Have you ever wondered how aircraft interiors and Formula 1 cars are so stiff and light? The secret is sandwich panels. Sandwich panels are used whenever lightness and stiffness are required for a flat or irregular shape. The main theory behind sandwich panels is the concept of mass moment of inertia. Increasing the mass moment of inertia directly increases the stiffness. So how do you increase the mass moment of inertia while keeping weight down?
First, let's consider a solid carbon fiber plate. Thicker plates will be stiffer, but not just because there is more material. When layers are further from the center (commonly called the neutral axis) they contribute more stiffness. Consider two tubes of different diameter. The large diameter tube will be stiffer than the small diameter tube, even if the amount of materials in them is equal! This is because the larger diameter tube has more material further from the center.
An I-beam works using the same principal. The web of the I-beam (the skinny center section) holds the flanges (the end pieces) far from the center, making the beam much stiffer than a solid plate using the amount of material. (See Figure 1.)