Antennas for Communications (AFC) Logo Radome Structural Analysis
Role of General Buckling

grn_ball.gif - 969 BytesIntroduction

Radomes protect antenna systems from wind, blowing sand, snow, ice, rain, ultra violet sun light, temperature, fungus and corrosion. In particular, wind, snow and ice loads place stringent demands on the structural properties of the radome. To support these environmental forces, radome structures are composed of panels, which when assembled form a truncated spheroid. Panels may be spherical sections or flat facets forming orange peel, triangular, hexagonal, pentagonal or other various panel shapes. Panel wall properties comprise composite sandwich, solid laminate or thin membrane units fabricated from various materials. To enable adjacent panel assembly, each panel is surrounded by a flange, which creates a radome framework characteristic of the different panel shapes. This framework may also have structural properties as is usually the case for geodesic radome designs. Degrading RF system performance, the framework also scatters electromagnetic energy into the antenna sidelobes and introduces transmission loss. Framework scattering loss accounts for most of the radome transmission loss being 4 to 100 times larger than the wall insertion loss. To minimize electromagnetic, RF degradation, radome structural strength must be compromised against the demands for better RF performance. What this means is that the radome structure supporting the wind, snow and ice loads must be designed just strong enough to meet environmental requirements. Beefing up the radome panel framework or making the wall sturdier degrades RF performance. To enhance RF performance, this balancing act between a stronger structure with heavy-duty sized members and RF performance determines that radomes are designed with structural safety factors. It is for this reason that AFC has defined radome structural safety factors by a criterion based on catastrophic failure and collapse of the radome.

This memorandum will show that radome catastrophic failure is a characteristic of general buckling, which depends on the complication of all the properties of the radome. From radome geometry and panel shape and size to framework and wall material properties, each of these characteristics impacts general buckling and the critical wind speed at which radomes fail. For if the unsuspecting radome is designed alone for just stress and strain, it would collapse at significantly less wind speed or snow loads as determined by general buckling.

red_ball.gif - 950 BytesWind Speed and Pressure Dynamics on Radomes

windload.gif - 23685 Bytes
Figure 1. Turbulent wind pressure over radome surface.
Wind flow over truncated spheres is itself a complicated subject. The characteristic type of fluid flow is determined by a property known as the Reynolds Number, Re=VD/ν, where V is the wind velocity, D the radome diameter and ν is the wind fluid viscosity. Depending on azimuth angle with respect to the wind direction, as shown in Figure 1, wind force pressure both pushes and pulls on the radome surface. Such a force distribution over the radome surface plays a significant role by decreasing the general buckling failure wind speed. Any dynamic structural analysis must take into account wind turbulent fluid flow over the radome and the complex nature of the pressure model.


grn_ball.gif - 969 BytesRole of General Buckling

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Figure 2. General Bucking of a Rectangular Column.
Structural engineers have known for a long time that column (beam) structures fail under compression loads F (see Figure 2) with values far less than that would be predicted by maximum compressive and tension loads. Experiments show that the failure load is inversely proportional to the square of the column beam length L and proportional to the cross sectional shape (moment of inertia I):

Fcr= π2EI/4L2,

where E is Young's modulus. The failure force, Fcr at which the beam collapses is given the name “Critical General Buckling Force.” In other words, when the column length is twice as long (2L), the failure occurs at 1/4 the load. More too, the failure load Fcr decreases even more rapidly when a second small force Fsmall is applied perpendicular to column.

Like the column, a radome structure is a framework structure of interconnected columns (beams). See Figure 3. As with the simple column, the framework members are also interconnected by a sandwich, solid laminate or thin membrane wall, which applies perpendicular forces on the column beams. Clearly, the radome represents a complicated general buckling problem that almost defies analytical solution. Recognizing the approximate nature of the early analytic approximate solutions, engineers introduced a safety factor into the general buckling solution.
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Figure 3. Radome structure of interconnected beams with perpendicular wall related forces.
Since wind forces on a radome increase as the square of the wind speed, V2, the safety factor is the ratio of the square of the general bucking failure wind speed divided by the maximum rated wind speed as defined by the radome specification. For example if the rated design wind speed is 125 mph, and a buckling safety factor of 4 is introduced into the design criteria, then the radome fails due to critical bucking at:

