Three-dimensional asymptotic finite element method for anisotropic inhomogeneous and laminated plates

Jiann Quo Tarn, Yi-Bin Wang, Yung-Ming Wang

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

An asymptotic finite element model for anisotropic inhomogeneous and laminated plates is developed within the framework of three-dimensional elasticity. The formulation begins with a Hellinger-Reissner functional in which the displacements and transverse stresses are taken to be the functions subject to variation. By means of asymptotic expansion the H-R functional for the problem is decomposed into functionals of various orders from which the asymptotic finite element equations are derived. In the multilevel computations the transverse stresses and displacements may be interpolated independently, and the midplane displacements are the only unknown nodal degree-of-freedoms (DOF) in the system equations, thus the total DOF at each level is less than that of a homogeneous Kirchhoff plate. The stiffness matrix remains unchanged ; the one generated at the leading-order level is always used at subsequent levels. The formulation is three-dimensional yet requires only two-dimensional finite element discretization with no need of interpolation in the thickness direction. The through-thickness effect can be accounted for in a consistent and hierarchical manner. Numerical comparisons with the benchmark solutions show that the method is effective in modeling of multilayered composite plates.

Original languageEnglish
Pages (from-to)1939-1960
Number of pages22
JournalInternational Journal of Solids and Structures
Volume33
Issue number13
DOIs
Publication statusPublished - 1996 Jan 1

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Laminated Plates
Asymptotic Methods
finite element method
Finite Element Method
Finite element method
Three-dimensional
Stiffness matrix
Transverse
degrees of freedom
Degree of freedom
Kirchhoff Plate
formulations
Elasticity
stiffness matrix
Interpolation
Composite Plates
Formulation
Numerical Comparisons
Finite Element Discretization
Stiffness Matrix

All Science Journal Classification (ASJC) codes

  • Modelling and Simulation
  • Materials Science(all)
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics

Cite this

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abstract = "An asymptotic finite element model for anisotropic inhomogeneous and laminated plates is developed within the framework of three-dimensional elasticity. The formulation begins with a Hellinger-Reissner functional in which the displacements and transverse stresses are taken to be the functions subject to variation. By means of asymptotic expansion the H-R functional for the problem is decomposed into functionals of various orders from which the asymptotic finite element equations are derived. In the multilevel computations the transverse stresses and displacements may be interpolated independently, and the midplane displacements are the only unknown nodal degree-of-freedoms (DOF) in the system equations, thus the total DOF at each level is less than that of a homogeneous Kirchhoff plate. The stiffness matrix remains unchanged ; the one generated at the leading-order level is always used at subsequent levels. The formulation is three-dimensional yet requires only two-dimensional finite element discretization with no need of interpolation in the thickness direction. The through-thickness effect can be accounted for in a consistent and hierarchical manner. Numerical comparisons with the benchmark solutions show that the method is effective in modeling of multilayered composite plates.",
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Three-dimensional asymptotic finite element method for anisotropic inhomogeneous and laminated plates. / Tarn, Jiann Quo; Wang, Yi-Bin; Wang, Yung-Ming.

In: International Journal of Solids and Structures, Vol. 33, No. 13, 01.01.1996, p. 1939-1960.

Research output: Contribution to journalArticle

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