##
**Analytical solution to a mixed boundary value elastic problem of a roller-guided panel of laminated composite.**
*(English)*
Zbl 1271.74077

Summary: This study presents an analytical solution to elastic field in a roller-guided panel of symmetric cross-ply laminated composite material. The mixed boundary value two-dimensional plane stress elasticity problem is formulated in terms of a single displacement potential function. This reduces the problem to the solution of a single fourth order partial differential equation of equilibrium as the other equilibrium equation is satisfied automatically. The solution is obtained in terms of an infinite Fourier series. To present some numerical results, a panel of glass/epoxy laminated composite is considered and different components of stress and displacement at different sections of the panel are presented graphically. To justify the present analytical solution, it is compared with the finite element solution obtained by using the commercial software ANSYS. It is found that the two solutions agree well with each other. This ensures that the formulation developed in this study, based on the displacement potential approach, can be used to obtain analytical solution of an elastic field in structural elements of laminated composite under any mode of boundary conditions prescribed in terms of either stress, displacement or any combination of these.

### MSC:

74G05 | Explicit solutions of equilibrium problems in solid mechanics |

74E30 | Composite and mixture properties |

### Keywords:

analytical solution; symmetric laminated composite; elasticity; panel; mixed boundary condition; displacement potential### Software:

ANSYS
PDF
BibTeX
XML
Cite

\textit{A. M. Afsar} et al., Arch. Appl. Mech. 80, No. 4, 401--412 (2010; Zbl 1271.74077)

Full Text:
DOI

### References:

[1] | Timoshenko S., Goodier V.N.: Theory of Elasticity. McGraw-Hill, New York (1979) · Zbl 0045.26402 |

[2] | Uddin, M.W.: Finite difference solution of two-dimensional elastic problems with mixed boundary conditions. M.Sc. Thesis, Carleton University, Canada (1966) |

[3] | Chow, L., Conway, H.D., Winter, G.: Stresses in deep bars. In: Trans ASCE, pp. 2557 (1952) |

[4] | Chapel R.E., Smith H.W.: Finite-difference solutions for plane stresses. AIAA J. 6, 1156–1157 (1968) |

[5] | Conway H.D., Ithaca N.Y.: Some problems of orthotropic plane stress. J. App. Mech. Trans. ASME 52, 72–76 (1953) · Zbl 0050.18603 |

[6] | Durelli A.J., Ranganayakamma B.: Parametric solution of stresses in bars. J. Eng. Mech. 115, 401–415 (1989) |

[7] | Ahmed S.R., Idris A.B.M., Uddin M.W.: An alternative method for numerical solution of mixed boundary-value elastic problems. J. Wave-Mater. Interact. 14(1–2), 12–25 (1999) |

[8] | Nath, S.K.D.: Displacement potential approach to solution of elasticity problems of orthotropic composite structures. Ph.D. Dissertation, Bangladesh University of Engineering and Technology, Bangladesh (2007) |

[9] | Nath S.K.D., Afsar A.M., Ahmed S.R.: Displacement potential approach to solution of stiffened orthotropic composite panels under uniaxial tensile load. J. Aero. Eng. I MechE. Part G 221, 869–881 (2007) |

[10] | Nath S.K.D., Afsar A.M., Ahmed S.R.: Displacement potential solution of a deep stiffened cantilever beam of orthotropic composite material. J. Strain Anal. IMechE 42(7), 529–541 (2007) |

[11] | Nath S.K.D., Afsar A.M.: Analysis of the effect of fiber orientation on the elastic field in a stiffened orthotropic panel under uniform tension using displacement potential approach. Mech. Adv. Mater. Struct. 16, 300–307 (2009) |

[12] | Afsar A.M., Nath S.K.D., Ahmed S.R., Song J.L.: Displacement potential based finite difference solution to elastic field in a cantilever beam of orthotropic composite. Mech. Adv. Mater. Struct. 15(5), 386–399 (2008) |

[13] | Jones R.M.: Mechanics of Composite Materials, 1st edn. Scripta Book Company, Washington (1975) |

[14] | Kao A.K.: Mechanics of Composite Materials. Taylor and Francis, New York (2006) |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.