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This problem demonstrates the ability to model pressure loading of a square composite three layer sandwich flat shell. Stresses and displacements are calculated and compared to a reference solution. Stresses and displacements are calculated at the surface of the composite three layer sandwich flat shell in MD Nastran. This test is recommended by the National Agency for Finite Element Methods and Standards (NAFEMS): Test R0031/3 from NAFEMS publication R0031, “Composites Benchmarks”, February 1995.
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Chapter 8: Three-layer Sandwich Shell under Normal Pressure Loading
8Three-layer Sandwich Shell under Normal Pressure Loading
Summary 121
Introduction 122
Requested Solutions 122
FEM Solution 122
Modeling Tips 124
Input File(s) 125
Video 125
121CHAPTER 8
Three-layer Sandwich Shell under Normal Pressure Loading
SummaryTitle Chapter 8: Three-layer Sandwich Shell under Normal Pressure Loading
Geometry • 2-D Shell (units: in)Length= 10Width = 10Thickness = 0.806
Material properties • Face sheets
• Core
Analysis type Quasi-static analysis
Boundary conditions Plate is simply supported fixed at four corners
Applied loads Pressure of applied to the top face (most positive in the z-axis)
Element type 2-D shell, 3-D solid shell
FE results Stresses and displacements compared with NAFEMS solution
uniform normalpressure
C
E
A
10
10
y
x
simply supported on all four edges
0.028
0.750
0.028
z
face sheet
face sheet
x
all dimensions in inches
core
E
A
E1 10 106Psi= 12 0.3= G12 1.875 10
6 Psi=
E2 4 106Psi= 13 0= G13 1.875 10
6 Psi=
E3 1 106Psi= 23 0= G23 1.875 10
6 Psi=
The values within the parenthesis are chosen to have a complete 3-D material model necessary for the solid elements.
E1 10Psi= 12 0= G12 10Psi=
E2 10Psi= 13 0= G13 3 104 Psi=
E3 10Psi= 23 0= G23 1.2 104 Psi=
100Psi
Three-layer Sandwich Shell Results
CQUAD4 CQUAD4 CHEXA
Quantity Units NAFEMS Linear PSHLN1 PCOMPLS
at C in -0.123 -0.123 -0.122 -0.122
at C kpsi 34.45 34.029 34.212 33.932
at C kpsi 13.93 13.294 13.167 13.406
at E kpsi -5.07 -5.040 -5.006 -5.020
uz
11
22
12
MD Demonstration Problems
CHAPTER 8122
IntroductionThis problem demonstrates the ability to model pressure loading of a square composite three layer sandwich flat shell. Stresses and displacements are calculated and compared to a reference solution.
Requested SolutionsStresses and displacements are calculated at the surface of the composite three layer sandwich flat shell in MD Nastran. This test is recommended by the National Agency for Finite Element Methods and Standards (NAFEMS): Test R0031/3 from NAFEMS publication R0031, “Composites Benchmarks”, February 1995.
FEM SolutionA numerical solution has been obtained with MD Nastran’s SOL 400 for the configuration shown in Figure 8-1. The plate consists of three layers, a core layer and two face sheets covering this layer. Thicknesses of the layers are shown in Figure 8-1. Only one quarter of the part is analyzed with the appropriate symmetry boundary conditions, and the two edges on the boundary of the plate are fixed. The three layers are modeled using the PCOMP entry, where the thickness of both layers is 0.028 in.
PCOMP 1 0. 0. 1 .028 0. YES 2 .75 0. YES 1 .028 0. YES
Figure 8-1 Three-layer Sandwich Shell under Normal Pressure Loading
Each lamina is modeled as one layer in the composite. The materials for the face sheets and core have the following orthotropic properties:
uniform normalpressure
C
E
A
10
10
y
x
simply supported on all four edges
0.028
0.750
0.028
z
face sheet
face sheet
x
all dimensions in inches
core
E
A
123CHAPTER 8
Three-layer Sandwich Shell under Normal Pressure Loading
Face sheets
and the core
These properties are entered using the MAT8 entry.
Two types of shell elements are analyzed: the CQUAD4 default and the CQUAD4 suitable for large deformations. The latter is activated using the PSHLN1 entry
PSHLN1 1 NO ++ C4 DCT L
For modelling with solid shell elements, the standard CHEXA elements are used to define the element connectivity. To activate the solid shell elements, PCOMPLS entry has to be used for assigning the property of the CHEXA.
PCOMPLS 1 -1
C8 SLCOMP ASTN
1 1 .028 0.
2 2 .75 0.
3 1 .028 0.
For shell-like structure with composite materials, the TSHEAR option on the NLMOPTS entry has to be given to obtain a parabolic shear distribution for composite layers in shells. This is particularly important for this structure because the inner core resists deformation in shear.
NLMOPTS TSHEAR TSHEAR
A uniform pressure of is applied on the top surface of the shell.
Table 8-1 shows the comparison of the face sheet stresses and midspan displacement with the NAFEMS results.
E1 10 106Psi= 12 0.3= G12 1.875 10
6 Psi=
E2 4 106Psi= 13 0= G13 1.875 10
6 Psi=
E3 1 106Psi= 23 0= G23 1.875 10
6 Psi=
E1 10Psi= 12 0= G12 10Psi=
E2 10Psi= 13 0= G13 3 104 Psi=
E3 10Psi= 23 0= G23 1.2 104 Psi=
100MPa
MD Demonstration Problems
CHAPTER 8124
Figure 8-2 Deformed Shape of the Model with Solid Shell Elements
Modeling TipsWhen modeling composite structures using shell elements that support large deformation and nonlinear material behavior (activated with the PSHLN1 entry), it is recommended to set the TSHEAR parameter on the NLMOPTS entry. This will result in a more parabolic shear distribution through the thickness, and in the output of interlaminar stresses.
Table 8-1 Three-layer Sandwich Shell Results
CQUAD4 CQUAD4 CHEXA
Quantity Units NAFEMS Linear PSHLN1 PCOMPLS
at C in -0.123 -0.123 -0.122 -0.122
at C kpsi 34.45 34.029 34.212 33.932
at C kpsi 13.93 13.294 13.167 13.5406
at E kpsi -5.07 -5.040 -5.006 -5.020
uz
11
22
12
125CHAPTER 8
Three-layer Sandwich Shell under Normal Pressure Loading
Input File(s)
VideoClick on the image or caption below to view a streaming video of this problem; it lasts approximately 18 minutes and explains how the steps are performed.
Figure 8-3 Video of the Above Steps
File Description
nug_08n.dat Linear Elements
nug_08m.dat Linear Elements using PSHLN1 Entry
nug_08d.dat Solid Shell Elements
