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The sandwich structure is of great interest because of its advantage of combining light weight and high flexural stiffness. Many previous researchers have studied the failure modes in sandwich structures and the effects on the load capacity caused by the change of the constituent materials’ properties. In this research, by applying Finite Element Analysis (FEA) method, we simulated a cantilever beam composed of a sandwich structure in Abaqus, to find out the preferred design principles that help decrease the stress and displacement in the beam when applied a uniform load. We also determined the effect of the core geometry on decreasing the displacement and the stress in the beam.

A Sandwich structure is normally composed of two thin outer layers (faces) with a large density and a thick inner layer (core) with a smaller density. Compared with traditional beams that consist of a single material, the sandwich panel is being more and more widely used in real applications because it can significantly reduce the beam weight while maintaining an adequate flexural stiffness. Decreasing the weight can reduce the possibility of the catastrophic failure caused by fatigue. And there are other factors that could lead to the failure. Under high pressure, once the axial stress on the faces exceeds the tensile stress of the constituent material, the structure would experience plastic strain and finally fail, so does the core. The failure modes in the composite structures have been extensively investigated through experimental or numerical methods [

Among previous published researches on sandwich structures, Miravete [

In this present work, we summarized the effect of Young’s modulus and thickness variation on the load capacity of the structure by simulation analysis with FEA method. The advantage of the simulation compared to previous experimental or numerical study is that we can clearly see the stress and displacement distribution in the beam when modifying the sandwich structure. The simulation also tells us that varying thickness is better in terms of load capacity compared to changing Young’s modulus.

Furthermore, we studied the effect of the core geometry on the stress and the displacement distribution. The focus of the study is on changing the hollow structure of the core and seeing its effect on the load capacity. What we found is that the side area of the hollow structures is one important factor that affects the load capacity. And this gives us guidance on the design of hollow core structures in sandwich beams in the future.

The simulation was run using FEA method in Abaqus 6.14. The details are described in the following sections.

In our simulation, two materials are employed in the models: steel and polystyrene (PS). The details of these materials are shown in the

The property of the steel here is from ASTM A36 carbon steel [

Steel | Polystyrene | |
---|---|---|

Density (g/cm^{3}) | 7850 | 1040 |

Young’s Modulus (GPa) | 209 | 3 |

Poisson’s Ratio | 0.3 | 0.3 |

Steel has a higher stiffness, PS can help with the load distribution and reduce the weight of the overall sandwich structure. In our sandwich structures, steel is used as the face materials as the core material.

To determine which element type to use, we built a cantilever beam with a rectangular cross section. The details of this model are shown in

When building a sandwich structure in Section 3.3, we made the thickness of the face and the core equal, as shown in

In all models, we used C3D20 as our element type with a mesh density of 0.01. The reason of choosing C3D20 will be elaborated in the following section.

To find out which element type works the best, we tried C3D4, C3D8 and C3D20 in the model of all steel cantilever beam and compared the free end displacement with analytical results. Here, the analytical vertical displacement y is determined by the equation below:

y = w x 2 ( x 2 + 6 l 2 − 4 l x ) 24 E I , I = b h 3 12

where w is known as the distributed load, E is the Young’s modulus, l is the length of the beam, b is the dimension parallel to the bending axis, and h is the

dimension perpendicular to the axis. In our condition, l = 0.4 m , b = 0.1 m , h = 0.05 m , p = 0.4 MPa and w = p ∗ b = 0.04 MN / m .

The comparison between the simulated and analytical vertical displacement solution is shown in

It can be seen that the result using C3D4 element type deviates the most from the analytical result, while either C3D8 or C3D20 gives a more accurate displacement.

To convince that sandwich structures are more applicable in construction than all steel beams, we compared the stress and displacement of these two structures

Element Type | Vertical Free End Displacement Magnitude (m) | Error (%) |
---|---|---|

C3D8 | 5.85E−04 | 0.44 |

C3D20 | 5.88E−04 | 0.08 |

Analytical | 5.88E−04 |

under the same amount of load. In the simulation, we used the single variable method: the only difference is the change of the inner material of the beam. The parameters of the panels are shown respectively in

From the graph shown above, the free-end displacement of the all steel beam is 44.30% smaller than that of the composite panel; the upmost stress of the all steel beam is 42.49% smaller than that of the composite panel. However, according to the data of both materials listed in Section 2.1, the density of steel is more than six times larger than that of the sandwich composite beam. The heavy burden caused by the weight of the all steel beam far exceeds the advantage brought by its smaller displacement and stress. Also, according to

