geometrically nonlinear

hello Dear friends

I am working on geometrically nonlinear behavior of 2D beam.

I used field consistent approach using total lagrangian. because of field consistency, satisfication tangent stiffness matrix is dependent to tangant of node angles. this means that when beam is subjected to pure bending when angle of rotation approches to 90 degree, tangent stiffness matrice become singular. can any one give solution to this problem. how about corotational formulation.

thanks a lot.

best regards.