Vibrations of thick plates and shells - Bridle, Michael D.J. (1973)
Using an asymptotic series approach, a thick shell theory is proposed for doubly curved sheIls with variable thickness. This theory includes the effects of transverse shear stresses and rotatory inertia. The displacement functions are designed to give non-zero transverse shear stresses internal to the shell, which satisfy the stress-free boundary conditions on the upper and lower surface. Use of the stress-free conditions makes the displacement functions, which vary through the thickness of the shell, dependent only on the middle surface displacements. This theory is applied to the twisted plate. A similar approach is applied to the cylindrical shell, but the effects of transverse normal stress are also included.