Contribution to Linear and Nonlinear Static and Dynamic Analysis of Thin Shells by Triangular and Quadrilateral Flat Shell Finite Elements with Drilling Rotational Degree of Freedom
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2015
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Abstract
Linear and geometrically nonlinear static and dynamic finite element analysis of thin shells using
triangular and quadrilateral flat shell elements with in-plane drilling rotational degree of freedom
is presented. The flat shell elements are obtained by combining the “DKT” and “DKQ” Discrete
Kirchhoff Theory plate bending elements and membrane elements with drilling rotation. The
membrane elements developed are a quadrilateral element with drilling rotation based on the
modified HUGHES and BREZZI variational formulation and a triangular element with drilling
rotation based on the Enhanced Strain formulation.
The transient dynamic analysis is carried out using Newmark direct time integration method,
while the nonlinear analysis adopts the updated co-rotational Lagrangian description. In this
purpose, in-plane co-rotational formulation that considers the in-plane drilling rotation is
developed and presented for triangular and quadrilateral membrane elements. Furthermore, a
simple and effective in-plane mass matrix that takes into account the in-plane rotational inertia,
which permit true representation of in-plane vibrational modes is adopted. Finally, these
developments are implemented into three dimensional flat shell finite elements with six degrees
of freedom. A finite element analysis program is also developed to check the accuracy of the
developed elements.
The developed elements are first thoroughly tested for static and dynamic analysis of plane stress
problems, then, they are tested for general shell problems. The effectiveness of these elements
shown by the selected numerical examples to predict the nonlinear dynamic response of shell
structures while remains economic, is adequate to ascertain that these elements would perform
well in the case of nonlinear static and dynamic analysis of general shells.