92038-有限元法-FEM1413-2

or
Plate/shell structure is thin in one direction.
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Finite Element Analysis for Plates and Shells
Classification of Plates/Shells For common engineering judgment, if h/b denotes the ratio of the
displacement parameters to formulate the plate element. 18
Finite Element Analysis for Plates and Shells
6.2.1 Thin Plate Theory Consider a thin plate with the Cartesian coordinates x, y and z,
points in midsurface (z = 0) are zero, and the transverse deflection
w at any point inside the plate can be expressed by the deflection
of midsurface as its irrelevancy to z coordinate.
shell structure.
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Finite Element Analysis for Plates and Shells
Boeing 717 – 200 Fuselage
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FiniBteoEeleimnegnt AAniarlcysrisaffotr Plates and Shells
Boeing 717 – 200 Fuselage
thickness, h, to the minimum one of other two dimensions, b
(such as width), of a plate/shell, we recognize that
1/80 ≤ h/b ≤ 1/10 for “thin” plate/shell;
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Finite Element Analysis for Plates and Shells FEM Modeling for Wing and Fuselage
Wing Structure
Fuselage
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Finite Element Analysis for Plates and Shells
u z w , v z w , w w(x, y)
x
y
(6.1)
Midsurface
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Finite Element Analysis for Plates and Shells
u z w , v z w , w w(x, y)
x
y
It is shown that the displacement components u and v at the
a lateral displacement w (inplane displacements u Fra biblioteknd v are
also experienced because of the rotation of the plate
element). In this case the plate is said to be under the action
yz and zx
Finite Element Analysis for Plates and Shells
• In the Kirchhoff theory，the effect of transverse shear deformations are neglected and the straight line normal to the midsurface remains perpendicular to the midsurface
during deformations.
• In the Mindlin- Reissner theory, the effect of transverse
shear deformations are included and therefore the line
originally normal to the midsurface does in general not
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Finite Element Analysis for Plates and Shells
Midsurface
⑴The stress through the thickness (i.e., perpendicular to the midsurface) of plate/shell is zero.
For the thin plate problem with small deflection, any deformation of a plate is fully determined by the transverse
deflection w of its midsurface. Therefore we can use the transverse deflection w and its partial derivatives as nodal
remain perpendicular to the midsurface during the
deformations.
Transverse Shear Strains : yz and z1x7
Finite Element Analysis for Plates and Shells
6.2 Thin Plate Elements u z w x
of ‘bending’ forces.
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Finite Element Analysis for Plates and Shells
The most important characteristics of plates/shells is their capability of carrying the transverse or normal loading and withstanding bending deformations in contrast to the 2D and 3D cases.
Finite Element Analysis for Plates and Shells
•6.1 Introduction
Plates and shells are important structural components in engineering. They are usually considered as the main ingredients of so called “thin walled structures” which are in fact the typical load carrying bodies in aerospace, ship and some civil engineering, etc.
where the coordinate plane x - y coincides with the midsurface of
the plate. According to the Kirchhoff assumptions, the plate
displacements can be expressed as
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Finite Element Analysis for Plates and Shells
If a structure is of plate or shell type then we expect to make reasonable assumptions for the variation of displacement or strain through the thickness, and so eliminate independent variable(s) and lead to a dimension reduction.
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Finite Element Analysis for Plates and Shells
Action of ‘Bending’ Forces
If the plate is subjected to transverse loads (and/or bending
moments), any point inside the plate experiences essentially
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Finite Element Analysis for Plates and Shells
The upper interstages
Carbon-epoxy lattice fuselage section
8
Finite Element Analysis for Plates and Shells What is the definition of plates and shells?
1/10 ≤ h/b ≤ 1/5 for “thick” plate/shell.
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Finite Element Analysis for Plates and Shells
Action of ‘Membrane’ Forces
If a plate is subjected to inplane loads only, it will undergo deformation in its plane. In this case the plate is said to be under the action of ‘membrane’ forces.
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Finite Element Analysis for Plates and Shells
Fig.6.1 Plate and shell structures
z 0
Assumption (1):
The stress normal to the midsurface is equal to zero. 16
The dimension of plates and shells in the z – direction （the thickness direction）is much smaller than that in other two directions compared with 3D solids.
Although traditional thin walled structures were formed by the isotropic metal - based materials, the composite materials used for thin wall structures draw much more attention nowadays simply because of their ultralight characteristic and superb mechanical performance.
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Finite Element Analysis for Plates and Shells
An aircraft wing can be idealized as a plate structure 2
Finite Element Analysis for Plates and Shells
The fuselage of an aircraft can be considered to be a typical
⑵ Material particles that are originally on a straight line perpendicular to the midurface of plate/shell remain on a straight line during deformations.