Design and Analysis of the Flat Honeycomb Sandwich Structures

Structural sandwich is a unique form of the composite structure, and it finds a widespread use in the aerospace industry, where weight saving is a primary concern. The major difference between analysis procedures for sandwich construction and those for homogeneous structural elements is the inclusion of core shear effects on deflection, buckling and stress. The design procedure given in this article is intended to guide the designer in sizing the sandwich parts for primary loading properly. These procedures are usually iterative, and optimum design may require the design of several face–core combinations. Comparing the results obtained through the analytical procedure and Finite Element Analysis (FEA) one can conclude their good agreement. Differences for most of the results are from 10% to 15%, which is quite satisfactory, taking into account that the analytical models are formed on the basis of a number of assumptions and approximations.


Mx
Depending on the condition that a plane or a missile is exposed to, the face material may be aluminum alloys, reinforced plastic, titanium alloys, heat resistant steel, etc. Materials and geometric forms of the core can be very diverse.A very popular type of the core is a "honeycomb core", which consists of a thin film formed in the hexagonal cell perpendicular to the faces [1].Structural sandwich is a unique form of the composite structure, and it finds a widespread use in the aerospace industry, where weight saving is a primary concern.Most commercial airliners and helicopters (Figure 2), and almost all military air and space aircraft widely used the sandwich construction [3].
From the structural point of view, the main role of the core is separating and keeping external faces at a given distance in A order to provide stability against buckling.Essentially, the existence and the thickness of the core create and maintain the required moment of inertia of the cross section.
The major difference between the analysis procedures for sandwich construction and those for homogeneous structural elements is the inclusion of core shear effects on deflection, buckling and stress [4].The reasons for the inclusion of this effect are discussed below.The analysis procedures outlined in this paper are intended for use in the structural analysis of both preliminary and final designs of sandwich parts.In fact, the analytical procedure of analysis with an example, which follows, is primarily intended to guide the designer in sizing the sandwich parts for primary loading properly.These procedures are usually iterative, and optimum design may require the design of several face-core combinations [5].

Analysis of the flat honeycomb sandwich panels with isotropic faces
This chapter presents data and methods for the design and analysis of simply supported flat sandwich panels under uniform pressure loads.

Sandwich Stiffness
The stiffness of a structure is defined as its ability to resist deformation when subjected to an applied load.The deformations of the sandwich structures, unlike those of monolithic beams, are significantly affected by the contributions of shear deformation.
The deflection of a monolithic beam or plate, according to the elementary beam theory, is governed by the solution of the following differential equations [4]: Mx -the bending moment at a given section D -flexural stiffness Vx -shear at the section N -shear stiffness For most monolithic beams having constant cross sections and large (compared to the beam depth) spans, the second term, which accounts for the shear deformation, may be neglected.This simplifying assumption may normally be made because the shear stiffness, N, is relatively large.However, since sandwich materials have relatively low core shear module, the shear stiffness of most sandwich elements is not so large and this assumption does not hold.Therefore, the deflection calculations for sandwich elements must include the shear contribution [4].[4] Shear module and strength allowable are based on the core ribbon direction, which may be oriented either parallel to side-a or side-b.Typical values should be used for the core shear module (G XZ , G YZ ), while statistically derived allowable should be used for the core shear strengths (F SL , F SW ).Both the shear modulus and shear strength must be corrected for core thickness and temperature.Core material properties, along with the appropriate correction curves can be found in the relevant literature (for example BDM-4231 through BDM-4240 [6]).Figures 3 and 4 more clearly define the terms associated with the core ribbon.

Analysis Procedure
The analysis procedure for the flat honeycomb sandwich panels with similar isotropic faces subjected to uniform pressure is outlined below and is followed by an example analysis [5].
Figure 5. Geometry and loading conventions [5] Using the data provided in Table 1, determine whether the given panel will withstand the design load.The configuration is shown in Fig. 5. Step 1: Determine the panel aspect ratio b/a.
Step 2: Identify G XZ as G L or G W using Fig. 3 and obtain core properties, for example by using data from BDM-4231 through BDM-4240.Use typical values for the core shear modulus corrected for the applicable thickness and temperature [6].
G xz = G L = 103900 psi (716,36 N/mm 2 ) Step 3: Determine the facesheet material properties E, μ, F cy and F tu , corrected for temperature (from BDM-4143 [7]).Determine the core thickness, c, and calculate (1 ) Step 4: Determine R. Using R and V, determine K 1b and K 1a from Figures 6 and 7. If Step 5: Calculate the distance between facing centroids d and determine the maximum face stresses.1, 265 (32,13mm) 2 (Note that since p is positive, f 1 is compressive and f 2 is tensile.F cy is used to calculate the MS for face-1 and F tu is used for face-2).
Step 6: Determine the margin of safety for each facesheet.
Step 7: Determine the coefficients K 2b and K 2a from Fig. 8 and calculate the maximum core shear stresses f sb and f sa .
Step 8: Determine the margins of safety for the core shear; the orientation of the core will determine how F sa and F sb correspond to the core shear allowable F SL and F SW , see Fig. 3. . .
Step 9: Determine the deflection coefficient K 3 from Fig. 9 and check the maximum deflection of the panel δ (at the center of the panel).
Step 10: Check the compressive face for local instability failure by consulting the appropriate BDM-6716 (Intracell buckling of the honeycomb sandwich structures), BDM-6718 (Face wrinkling of the flat honeycomb sandwich panels with isotropic faces) and BDM-6720 (Shear crimping of the honeycomb sandwich structures).
The obtained maximum stresses in the faces and the maximum core shear stresses on the side b are below the allowable limit stresses.However, the maximum shear stress on the side a is above the limit stress, due to which designed honeycomb sandwich beams do not provide the required level of security.In order to ensure the appropriate level of security the plates will increase the thickness of faces.As already mentioned, these procedures are usually iterative and optimum design may require the design of several face-core combinations.
It is evident that increasing the thickness of faces resulting in increased margins of safety for faces and core.However, increasing the thickness of faces does not significantly affect the increase in the margins of safety for core shear.Therefore, we will increase the thickness of the core.

