A Comparison Between 7- and 12-Parameter Shell Finite Elements for Large Deformation Analysis

Abstract

In this study two continuum shell finite elements are developed. The first one is based on the first-order shear deformation theory with seven independent parameters and the second one is based on the third-order thickness deformation theory with twelve independent parameters. Continuum shell finite elements are developed and utilized in the numerical simulations of isotropic, laminated composite, and functionally graded structures undergoing large deformations. High-order spectral interpolation of the field variables is used to avoid all forms of numerical locking, allowing the development of robust shell elements in a purely displacement based setting.

This thesis includes static and transient analysis of various structures using aforementioned two shell elements. This is the first time that the seven-parameter formulation is used to compute a full transient response of shell structures. Deflections and maximum stresses are computed and compared between the two formulations and, in some cases, also with the results obtained using commercial codes ANSYS and ABAQUS. Furthermore, the influence of the variation of the temperature through the thickness for functionally graded shells is studied. In all the simulations, static condensation of degrees of freedom associated with the internal nodes of the element is implemented, which allows us to reduce the computational time and make use of parallel computation when this feature is available. This makes the higher-order elements used computationally competitive with standard finite elements.