Geometrically nonlinear analysis of plane trusses and plane frames
The results of this work are the closed-form expressions for the tangent and secant stiffness matrices of the 3-node Mindlin frame element. From the study of two solution methods and the behavior of the three elements, several conclusions have been made as follows:
Because the Mindlin frame element uses quadratic polynoms for the interpolation functions, at least two elements are needed for modelling a member of a plane frame structure.
The Mindlin frame element will give a more flexible structure due to the shear deformation effect, but the effect is not always significant.
The Mindlin frame element requires about twice degree-of-freedoms than the Bernoulli-Euler frame element requirement.
The formulation of tangent stiffness matrix can be simplified, in condition that the internal forces calculations are done using the appropriate nonlinear formulation. The calculation of the tangent stiffness matrix and the internal element forces can be done using different formulations.