Analysis of the flat honeycomb sandwich plates by the Finite Element Method
The modern design processes of the new, as well as monitoring the integrity of the existing structures in the real exploitation conditions, is unthinkable outside the environment of computer mechanics.Specific engineering problems are being solved by using numerical methods implemented on computers.One of the main advantages of the computer designing is short time and inexpensive simulation of behavior of the model of a real object observed.
At an early stage of design, these programs provide an opportunity to obtain reliable information about the validity of the assumed size and accuracy of the provided constructive solutions.The advantage of using these packages in the design is primarily reflected in the ease of making model and its correction.
Most software packages that have the ability of structural analysis are based on the Finite Element Method -FEM (Finite Element Analysis -FEA).The basic idea of this method is division of the structure into the finite number of small elements that constitute the basis for all considerations [8].

Analysis of the flat honeycomb sandwich panels under uniform load using the ALGOR software package
In this case, the subject of the analysis is a flat honeycomb sandwich plate under the uniform load, whose dimensions and margins of safety for provided constructive solutions are previously analyzed analytically.
Comparing the results obtained through analytical and computer procedures, one can conclude their good agreement.Differences for most of the results are from 10% to 15%, which is quite satisfactory, taking into account that the analytical models are formed on the basis of a number of assumptions and approximations.

Conclusion
Structural sandwich is a unique form of the composite structure, and it finds a widespread use in the aerospace industry, where weight saving is a primary concern.Most commercial airliners and helicopters, and nearly all military air and space vehicles, make the extensive usage of the sandwich construction.
The major difference between the analysis procedures for sandwich construction and those for homogeneous structural elements is the inclusion of core shear effects on deflection, buckling and stress.
The design procedure given in this article is intended to guide the designer in sizing the sandwich parts for primary loading properly.These procedures are usually iterative, and optimum design may require the design of several face-core combinations Comparing the results obtained through analytical and computer procedures, one can conclude their good agreement.Differences for most of the results are from 10% to 15%, which is quite satisfactory, taking into account that the analytical models are formed on the basis of a number of assumptions and approximations.

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Bending moment at a given section D -Flexural stiffness Vx -Shear at the section N -Shear stiffness a -Length of the longer side of a pressure loaded panel b -Length of the shorter side of a pressure loaded panel c -Thickness of the core d -Distance between the centroids of the faces h -Total thickness of the sandwich element t 1 , t 2 -Thicknesses of faces 1 and 2 L -Longitudinal direction, parallel to the core ribbon direction T -Short transverse direction, trough the core thickness W -Transverse direction, perpendicular to the core ribbon direction F sL -Allowable core shear stress in the LT plane F sW -Allowable core shear stress in the WT plane G L -Core shear modulus in the LT plane G W -Core shear modulus in the WT plane G XZ -Core shear modulus in the XZ plane G YZ -Core shear modulus in the YZ plane F sL -Allowable core shear stress in the LT plane F sW -Allowable core shear stress in the WT plane K thkW -Thickness correction factor K thkL -Thickness correction factor V -Dimensionless shear parameter E -Elastic modulus of the facing material μ -Poisson's ratio for the facing material R -Mean radius of curvature at the neutral axis of the panel, or G YZ /G XZ K 1b -Face stress coefficient for the "b" direction K 1a -Face stress coefficient for the "a" direction K 2b -Core shear coefficient for side-b K 2a -Core shear coefficient for side-a K 3 -Panel deflection coefficient f 1,2 -Maximum face stresses f sb -Core shear stress at the midlength of side-b f sa -Core shear stress at the midlength of side-a MS 1,2 -Margin of safety for each facesheet MS sb,sa -Margins of safety for core shear Introduction sandwich panel consists of three discrete structural elements: two relatively thin facings, bonded to a thicker, lightweight core (Fig.1).

Figure 1 .
Figure 1.Elements of the honeycomb sandwich structures

Figure 3 .
Figure 3. Core orientation to determine F sa , F sb , G XZ and G YZ[4]

Figure 15 .
Figure 15.Stress state of the panel (view from above).

Figure 16 .
Figure 16.The resulting deflections of the honeycomb sandwich panel under uniform load.

Figure 17 .Figure 18 .
Figure 17.Local values of stress and deflection in the center panel on the upper face

Table 1 .
Example data for a uniform pressure loaded flat panel