Explicit tangent stiffness matrix for the geometrically nonlinear analysis of laminated composite frame structures

In this paper, based on Von Kármán's nonlinear theory and the classical lamination theory, a closed form expression is derived for the tangent stiffness matrix of a laminated composite beam element undergoing large deformation and rotation under mechanical and hygrothermal loads. Stretching, bending and torsion have been considered. A co-rotational element reference frame is used as the Updated Lagrangian (UL) formulation. The model has been verified in different problems by comparison with the results of Nastran and ANSYS composite laminate tools, and the difference in the resulting large deformations is less than 5%. The major advantage of the proposed approach is that the composite structure is modeled using 1D beam elements rather than 2D shell or 3D solid elements as in the case of Nastran and ANSYS where laminates are defined over surfaces or 3D solids. The availability of an explicit expression for the tangent stiffness matrix makes the proposed model highly efficient specially when dealing with large composite space frame structures. The saving in computational time could reach 93% compared to regular FE software packages. The developed model is very useful for modeling and designing flexible composites used in new applications such as morphing aerospace structures and flexible robots.