A Triangular Finite Element for the Geometrically Nonlinear Analysis of Composite Shells

摘要

This paper is devoted to the development of a new geometrically nonlinear finite element for composite-material shell structures. rnA unique approach for deriving the geometric stiffness matrix is presented. It is based on load perturbation of the linear discrete equilibrium equations and defines the geometric stiffness matrix as the gradient of the element nodal force vector in global coordinates. Because of obvious difficulties in taking derivatives of the rotation matrix with respect to the nodal coordinates, all evaluations are performed in the local coordinate system. The out-of-plane geometric stiffness matrix is introduced to circumvent the need of rotation matrix derivatives. Buckling is detected by monitoring the tangent stiffness matrix throughout the incremental analysis process. Stress retrieval is performed using linear, kinematic and constitutive, relationships because the resulting pure deformations are small due to efficient unique procedures for the removal of rigid body displacements and rotations. rnFinally the presented finite element was coded in FORTRAN and a few examples were run.