Finite Element Analysis of Geometric Non-Linearity in Plane Frameworks

Three methods of taking the deformed geometry of a 1-dimensional beam element into consideration in a finite element analysis are discussed. The difference between the methods is in the expression used to derive the axial strain-nodal displacements relation of the element. One method uses the expression defining the axial strain at any point in the element. The other two methods are based on the average axial strain in the element. These methods, together with a finite element theory presented, are developed into a FORTRAN 77 program and then used to analyse an aluminium toggle tested elsewhere. The results of the analysis show that the methods based on the average strain are more efficient, as reasonably accurate results are obtained even when long finite elements are used. The approach allows use of total nodal displacements rather than increments of displacement.

A.T. Salami and C.T. Morley