Beam on elastic foundation methods

Note These calculations are based on a beam on elastic-foundation methods. 

Beam on elastic foundation methods where the elasHc foundation is the vessel shell. 

For local loads where a partial ring stiffener is to be used to reduce local stresses, the beam on elastic foundation method provides an ideal method for sizing the partial rings or stiffener plates. The stresses in the shell must then be analyzed by another local load procedure. Shell stresses can be checked by the beam-on-elastic-foundation method for continuous radial loads about the entire circumference of a vessel shell or ring. 

Skirt construction permits radial growth of pressure vessel due to pressure and temperature through the bending of skirt acting like a beam on an elastic foundation. The choice of proper height of the skirt support ensures that bending takes place safely. Finite-element methods can be effectively used to determine the stresses and deflections due to imposed pressure and temperature distribution. 

Guo Y, Weitsman YJ (2002) Solution method for beams on nonuniform elastic foundations. J Eng Mech 128(5) 592-594... 

Another fundamental mechanics solution that has many applications in bonded joints is that of a beam on an elastic foundation. Emil Winkler first reported this analysis in 1867 [49]. The method has been widely applied to a variety of problems, perhaps most obviously that of trains passing over rails supported by the earth, and has been included in most texts on advanced mechanics of materials [16]. Since many bonded Joints have beam-like adherends supported by a more flexible adhesive layer, this model of a beam on an elastic foundation is also of great importance for a variety of joints ranging from the lap shear specimen to fracture specimens, from peel specimens to the loop tack test. 

---