Calculate bending stiffness, core shear deflection, face-sheet stress, and face wrinkling limit (Hoff-Mautner formula) in real time. Visualize the shear deflection contribution to avoid underestimating core shear deformation.
Sandwich Beam in Bending (Live)
While paused, the animation is frozen. Press play to resume the automatic animation.
Sandwich beam deflection (simply supported, central point load). \(D = E_f t_f d^2 / 2\) is the flexural rigidity, and \(A_G = G_c b d\) is the shear rigidity.
Face bending stress \(\sigma_f\) and core shear stress \(\tau_c\). \(d = t_c + t_f\) is the representative through-thickness distance, and \(Q\) is the shear force.
Approximate face-wrinkling stress. \(E_f\): face modulus; \(E_c\), \(G_c\): the core elastic and shear moduli [MPa].
What is Sandwich Panel Analysis?
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What exactly is a "sandwich panel" and why is it so special in engineering?
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Basically, it's a lightweight structure with two stiff, thin face sheets bonded to a thick, lightweight core—like a structural Oreo cookie. The magic is in the separation: it creates incredible bending stiffness for very little weight. In practice, you see this everywhere from aircraft floors to wind turbine blades. Try selecting different Face Sheet Materials in the simulator above; you'll see how switching from aluminum to carbon fiber dramatically changes the panel's behavior.
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Wait, really? So the core isn't just filler? What's its main job?
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Great question! The core's primary job is to keep the faces apart, which gives the panel its high bending stiffness, but it also has to carry shear forces. A common case is an aircraft wing panel: the core prevents the top and bottom skins from sliding past each other under load. If the core is too weak, the panel fails in shear. Slide the Core Thickness h_c control up and down. You'll see that a thicker core increases overall stiffness but also changes the shear stress distribution.
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The simulator shows "Flexural" and "Shear" deflection. Why are they separate, and what's "face wrinkling"?
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In practice, the total deflection is the sum of bending (flexural) and shear components. For a short, thick panel, shear deflection can be huge! Face wrinkling is a sneaky local buckling failure where the face sheet dimples into the core. For instance, if you use a very soft foam core with a thick carbon fiber face, the face might wrinkle under compression long before the panel bends too much. Change the Load Type to "Distributed" and increase the Load P in the simulator. Watch how the failure mode predictions change based on which limit is reached first.
Physical Model & Key Equations
The total bending stiffness of the sandwich panel, D, combines the stiffness from the face sheets bending about the panel's neutral axis and their own local bending. This is the core principle behind the "equivalent stiffness" method.
$$D=\frac{E_f t_f d^2}{2}+\frac{E_f t_f^3}{6}$$
Where: E_f = Young's modulus of the face sheet material t_f = Thickness of one face sheet d = Distance between the centroids of the two face sheets (d = h_c + t_f)
The first term (E_f t_f d^2/2) is dominant and represents the faces working as a couple. The second term (E_f t_f^3/6) is their minor local bending stiffness.
The total deflection under a central point load is the sum of flexural (bending) and shear contributions. Each failure mode has a governing stress or critical load.
Face Wrinkling Stress: \(\sigma_{\text{wr}}=0.5(E_f E_c G_c)^{1/3}\)
Where: P = Applied load L = Span length S = Shear stiffness of the panel core E_c = Core Young's modulus G_c = Core shear modulus
The wrinkling stress shows it's an instability governed by the interaction of face stiffness (E_f) and core support (E_c, G_c).
Frequently Asked Questions
You need the face sheet thickness (t_f), Young's modulus (E_f), and the distance between face sheets (d). d is the sum of the core thickness and the face sheet thickness. The bending stiffness of the core itself is usually ignored.
The effect becomes significant when the core's shear modulus (G_c) is small, or when the panel thickness is large relative to the span length (L). If the shear component accounts for 10% or more of the total deflection in the deflection breakdown graph, caution is needed.
It applies to sandwich panels with thin face sheets and a relatively stiff core. It is valid when the buckling wavelength of the face sheet is sufficiently smaller than the core thickness, and it is a theoretical formula that accounts for the elastic support effect of the core.
