NONLINEAR BENDING OF BEAMS USING
THE FINITE ELEMENT METHOD
Computers and Structures, (1977)Аннотация
In this paper a finite element formulation for determining the finite deflection of thin bars is presented.
The nonlinear stiffness equations are generated after simple approximate expressions involving the nodal
parameters are used to replace the nonlinear terms in the energy functional. The procedure used results in a
simplified set of nonlinear algebraic equations which are more amenable to solution than the equations usually
presented. The applicability and accuracy of the method together with an evaluation of three incremental solution
techniques, a step by step method. a one step Newton-Raphson procedure, and a variable interpolation technique
is demonstrated by solving a cantilever beam with a point load acting on the end. Curves showing the sensitivity to
increment size and to the number of elements are also presented. The results indicate that the formulation is
accurate and inexpensive in terms of computational effort.
