Structural Calculator
Sandwich Panel Bending Calculator
Real-time calculation of face sheet stress, core shear stress, mid-span deflection, buckling load, wrinkling stress, and bending stiffness. Ideal for aerospace, civil, and automotive composite panel design.
Equivalent bending stiffness:
$$D = \frac{E_f t_f d^2}{2}+ \frac{E_f t_f^3}{6}+ \frac{E_c t_c^3}{12}$$
where $d = t_c + t_f$ (distance between face centroids)
Face stress: $\sigma_f = \dfrac{M \cdot e}{D}$, $e = d/2$
Core shear stress: $\tau_c = \dfrac{V}{d \cdot b}$
Mid-span deflection (UDL, SS, with shear):
$$\delta = \frac{5qL^4}{384D}+ \frac{qL^2}{8 A_c G_c}$$
Wrinkling stress: $\sigma_w \approx 0.5(E_f E_c G_c)^{1/3}$
CAE Note
When modelling in Abaqus or Nastran, the sandwich can be represented as equivalent single-layer shell elements using homogenized properties, or as layered composite shells. Core shear moduli are typically obtained via homogenization of the cellular geometry.
What is Sandwich Panel Bending?
🙋
What exactly is a "sandwich panel," and why is its bending so special compared to a solid slab?
🎓
Basically, it's like an engineering Oreo cookie. You have two stiff, strong face sheets (like aluminum or carbon fiber) bonded to a thick, lightweight core (like foam or honeycomb). The magic is in the separation: it creates incredible bending stiffness for very little weight. Try moving the 'Core Thickness' slider in the simulator—you'll see how a thicker core dramatically increases stiffness without adding much mass.
🙋
Wait, really? So the core isn't just filler? How does it contribute to the bending?
🎓
Exactly! The core has two key jobs. First, it keeps the faces apart, which is the main source of stiffness—think of how an I-beam works. Second, it must resist shear forces to stop the faces from sliding past each other. In the simulator, set the 'Core Shear Modulus' to a very low value. You'll see the deflection spike because the panel is now failing in shear, a common failure mode in practice.
🙋
That makes sense. So when we calculate stress, is it just in the faces? And how do we know if it will buckle?
🎓
Great questions. The faces carry almost all the bending stress, while the core carries the shear. The simulator calculates face stress using the bending moment and the distance to the face. Buckling is a separate, critical check—if the face is too thin or the core too weak, the compressed face can wrinkle locally. Adjust the 'Face Thickness' down and watch the stress and buckling risk increase. This is precisely what engineers check when designing aircraft floors or wind turbine blades.
Physical Model & Key Equations
The core of the analysis is calculating the panel's equivalent bending stiffness (D). This combines the stiffness contributions from the bending-resistant faces and the core itself, though the core's contribution is often small.
$$D = \frac{E_f t_f d^2}{2}+ \frac{E_f t_f^3}{6}+ \frac{E_c t_c^3}{12}$$
Here, $E_f$ and $E_c$ are the face and core elastic moduli, $t_f$ and $t_c$ are their thicknesses, and $d = t_c + t_f$ is the distance between the centroids of the two face sheets. The first term ($E_f t_f d^2/2$) is dominant and shows why separating the faces is so effective.
For a simply-supported panel under a uniform load, the total deflection combines bending and shear deformation. Shear deflection is crucial for sandwich panels because the soft core can deform significantly.
$$\delta_{total}= \frac{5qL^4}{384D}+ \frac{qL^2}{8 A_c G_c}$$
$\delta_{total}$ is the max deflection, $q$ is the load intensity, $L$ is the span, $D$ is the bending stiffness from above, $A_c$ is the core's shear area (≈ $b \cdot t_c$), and $G_c$ is the core shear modulus. The second term is the shear contribution. If $G_c$ is low, this term dominates.
Real-World Applications
Aerospace Interiors: Aircraft cabin floors and overhead bins are classic sandwich panels. They must be extremely light to save fuel but stiff enough to support passenger loads and resist buckling under impact. Engineers use calculations from this simulator to optimize face and core materials.
Wind Turbine Blades: Modern blades are massive sandwich structures with composite faces and foam or balsa wood cores. The bending stiffness is critical for aerodynamic efficiency and avoiding tower strike, while shear strength prevents delamination under turbulent loads.
Marine & Transportation: High-speed boat hulls and train carriages use sandwich panels for a stiff, lightweight structure that dampens vibration and noise. The core material is often chosen for its buoyancy or fire-resistant properties in addition to shear strength.
Building Facades & Cleanrooms: Architectural panels provide thermal insulation and a smooth surface. The core acts as the insulator. The analysis ensures the panel can withstand wind loads (uniform pressure, 'q') without excessive deflection that could break seals or cause visual sagging.
Common Misconceptions and Points to Note
When you start using this calculator, there are a few common pitfalls you might encounter. The first one is treating increases in face sheet and core thickness as equivalent. While making either thicker seems like it would increase strength, increasing the core thickness t_c by 1mm versus increasing the face sheet thickness t_f by 1mm contributes completely differently to bending stiffness. Look at the first term in the equation $$D = \frac{E_f t_f d^2}{2} + ...$$. You can see the squared distance d between the face sheet centroids has a major effect. In other words, thickening the core to separate the face sheets is the key point for increasing stiffness while keeping weight down. Think of thickening the face sheets as a last resort for when you need to increase tensile/compressive strength or prevent local buckling (wrinkling).
The second pitfall is assuming everything is fine just because the calculated deflection is small. This tool is based on a simple one-dimensional simply supported beam model. Actual panels are plates supported on four sides, and the effects of boundary conditions, holes, or anisotropy (strength varying by direction) are not considered. For example, even if the calculation shows safety, "interlaminar debonding" could occur where the adhesive bond between the core and face sheet fails under shear stress. It's essential to always apply a safety factor to simulation results and verify them with physical testing or more detailed FEM analysis.
The third pitfall involves unit errors when entering parameters, especially with the unit systems for Young's modulus E and shear modulus G. For instance, aluminum's Young's modulus is about 70 GPa (70,000 N/mm²), but if you enter just "70", your results will be off by a factor of 1000! Always check the units (Pa, MPa, GPa, etc.) noted next to the input fields and get into the habit of entering values in a consistent unit system.