First, check whether the loading conditions (concentrated load or distributed load) and support conditions (simply supported or fixed) match. Next, verify whether the core's shear modulus is correct and whether the face sheet's Young's modulus has any anisotropy.
Real-World Applications
Aerospace Structures: Floor panels, wing skins, and rudders in aircraft and satellites use sandwich construction to achieve minimum weight for required stiffness and strength. A common case is a honeycomb core with carbon fiber faces, analyzed to prevent shear crimping or face wrinkling under aerodynamic loads.
Wind Turbine Blades: The long blades are essentially giant sandwich beams. The thick core (often PVC foam) provides shear resistance and keeps the aerodynamic shell profiles rigid, while the deflection formulas are critical for ensuring blade-tower clearance during operation.
Marine & Transportation: High-speed boat hulls, train interior panels, and cargo container walls use sandwich panels for stiffness, impact resistance, and thermal/acoustic insulation. Engineers must check core shear stress from slamming waves or distributed cargo loads.
Building Facades & Industrial Doors: Architectural cladding and large industrial doors use metal-faced foam core panels. The analysis ensures they don't deflect excessively under wind pressure (distributed load) and that the faces don't buckle or "oil-can" (a form of wrinkling).
Common Misconceptions and Points to Note
When starting to use this tool, there are several pitfalls that beginners often encounter. First and foremost is the idea that simply making the face sheets thicker solves everything. While increasing the face sheet thickness \(t_f\) does raise the bending stiffness \(D\), the weight also increases linearly. For example, doubling a CFRP face sheet from 1mm to 2mm improves stiffness by nearly a factor of 4, but the weight also roughly doubles. On the other hand, increasing the core thickness \(h_c\) from 10mm to 20mm results in a minimal weight increase, yet the bending stiffness \(D\)—proportional to \(d^2\)—jumps by about a factor of 4. In aerospace, where weight reduction is paramount, this "thicken the core" strategy is extremely effective.
Next is the trap of material data "representative values". The tool uses standard material properties, but actual materials vary by manufacturing lot and temperature. For instance, even "aluminum honeycomb" can have vastly different shear stiffness \(G_c\) depending on cell size and foil thickness. Rather than trusting simulation results blindly, you should develop the habit of applying a safety factor or verifying values against the material manufacturer's actual measured data sheets. Finally, the tool calculates under ideal conditions of "simply supported, center point load". Real-world conditions involve complex loading such as fixed boundaries, distributed loads, and impact loads. Use this tool strictly for initial sizing and trend understanding; for detailed design, it's a golden rule to always verify the full model using FEA (Finite Element Analysis).
Enter face sheet thickness (tf) in mm—typical values: 1.5–4 mm for fiberglass or aluminum skins
Set core height (hc) in mm—standard foam or honeycomb: 25–150 mm depending on load requirements
Input span length (l) in mm—clear distance between supports where distributed load p (N/mm) applies
Define distributed load p—enters as N/mm for uniform loading across panel width
Click Calculate to compute equivalent bending stiffness (EI), maximum deflection, core shear stress, and face wrinkling criterion
Review failure mode indicators: if wrinkling index >1.0 or core shear stress exceeds material limit, redesign geometry or upgrade core material
Worked Example
With the default CFRP faces (tf=1.5 mm), PVC Foam H60 core (hc=25 mm), panel width b=100 mm, span L=600 mm, and central point load P=2000 N, the calculator gives total deflection δ≈7.89 mm, face stress σ_f≈75.5 MPa, and core shear stress τ_c≈0.40 MPa. Safety factors are about 7.95 for the faces, 1.50 for core shear, and 2.86 for face wrinkling, all reproducible from available presets.
Practical Notes
Core shear governs short spans (<500 mm)—increase hc before thickening faces to improve shear area without excess weight in composite aerospace panels
Face wrinkling dominates when E_face/E_core ratio falls below 1000; switch to stiffer cores (aramid honeycomb, G=12 MPa) or higher-modulus faces (carbon fiber, E=160 GPa)
Deflection L/250–L/300 is typical manufacturing tolerance; sandwich panels inherently light but require careful core selection to avoid shear-dominated failure in thin-walled structures
Wet core reduces G significantly (up to 40% loss in foam)—account for moisture in marine or humid-storage applications