CEGNL-Complete Expressions for Geometric Nonlinear Analysis

A unified method to obtain a complete tangent stiffness matrix and shape functions for 3D geometric nonlinear analysis.

Contains functions to reach complete tangent stiffness matrix and interpolation functions of a spatial bar element in directly way. The stiffness matrix can be implemented in a structural analyses software to solve nonlinear problems, and the interpolation functions can be used in graphics programs to draw the deformed shape of the structure. The formulation contains the infinitesimal element nonlinearity, the higher-order terms in the strain tensor, finite rotations, and also, the shear deformation (Timoshenko bending theory). The method provides an element efficient to predict the critical load buckling for spatial structures with small slenderness and with interaction between axial and torsion effects considering just one element in each member or a reduced discretization.