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Asymptotic finite strip analysis of doubly curved laminated shells
- Source :
- Computational Mechanics. 27:107-118
- Publication Year :
- 2001
- Publisher :
- Springer Science and Business Media LLC, 2001.
-
Abstract
- On the basis of the Hellinger–Reissner (H–R) principle, an asymptotic finite strip method (FSM) for the analysis of doubly curved laminated shells is presented by means of perturbation. In the formulation the displacements and transverse stresses are taken as the functions subject to variation. Imposition of the stationary condition of the H–R functional, the weak formulation associated with the Euler–Lagrange equations of three-dimensional (3D) elasticity is obtained. Upon introducing a set of appropriate dimensionless scaling and bringing the transverse shear deformations to the stage at the leading-order level, the weak formulation is asymptotically expanded as a series of weak-form equations for various orders. An asymptotic FSM according to the present formulation is then developed where the field variables are interpolated as a finite series of products of trigonometric functions and crosswise polynomial functions independently. Through successive integration, the present formulation turns out that three mid-surface displacement degrees-of-freedom (DOF) and two rotation DOF for each node in a strip element are taken as the independent unknowns in the system equations for various orders. The solution procedure for the leading-order level can be repeatedly applied level-by-level in a consistent and hierarchic way. Application of the asymptotic FSM to a benchmark problem is demonstrated.
- Subjects :
- Applied Mathematics
Mechanical Engineering
Finite strip method
Weak solution
Numerical analysis
Mathematical analysis
Computational Mechanics
Ocean Engineering
Weak formulation
Euler–Lagrange equation
Computational Mathematics
Transverse plane
Computational Theory and Mathematics
Trigonometric functions
Scaling
Mathematics
Subjects
Details
- ISSN :
- 14320924 and 01787675
- Volume :
- 27
- Database :
- OpenAIRE
- Journal :
- Computational Mechanics
- Accession number :
- edsair.doi...........ecf1d3df8cc3d4aa7c44013def9c49d2