Transcript Imperial College London

22ND ACME CONFERENCE ON COMPUTATIONAL MECHANICS - 2-4 APRIL - EXETER - UK
Co-rotational Formulation for Sandwich
Plates and Shells
Yating Liang, Bassam A. Izzuddin
COMPUTATIONAL STRUCTURAL MECHANISM GROUP (CSM)
DEPARTMENTAL OF CIVIL AND ENVIRONMENTAL ENGINEERING
IMPERIAL COLLEGE LONDON
Background
Sandwich structures in civil engineering:
Insulation walls
Roof panels
Curtain wall glazing
Outline of Presentation
Zigzag Displacement Fields
•Four orthogonal through-thickness displacement modes:
•Seven displacement parameters per node
• Five basic nodal freedoms
(u i ,vi ,w i ,θ xi ,θ yi )
• Two additional freedoms
(xi ,yi )
Transverse Shear Stress Through Thickness
•Modulus ratio R=
R=10
E face
E core
R=102
R=105
R=106
Bisector Co-rotational Framework
• Local x- and y- axes are set to
be the bisectors of the two
element diagonals in both the
initial undeformed and the
current deformed configuration.
• Basic freedoms (u i ,vi ,w i ,θ xi ,θ yi )
are defined in this co-rotational
system.
Izzuddin & Li (2004)
Shell Coordinate System
• Additional freedoms (xi ,yi ) are defined in local shell coordinate
system.
• Two considerations:
• Computational efficiency
• Consideration of composite materials
α
Shell Coordinate System
Additional freedoms (xi ,yi ) are defined in local shell coordinate
system.
n
Shell Coordinate System
Additional freedoms (xi ,yi ) are defined in local shell coordinate
system.
z
Consideration of Composite Materials
With the use of the shell coordinate system, the relative orientation
of the composite material fiber relative to the element coordinate
system is readily determined.
α
β
x-axis of element
coordinate system
α
Layer-wise Theory
Hellinger-Reissner
Variation Principle
Numerical Example 1
Sandwich plate under bi-directional sinusoidal transverse loading
Moderately
thick
plate (a/h=10)
Thin plate
(a/h=100)
results
Normalised
Normalised results
1.2
1
0.8
SS-AO3
0.6
FSDT
0.4
0.2
0
w
σx
σy
τxz
τyz
τxy
Numerical Example 2
Annular sandwich plate under uniform transverse shear at one end
20.0
30.0
SS-AO3 (0/90/0), A
SS-AO3
(0/0/0),AA
SS-AO3
(90/0/90),
SS-AO3
(-30/60/-30),
A
SS-AO3
(0/0/0), B
SS-AO3
(45/-45/45),
A
SOLSH190
(0/90/0),
A A
FSDT-AO3
(0/0/0),
SOLSH190 (90/0/90), A
FSDT-AO3
(0/0/0), B
SOLSH190
(-30/60/-30),
A
SOLSH190 (45/-45/45), A
α
Transverse shear loading q
18.0
25.0
16.0
14.0
20.0
12.0
SOLSH190 (0/0/0), A
SOLSH190 (0/0/0), B
15.0
10.0
8.0
10.0
6.0
4.0
5.0
2.0
0.0
0.0
0.0
0.0
3.0
3.0
6.0
Displacement
9.0
Numerical Example 3
Cylindrical sandwich shell under point load
30
Force P (103)
25
20
15
10
SS-AO3 (4x4)
FSDT-AO3 (4x4)
5
BK20 (32x32x6)
0
0.0
0.3
0.6
0.9
Displacement
1.2
Summary
Thank you!
Questions?