Frame nonlinear analysis by force method

The focus of this paper is on the force-based finite element for analysis of planar frames. Both material and geometrical nonlinear behavior are considered in this study. The formulations are based on the two-field Hellinger-Reissner functional. Nonlinear effects of the internal forces interactions are considered by using 2D tangent material stiffness and fiber discretization technique. Due to presence of the rigid body modes in the global coordinates, the element is formulated in a basic coordinate system. Corotational approach transforms responses of the basic coordinate system to the global one and makes the element applicable for structures with arbitrarily large rigid body displacements and rotations. Moreover, shear-locking problem is removed in this formulation. Two iterative and non-iterative algorithms for the element state determinations are proposed. Finally, the new element accuracy and also efficiency are verified by some numerical examples.