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Three-dimensional asymptotic finite element method for anisotropic inhomogeneous and laminated plates
- Source :
- International Journal of Solids and Structures. 33:1939-1960
- Publication Year :
- 1996
- Publisher :
- Elsevier BV, 1996.
-
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.
- Subjects :
- Discretization
Applied Mathematics
Mechanical Engineering
Numerical analysis
Mathematical analysis
Geometry
Mixed finite element method
Elasticity (physics)
Condensed Matter Physics
Finite element method
Mechanics of Materials
Modeling and Simulation
General Materials Science
Calculus of variations
Asymptotic expansion
Mathematics
Stiffness matrix
Subjects
Details
- ISSN :
- 00207683
- Volume :
- 33
- Database :
- OpenAIRE
- Journal :
- International Journal of Solids and Structures
- Accession number :
- edsair.doi...........2b87c3702b7010d67b75b8308271759d