New Semi-Analytical Shell Elements

New semi-analytical shell elements are developed using the scaled boundary finite element method. A shell element is treated as a three-dimensional continuum whose midsurface, the generalized “boundary” of the continuum, is characterized with a quadrilateral spectral element. It is along the thickness direction ξ that the midsurface is scaled to represent the three-dimensional geometry and that the analytical displacement solution is sought. Neumann expansion is used to approximate the inverse of the Jacobian as a quadratic matrix polynomial of ξ while the assumed natural strain method is applied to alleviate the shear and membrane locking. The virtual work principle considering body forces is utilized to derive the scaled boundary finite element equation, which is directly solved via the differential quadrature method. Numerical examples show that the shell elements with five displacement sampling points along ξ can efficiently analyze thin to very thick general shells.