AA SM 113Composites SandwichPanelsUnderPressure

Standard Stress Methods Doc: AA-SM-113

Revision: A

Pressure Loaded Flat Isotropic Panels Page: 1

D.1.0.0 FLAT SANDWICH PLATES UNDER UNIFORMLY DISTRIBUTED NORMAL LOADS(SMALL DEFLECTIONS)

Reference:

Applicability:

Fig. 1

Fig. 2

K1 For Determining Maximum Deflection d

K2 For Determining Facing Stress F

Method of analysis is per NASA Structures Manual TM X-73305, Chapter B9.6 Structural Sandwich Plates, Subchapter B9.6.1.1 Basic Principles for Design of Flat Sandwich Panels under Uniformly Distributed Normal Load.

Flat sandwich panels with isotropic facings and orthotropic cores. Small deflection theory, ratio of deflection to sandwich thickness d/h must be less or equal to 0.5. Equal facings. The following procedures are resticted to linear elastic behaviour.

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20

0.04

0.05

0.06

0.07

0.08

0.09

0.10

0.11

0.12

0.13

0.14

f(x) = − 0.3125 x⁵ + 0.9181964 x⁴ − 0.809914 x³ + 0.1299206 x² − 0.0026942 x + 0.1249205

b/a

K2

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20

0.000

0.005

0.010

0.015

0.020

0.025

0.030

f(x) = − 0.0637255 x⁶ + 0.130279 x⁵ − 0.045494 x⁴ − 0.0387263 x³ + 0.00859912 x² − 0.000235843 x + 0.0129976

b/a

K1 v1.0

0.40.20.0

Prepared by: G. Krolikowski Date: March 2006 Checked by:___________________Date:__________


Revision: A


D.1.0.0 FLAT SANDWICH PLATES UNDER UNIFORMLY DISTRIBUTED NORMAL LOADS(SMALL DEFLECTIONS) (continued)

Fig. 3

Equations used in calculations:

The Average Facing Stress Equation 1(Stress at Facing Centroid)

Relative Stiffness of Core Equation 2to Facings

Equation 3

The Maximum Core Equation 4Shear Stress

Deflection of the Centre Equation 5

K3 For Determining Core Shear Stress FSC

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20

0.20

0.25

0.30

0.35

0.40

0.45

0.50

f(x) = − 0.261438 x⁶ + 1.040724 x⁵ − 1.534439 x⁴ + 0.934766 x³ − 0.233367 x² + 0.018967 x + 0.364929

b/a

K3

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20

0.20

0.25

0.30

0.35

0.40

0.45

0.50f(x) = 1.39706 x⁶ − 5.10464 x⁵ + 7.08588 x⁴ − 4.45212 x³ + 0.968724 x² − 0.0631051 x + 0.50008

b/a

K3

F=K2pb2

ht

V=π2Db2U

=π2 t c Et

2 λb2G c

λ=1−μ2

FCS=K3 pbh

δ=2K1K2

λFEb2

h

of the Panel



Revision: A


D.1.0.0 FLAT SANDWICH PLATES UNDER UNIFORMLY DISTRIBUTED NORMAL LOADS(SMALL DEFLECTIONS) (continued)

0.0468 MPa Normal Pressure on the Panel6.79 psi Normal Pressure on the Panel1.18 mm Facing Thickness

4.00 mm Core Thickness5.18 mm Distance Between Facing Centroids

32155 MPa Young's Modulus of Facingsm = 0.44 Poisson's Ratio

311 MPa Facing Tension Strength (Warp & Weft)

193 MPa Facing Compression Strength (Warp & Weft)

19 MPa Shear Modulus of the Core

0.75 MPa Shear Strength of the Core430 mm Long Edge200 mm Short Edge

0.47 #ADDIN?

#ADDIN? From Fig. B9-30

0.106 From Fig. B9-29

0.366 From Fig. B9-31, For Shear Along Edge b

0.467 From Fig. B9-31, For Shear Along Edge a

l = 0.80640 #ADDIN?1.22 #ADDIN?

Deflection of the Panel Centre, From Equation 5#ADDIN? mm #ADDIN?

The Average Facing Stress, From Equation 132.6 MPa #ADDIN?

Max. Core Shear Along Edge b, From Equation 4

0.66 MPa #ADDIN?Max. Core Shear Along Edge a, From Equation 4

0.84 MPa #ADDIN?Margin of Safety for Tension in Facing

#ADDIN? = 854%Margin of Safety for Compression in Facing

#ADDIN? = 492%Margin of Safety for Shear in the Core

#ADDIN? = -11%

p =p =t =

tC =h =

Et =

FTU =

FCU =

GC =

FSU =a =b =

K1 =

K2 =

K3 =

K3 =

v =

d =

F =

FCSa =

FCSb =

MSTENS

MSCOMPR

MSSHEAR

= b / a

= 1 - m2

= p2tCEtt / (2lb2GC)

= 2(K1 / K2)lFb2 / (Eth)

= K2pb2 / (ht)

= K3pb / h

= K3pb / h

= FTU / F - 1

= FCU / F - 1

= FSU / max(FCSa , FCSb) - 1

δ=2K1K2

λFEb2

h

Check for Wrinkling in Facings



Revision: A


D.2.0.0 MEMBRANE AND BENDING STRESSES IN FLAT SANDWICH PLATES(LARGE DEFLECTIONS)

Reference: Bruhn, Para. A17.7, Large Deflections TheoryThis is the method from reference above modified for use with sandwich plates.It is assumed that the ratio of bending stresses to membrane stresses in sandwichpanels follows the same relations as for isotropic plates. The method modifiesthe stiffeness of the material, such that it takes into account the effect of foamcore (much smaller stiffness than the facings material).

