential equations are in an arbitrarily polynomial form, then the exact solution for the static deflection of the beam can be obtained.

UR - http://www.scopus.com/inward/record.url?scp=0028762834&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0028762834&partnerID=8YFLogxK

U2 - 10.1016/0045-7949(94)90058-2

DO - 10.1016/0045-7949(94)90058-2

M3 - Article

VL - 51

SP - 513

EP - 519

JO - Computers and Structures

JF - Computers and Structures

SN - 0045-7949

IS - 5

ER -