safety-factor.gif - 1157 Bytes

With the advent of computers, powerful structural analysis software became available that enabled complicated structures, such as radomes, to be analyzed for their survival in high winds or under snow loads. Such software goes by the name Finite Element Analysis or FEA for short. Using time-dependent nonlinear FEA, one can trace how a radome fails over time when it is subjected to high-speed wind or significant snow and ice accumulation. With FEA analysis tools, general buckling failure modes are determined at wind speeds or snow loads several times less than that would be predicted from stress and strain calculations alone. Radome collapse by general buckling failure is a global system property of the entire radome structure. Indeed, general buckling depends on the complexity of radome diameter and geometry, panel shape and size, framework and wall material properties and dimensions. The next several paragraphs examine the influence of the radome geometry type and of the choice of panel wall and framework material on general buckling.

red_ball.gif - 950 BytesCase Example 1: Critical Buckling Wind Speed Dependance on Radome Geometry
Quasi-Random vs. Symmetric Orange Peel

Radome geometry is one of the most important parameters in determining the critical buckling failure wind speed. Table 1 compares the design choice between the quasi-random and symmetric orange peel radome geometry. For a sandwich 35ft (10.7m) diameter radome example, Table 1 shows that a quasi-random radome geometry is significantly stronger than the symmetric orange peel geometry. The quasi-random radome is 119 percent stronger than the symmetric orange peel unit and has an appropriate safety factor of 2.19 for a 150 mph (241km/hr) specification wind speed. In contrast, the symmetric orange peel radome only has a 1.0 critical buckling safety factor. For a safety factor of 2.0, the symmetric orange peel radome is only useful to a 106 mph (170 km/hr) de-rated design wind speed requirement. Table 1 analyzes sandwich radomes with 0.5 inch (12.7mm) core thickness for operational frequencies up to 5.0 GHz.

Table 1. Critical Buckling Failure Wind Speed
Dependance on Radome Geometry
Quasi-Random vs. Symmetric Orange Peel
Radome Geometry Critical Buckling Wind Speed Safety Factor at 150mph Wind Speed Picture
Quasi-Random 222 mph

357 km/hr

2.19 quasi-radome-p1.gif - 14789 Bytes
Symmetric Orange Peel 150 mph

241 km/hr

1.00 sym-radome-p2.gif - 14217 Bytes

grn_ball.gif - 969 BytesCase Example 2: Critical Buckling Wind Speed Dependance on
Sandwich Core Thickness

Sandwich radome design depends on both the maximum frequency of operation and wind speed specifications. From Table 2, as the sandwich core thickness increases, the critical buckling failure wind speed increases as well as the safety factor margin. Note that the maximum operating frequency simultaneously decreases inversely proportional to the core thickness. Therefore for a constant critical buckling safety factor, the radome wind speed specification must decrease with increasing operating frequency. As an example from Table 2, the 0.25 inch core thickness radome critical buckling wind speed is 180 mph (290 km/hr) with a safety factor of 1.44. For a critical buckling safety factor of 2, this 9 Ghz design is inadequate. The radome wind speed specification requirement should be reduced to 127 mph (204 km/hr).

This analysis is for a 35ft (10.7m) diameter quasi-random radome.

Table 2. Critical Buckling Failure Wind Speed Dependance on Sandwich Core Thickness
Quasi-Random Radome Geometry
Radome Core Thickness Critical Buckling Wind Speed Safety Factor at 150mph Wind Speed Maximum Von Mises Stress within Panels at 150 MPH (lb/in2) Worst Case Stress within Framework 150MPH (lb/in2) Maximum Frequency of Operation Picture
0.25 inch
6.4 mm
180 mph
290 km/hr
1.44 916.25 765.21
-1005.71
9.0 GHz quasi-radome-p1.gif - 14789 Bytes
0.5 inch
12.7 mm
222 mph
357 km/hr
2.19 814.76 572.12
-981.41
5.0 GHz
1.0 inch
25.4 mm
290 mph
467 km/hr
3.73 780.18 526.30
-956.91
3.5 GHz

red_ball.gif - 950 BytesCase Example 3: Critical Buckling Failure Wind Speed Dependance on
Choice of Framework and Thin Membrane Material