In the design of sandwich structures, people use two materials with different densities and stiffnesses. To determine whether the stiffer material should be employed as the core or the faces, we simulated a composite composed of steel and PS. The model used here is shown in

to 1E−03 m while that of model (2) goe sup to 4E−03 m, about three times larger. For the maximum stress, the one in model (2) is about 2 times of that in model (1). This indicates that having the stiffer material as faces is a better choice in terms of smaller displacement and stress. From

The reason we chose PS as the core material is that it has a small density but a medium stiffness. This not only reduces the possibility of the failure caused by the heavy weight of the beam, but also maintains the overall stiffness of the structure. However, failure could also occur when either the axial stress on the facings or the shear stress in the core exceeds the yield stress of the constituent material. Therefore, we considered the following methods to optimize the sandwich structure:

− Increase the Young’s modulus of the face material

− Increase the Young’s modulus of the core material

− Increase the thickness of the face

− Increase the thickness of the core.

By increasing the Young’s Modulus of the material, we meant to increase the overall stiffness of the sandwich structure. When increasing the Young’s modulus of the materials, we increased it by 50% while keeping other properties the same as in

In

From the simulation results listed above, we can observe that the stiffer-core beam has a better affect on decreasing the stress on the beam while the stiffer-face beam has an advantage in decreasing the free-end displacement. It can be clearly seen that increasing the core stiffness is a better choice as it decreases both the stress and the displacement in the beam.

Types of Structures | Change of Stress on Steel | Change of Stress on PS | Change of Displacement |
---|---|---|---|

Original | 0.00% | 0.00% | 0.00% |

Stiffer Face | +10.60% | +10.68% | −22.26% |

Stiffer Core | −8.039% | −7.450% | −11.6% |

(+stands for increasing, and −stands for decreasing).

On the other hand, we hope to reduce the stress in the beam through increasing the thickness of the faces or the core. We first increased the thickness of the core by 10 mm. This adds to the overall beam mass. To make sure the mass is the same either increasing the thickness of faces or the core, we calculated the corresponding increase of the face thickness. The details of the beam dimensions are shown in

When we tried modifying the thickness of the beam, the improvement is much more obvious. The comparison between

From

We hypothesized a reason for this result. As a buffer layer in the panel, the PS core has an effect on spreading and mitigating the stress distribution on the beam. Increasing the thickness of the core means increasing the space where the load could be spread out, so the amount of load distributed on every point of the beam will decrease. Besides, since PS is a light material, increasing the core thickness would not lead to a significantly large burden on both steel faces. Therefore, we think increasing the thickness of the core is the preferred choice to improve the load-bearing capacity of the cantilever beam.

Although the data seems to show that increasing the core thickness has a better scenario in reducing both the stress and the displacement than increasing the core stiffness does, we can suppose that if we enlarge the degree of increase in the core stiffness, the reduction in the stress and displacement would surpass that of the thicker-core beam shown in

Types of Structures | Change of stress on Steel | Change of stress on PS | Change of displacement |
---|---|---|---|

Original | 0.00% | 0.00% | 0.00% |

Thicker Face | −5.405% | −5.546% | −7.071% |

Thicker Core | −15.04% | −15.15% | −26.57% |

+ stands for increasing, and − stands for decreasing.

timize the design, and applied the thicker-core model (shown in

In order to reduce the overall beam weight, were placed the solid core with hollow structures.

This not only saves the cost, but also decreases the burden caused by the beam weight. We believe that if the contact area between the face and the core stays unchanged, the load-bearing capacity of the cantilever panel can be determined by the side surface area of the hollow parts. To confirm this, we did a series of control experiments. The designs of the hollow cores are shown in ^{2}, (b) S = 33573 mm^{2}, and (c) S = 37388 mm^{2}. The hollow structures only differ in the shape of the hollow parts, other parts remain the same as in

According to the results shown in

The sandwich structures in our models effectively combine the high stiffness of the steel and the lightweight of the PS. Using steel as faces, they bear the most of the stress and control the panel under certain an acceptable deflection. The PS core reduces the overall weight of the beam and undertakes a certain fraction of the load.

In addition, we figured out that increasing the thickness of the core is one preferred method to optimize the design of the sandwich structure.

Moreover, digging hollow parts in the solid core of the sandwich structure can further decrease the weight of the beam. Surely, it will increase the overall displacement and stress. However, we find out that by increasing the side area of the hollow parts, we can reduce the maximal stress and displacement.

There are other factors, such as the geometrical distribution of the hollow parts, which can also affect the stress and displacements. More study will be carried out in the future.

This research is sponsored by Embark Education. We are also grateful to the graduate student Weizi Yuan from Northwestern University for her encouragement.

Hu, T. (2017) Optimizing the Sandwich Composite Structure in the Cantilever Beam. Modern Mechanical Engineering, 7, 127-143. https://doi.org/10.4236/mme.2017.74009