On implementation of a nonlinear four node shell finite element for thin multilayered elastic shells (Q1904911)

The authors present a simple nonlinear stress resultant four node shell finite element. The underlying shell theory is developed from three-dimensional continuum theory via standard assumptions on the displacement field. A model for thin shell is obtained by approximating terms describing the shell geometry. The rotation of the shell director is parameterized by two Euler angles, although other approaches can also be easily accomodated. A procedure is provided to extend the presented approach by including the through-thickness variable material properties. These may include a general nonlinear elastic material with varying degree of orthotropy, which is typical for fibre reinforced composites. Thus a simple and efficient model suitable for analysis of multilayered composite shells is obtained. Shell kinematics is consistently linearized, leading to the Newton-Raphson numerical procedure, which preserves quadratic rate of asymptotic convergence. A range of linear and nonlinear tests is provided and compared with available solutions to illustrate the approach.