Dielectric vs. Metal Space Frame Radome

Space frame radomes are assembled from panels, which are composed of a structural framework with an attached thin membrane wall. For the Dielectric Space Frame (DSF) radome, the radome panel framework and thin membrane walls are laminated one piece monolithic units manufactured form Fiberglass Reinforced Plastic (FRP) materials. The panel flanges form the radome framework. In contrast for the Metal Space Frame (MSF) radome, the thin membrane wall is attached to an Aluminum metal framework. To accomplish the attachment process, the membrane material must be very pliable. The usual material choice is Dacron. While dielectric space frame FRP radomes have a rigid membrane wall, a Dacron membrane wall metal space frame radome is easily recognizable by flapping panel membranes. At moderate wind speed levels, metal space frame radomes require pressurization to reduce membrane oil-canning, sound/vibration noise, microphonics and fatigue failure. Table 3 demonstrates the role that critical buckling plays for identical 41ft (12.6m) diameter geodesic quasi-random space frame radomes. In each case, the framework member size (width and depth) is the same for both radome types. Just Aluminum material properties are substituted for the FRP material. And Dacron thin membrane wall material properties are substituted for FRP.

Clearly Aluminum is stronger than FRP. One would expect the Aluminum framework strength to dominate the structural analysis results. Yet that is not the case. The panel membrane material has a significant and major role in determining the critical buckling failure wind speed. Due to the panel membrane material, observe from Table 3 that the dielectric space frame radome is 150 percent stronger than the metal space frame unit. While the dielectric space frame radome 2.5 safety factor is adequate for a 200 mph (322 km/hr) wind speed requirement, the equivalent metal space frame radome has only a 1.0 safety factor. In order to increase the metal space frame critical buckling safety factor to 2, one must reduce its rated wind speed to 142 mph (228 km/hr).

The only way for the metal space frame radome to safely meet a 200 mph (322 km/hr) specification wind speed is to increase the Aluminum framework member size or change the membrane to a stronger material. Since a flexible membrane material is necessary for the fabrication of the metal space frame panel, there is little choice but to stay with Dacron. The only decision available for the metal space frame radome is increasing the Aluminum framework members’ size.

There is, however, a penalty to pay for increasing the Aluminum framework size. The penalty comes in the form of a simultaneous increase in transmission loss and deterioration of RF performance. We refer the reader to AFC’s Transmission loss and Antenna Pattern Degradation web page.

Table 3 clearly shows that all properties of the radome are important in determining radome collapse at the critical buckling failure wind speed. Structural critical buckling safety factors dominate the compromise between a stronger structure with heavy-duty sized members and RF performance.

Table 3. Critical Buckling Failure Wind Speed Dependance on Framework and Thin Membrain Material
Dielectric vs. Metal Space Frame Radome
Radome Design Paramter Dielectric Space Frame Radome
DSF
Metal Space Frame Radome
MSF
Picture
Flange Framework Material FRP Aluminum quasi-radome-41ft.gif - 9271 Bytes
Panel Membrain Material FRP Dacron
Critical Buckling Wind Speed 316 mph
509 km/hr
201 mph
323 kn/hr
Safety Factor at 200 mph Wind Speed 2.50 1.01

grn_ball.gif - 969 BytesCase Example 4: Structural Analysis of 41ft (12.6m) Diameter Thin Membrane Geodesic Dielectric Space Frame Radome.

Table 4 provides the time dependant nonlinear FEA structural analysis data for a 41ft (12.6m) diameter dielectric space frame thin membrane radome designed for 200 mph (322 km/hr) wind speed and 50 lb/ft2 snow/ice loads. In particular, Table 4 identifies the critical buckling wind speed and snow load, safety factors for critical bucking under wind and snow loads, Von Mises safety factors for membrane stress, safety factors for worst framework stress and radome displacement under maximum loads.

As stated earlier, please note that the critical buckling safety factor for wind speed is the smallest safety factor in the structural analysis set and the chief requirement for radome structural integrity. From a design point of view, if the critical bucking safety factors are adequate, then the other safety factors are easily met. In contrast, the opposite is not true. Should one design just for stress and strain Von Mises and Worst Framework Stress criteria, then the radome may be subject to catastrophic collapse at significantly less wind speed and snow loads. Figure 4 pictorially displays the radome displacement, Von Mises membrane stress and the framework stress for the radome at 212 mph (342 km/hr) wind speed and 50 lb/ft2 snow loads. For better viewing, each picture maybe enlarged by clicking on the image.

