On linearization in non-linear structural finite element analysis

A certain discussion of the traditional formulations in the non-linear finite element analysis is presented in relation to the well-known monograph of Bathe [Finite Element Procedures, Prentice Hall, 1996]. The authors derived formulas for the tangent stiffness matrix, concurrently, following the principle of virtual work and the weighted residual formulation. The observations were illustrated by an example of the 2D Timoshenko beam element. The implementation of the element, directly following the equations discussed, appeared to be very simple. The procedure can easily be applied to more complex structures.