Beams sandwich

FIGURE 9.6 Bending of a sandwich beam, (a) Geometry, (b) strain distribution, and (c) stress distribution. 

The bending moment M on the cross section is found by integrating the differential force (O dA) times the moment arm (z) over the cross-sectional area as follows  

Substitution of Equation 9.18 into Equation 9.17 and evaluation of the integrals give  

The bending stiffness of a homogeneous beam of material 1 is ,/. Thus, the effective bending stiffness of the sandwich beam has been reduced by the factor a, by replacing the core by material 2 with a lower modulus 2 but with a lower density P2. However, the stiffness-to-weight ratio has been increased as shown by Example 9.2. 

the example sandwich beam is 81% more effective on a stiffness-to-weight basis. 

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Example 2.9 A solid polyethylene beam is 10 mm thick and IS mm wide. If it is to be replaced with a sandwich section with solid polyethylene in the two outer skins and polyethylene foam (density = 200 kg/m ) in the centre, calculate the dimensions of the sandwich beam if it is to have optimum stiffness at the same weight as the solid beam. If the foam material costs 20% more than the solid material, calculate the increase or decrease in cost of the sandwich beam. 

The stiffness ratios (i.e. stiffness of the foam sandwich beam relative to the original solid beam) are also given in Fig. 2.21. In both cases the values given are independent of the original solid material or its dimensions, so this provides a good design chart. The design of solid/foam sandwich structures is also considered in Chapter 3 in the laminate analysis. 

In these composites, the layers are bonded together. A sandwich panel beam is symmetrical if the skins have equal thickness, and are made of the same material. The neutral surface is at the mid-thickness, so the analysis of Appendix C can be used. Figure 4.6 shows the stress variation through a sandwich beam, calculated using Eq. (C.4) separately for the skins with high Young s modulus E, and the core with low modulus Eq. 

Figure 3.26 Three-point bending of a sandwich beam that consists of stiff faceplates on a lightweight core.

As mentioned in Section 3.8, use can be made of composite beams. In a sandwich beam, such as that shown in Fig. 3.26, the core usually has lower values of Young s and shear modulus than the thin faces. The Young s modulus of the faces and core will be denoted by and E, respectively. One approach to stress analysis in these sandwich beams, is to transform the cross-section into a geometry with an equivalent flexural rigidity but consisting of a single material. This transformation is shown in Fig. 4.10 in which the core is replaced by the same material as the faceplates but with a width bE IE ). In sandwich beams, the faces are usually much thinner than the cores and the equivalent flexural rigidity can be written approximately as... 

Figure 4.19 Residual stresses can arise in a sandwich beam, if the thermal expansion coefficient of the faces is different from that of the core.

Many resins are prone to photooxidative attack. Moisture will be a further complication in all except desert climates. Outdoor exposure in Australia over a period of several years caused unpainted carbon/epoxy sandwich beam specimens, representative of an aircraft structure, to lose weight, because the degraded resin surface was readily removed by wind and rain [27], In some locations, the weight loss eventually stabilized, but in others, erosion removed loose fibres from the surface as well and the weight loss continued. Painted samples were not affected in the same way but it was recommended that aircraft should be kept in hangars as much as possible to extend paint life when used in similar climatic conditions. 

Figure 1.3 shows the indentation on a sandwich beam and Figure 1.4 shows top skin delamination after a low velocity impact by a DynaTup 8250HV machine with a hammer weight of 33 kg and velocity of 3.83 m/s, which translates to an impact energy of 242 J. The tup nose has a semispherical shape with a diameter of 12.7 mm. The sandwich beam has a carbon... 

Liu, T., Deng, Z.C., and Lu, T.J. (2008) Analytical modeling and finite element simulation of the plastic collapse of sandwich beams with pin-reinforced foam cores. Interrmtioruil Journal of Solids and Structures, 45, 5127 5151. 

Dweib MA, Hu B, O Doimell A et al (2004) All natiual composite sandwich beams for structural applications. Compos Struct 63 147—157... 

The US Army is interested in developing a rotor control system in helicopters. Figure 4.1.26 shows a bearingless rotor flexbeam with attached piezoelectric strips [48]. Various types of PZT-sandwiched beam structures have been investigated for such a flexbeam application and for active vibration control [49]. 

Ben and Shoji (2005) designed a technique to mould a sandwich beam in which the phenolic foam as a core and a thin fibre-reinforced phenolic composites as a facesheet are used. 

Ben, G. and Shoji, A. (2005), Pultrusion techniques and evaluations of sandwich beam using phenohc foam composite , Ariva/iceri Composite Materials, 14, 277—288. 

Compression ASTM D-695 (modified for high-modulus composites) Celanese, ASTM D-3410 IITRI, ASTM D-3410 sandwich beam, ASTM D3410... 

In the formation of sustainable thermoset resins, epoxidized and acrylated epoxy-dized plant oils and fatty acids have been largely utihzed, as reported from hterature [51]. For composite applications, acrylated epoxydized soy bean oil (AESO) resin is mainly used because it is commercially accessible [52]. The synthesis of AESO is shown Figure 6.10 the carbon-carbon double bonds in the fatty acid chains are modified to append different polymerizable functionalities, such as epoxides and acrylates, to increase the reactivity of the vegetable oils [53], AESO can be cured at room and high temperatures, depending on the initiator, and can be blended with a reactive diluent such as styrene in order to improve the processing flowability and the mechanical performance. Structural applications such as sandwich beams... 

Shenton, H., and Wool, R. (2004) All natural composite sandwich beams for stmctural applications. Compos. Struct., 12. 

Using bonded sandwich beams, of different core thicknesses (t and 3t), in place of all metal components (a bonded metal beam of overall thickness t), it is possible to increase the stiffness and strength, with minimum weight penalty. This can be seen in Table 2. 

Figure 8.11. Comparison of the dynamic response of the baseline beam and nanotube reinforced sandwich beam for a frequency-sweep test at 50 Vrms. (cantilevered length of 22.86 mm) [60],...

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