Table 4. Structural Analysis 41ft (12.6m) Diameter Dielectric Space Frame
Thin Membrane Geodesic Radome
Critical Buckling Wind Speed Saftey Factor
Critical Buckling at 200MPH
Saftey Factor
Maximum Von Mises Stress within Panels at 200MPH
Safety Factor
Worst Framework Stress at 200MPH
Maximum Radome Displacement at 200MPH
316 MPH (316/200)2 = 2.5 29651/8719.6 = 3.4 29651/9738.6 = 3.0 1.3 inch
Critical Buckling Snow/Ice Load Saftey Factor
Critical Buckling at 50 lb/ft2 Snow/Ice Load
Saftey Factor
Maximum Von Mises Stress within Panels at 50 lb/ft2 Snow/Ice Load
Safety Factor
Worst Framework Stress at 50 lb/ft2 Snow/Ice Load
Maximum Radome Displacement at 50 lb/ft2 Snow/Ice Load
272 lb/ft2 272/50 = 5.4 29651/1968.3 = 15.1 29651/1881.4=15.8 0.52 inch

Figure 4. Force and Dispalcement Distrubtion on a 41ft (12.6m) Diameter Dielectric Space Frame Thin Membrane Geodesic Radome at 212 mph wind speed and 50 lb/ft2 Snow Loads
41dsf36-displacement.gif - 11757 Bytes 41dsf36-von-mises.gif - 11588 Bytes 41dsf36-beam-stress.gif - 8801 Bytes
Displacement at 212MPH
Scale factor =20
Von Mises Stress at 212MPH Framework Stress at 212MPH
41dsf36-snow-displacement.gif - 10596 Bytes 41dsf36-snow-von-mises.gif - 10370 Bytes 41dsf36-snow-beam-stress.gif - 8273 Bytes
Displacement under Snow Load
50 lbs/ft2
Scale factor =30
Von Mises Stress under Snow load
50 lb/ft2
Framework Stress under Snow Load
50 lb/ft2

red_ball.gif - 969 BytesCritical Bucking Safety Factors

Antennas for Communications (AFC) has been deploying radomes worldwide since 1987 and composite material antennas since 1972. Our radomes have been subjected to every environmental condition. Over the years, many of these radomes have also been subjected to hurricane, typhoon and cyclone winds. Each of these radomes experience constant environmental exposure to sunlight, UV and corrosive atmosphere as well as the inconsistencies of manufacturing tolerances, installation errors and infrequent maintenance. End-of-life issues generally characterize this slow degradation process. Using natures environmental test laboratory as a guide, we have analyzed these successful radome designs using the time dependant nonlinear FEA tools at our disposal. Our concern is how much safety factor margin do we need to guarantee a life-time of structural performance. Based on those FEA analyses, we come to the following criteria on critical bucking safety factors:
        Critical Buckling Safety Factors
      • Large Radomes > 1.9
      • Small Radomes > 4.0
The critical bucking criteria transition between small and large radomes has been of considerable debate within our company. There are good theoretical and practical grounds for this transition, which we leave to the reader to explore further. As a side note, the building industry typically uses a safety factor of 2 when designing new building structures. It is remarkable that our extensive FEA studies have lead to a similar general buckling criterion for large radome structures.

AFC manufactures, markets and sells worldwide satellite dish antennas, conical horn antennas, radomes, antenna feeds, microwave and waveguide components, ultra low loss waveguide transmission line Tallguide ®, and shelters. Our customers serve the broadcast, communications, radar, weather and cable industry, defense, government, and government agencies worldwide. AFC's quality control manufacturing standards are certified under ISO 9001 : 2008.

For more information on AFC's radome product line, please refer to AFC's Radome Network Home Page on thin membrane wall, solid laminate and 3-layer sandwich radomes. A complete Internet WWW AFC document index may be found in Antennas for Communications (AFC) Home Page Document Summary List.

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