0.0862 MPa Normal Pressure on the Panel12.50 psi Normal Pressure on the Panel

914 mm Long Edge914 mm Short Edge

8.00 mm Core Thickness

1.00 mm Facing Thickness9.00 mm

10.00 mm Plate Thickness

48500 MPa Young's Modulus of Facings

#ADDIN? mm Maximum Deflection

#ADDIN? MPa Total Stress in the Plate

#ADDIN? MPa Membrane Stress

#ADDIN? MPa Bending Stress

Check for Wrinkling in Facings

p =p =a =b =

tC =

tF =h =t =

E' =

w =

s =

sM =

sB =



Revision: A


D.3.0.0 DEFLECTIONS IN FLAT SANDWICH PLATES (LARGE DEFLECTION THEORY)

Reference: NASA Structures Manual TM X-73305, Chapter B9.6.2

Applicability: Fixed edge conditions.

0.0862 MPa Normal Pressure12.50 psi Normal Pressure

914 mm Long Edge914 mm Short Edge

1.00 mm Facing Thickness

48500 MPa Facing Young's Modulus

0.443 Facing Poisson's Ratio

8.00 mm Core Thickness

25.0 MPa Core Shear Modulus

0.300 Core Poisson's Ratio

1.00 #ADDIN?28.94 #ADDIN?

p =p =

a =b =

tF =

EF =

nF =

tC =

GC =

nC =

l =Q =

= b / a

= 12(b / 2)3(1 - nC2)p / (tFtC2EF)

1.4 From Fig. B9-34 (manual input)

11.20 mm Centre Deflection of Plate


wO / tC =

wO =

= 12(b / 2)3(1 - nC2)p / (tFtC2EF)

Wrinkling#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?

KEY2#NAME?#NAME?

#NAME? psi = 1#NAME? psi = 2#NAME? psi = 3#NAME? psi = 4#NAME? psi = 6#NAME? psi = 8#NAME? psi = 12#NAME? psi = 20#NAME? psi = 40#NAME? psi = 80

Err:520#NAME?#NAME?#NAME?

KEY3

#NAME?#NAME?

#NAME? psi = 1#NAME? psi = 2#NAME? psi = 3#NAME? psi = 4#NAME? psi = 6#NAME? psi = 8#NAME? psi = 12#NAME? psi = 20#NAME? psi = 40#NAME? psi = 80

Err:520#NAME?#NAME?#NAME?

mem11#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?

#NAME?#NAME?#NAME?#NAME?#NAME?





Kone#NAME?#NAME?

#NAME?#NAME?#NAME?

#NAME?#NAME?#NAME?

Torsion#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?

CorrectBend#NAME? bend<100

#NAME? bend>100

#NAME?

CorrectCompr#NAME? compr<100

#NAME? compr>100

#NAME?

psi = 12psi = 20psi = 40psi = 80

psi = 12psi = 20psi = 40psi = 80

bend<100 y = -6.21693E-11x5 + 1.86508E-08x4 - 2.19709E-06x3 + 1.33155E-04x2 - 5.51717E-03x + 9.23873E-01

bend>100 y = -1.66584E-15x5 + 5.07564E-12x4 - 6.04927E-09x3 + 3.68289E-06x2 - 1.41239E-03x + 8.59968E-01

compr<100 y = 2.10813E-11x5 - 2.93899E-09x4 - 2.72817E-07x3 + 6.94494E-05x2 - 5.55496E-03x + 9.18905E-01

compr>100 y = -3.27381E-16x5 + 1.50298E-12x4 - 2.67560E-09x3 + 2.43095E-06x2 - 1.35352E-03x + 8.15571E-01

y = -6.21693E-11x5 + 1.86508E-08x4 - 2.19709E-06x3 + 1.33155E-04x2 - 5.51717E-03x + 9.23873E-01

y = -1.66584E-15x5 + 5.07564E-12x4 - 6.04927E-09x3 + 3.68289E-06x2 - 1.41239E-03x + 8.59968E-01

y = 2.10813E-11x5 - 2.93899E-09x4 - 2.72817E-07x3 + 6.94494E-05x2 - 5.55496E-03x + 9.18905E-01

y = -3.27381E-16x5 + 1.50298E-12x4 - 2.67560E-09x3 + 2.43095E-06x2 - 1.35352E-03x + 8.15571E-01

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AA SM 113Composites SandwichPanelsUnderPressure