Somigliana's Theorem

Somigliana's Theorem is a principle in elasticity theory that relates the displacement at a point inside a solid to the distribution of forces on its surface. It states that the displacement can be calculated by integrating the effects of surface forces, each weighted by a specific function called the kernel (or Somigliana tensor). Essentially, it allows engineers and scientists to determine how a material deforms internally based on forces applied or distributed on its surface, facilitating the analysis of how structures respond to loads without needing to examine every internal point directly.