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A non-linear element for analysing elastic frame structures at large deflections

A non-linear finite element for analysing elastic frame structures at large deflections is presented. A co-rotational technique combined with Classical beam theory with the inclusion of the effect of axial forces is adopted. The element nodal force vector is derived from the strain energy of the element. | Vietnam Journal of Mechanics, NCST of Vietnam Vol. 22, 2000, No 1 (19 - 28) A NON-LINEAR ELEMENT FOR ANALYSING ELASTIC FRAME STRUCTURES AT LARGE DEFLECTIONS NGUYEN DINH KIEN Institute of Mechanics, 264 Doi Can, Hanoi '. ABSTRACT. A non-linear finite element for analysing elastic frame structures at large deflections is presented. A co-rotational technique combined with Classical beam theory with the inclusion of the effect of axial forces is adopted. The element nodal force vector is derived from the strain energy of the element. The element tangent stiffness matrix is obtained by differentiating the nodal force vector , with respect to the degree of freedom (d.o.f.). The obtained formulations have a simple and compact mathematical forms which are easy to implement into a computer program. An incremental interactive technique based on Newton-Raphson method is adopted to solve the non-linear equation and to trace the equilibrium paths of the structures. Numerical examples are presented to show the accuracy and efficiency of the proposed formulations. 1. Introduction The use of finite element method in engineering practice is increasing rapidly. This trend is observed because the integrated use of finite element softwares in CAD can have a significant benefit on-the productivity of a design team, increase the funct ionality of the design and decrease its cost [1]. Lately, the finite element method has proven to be very effective in linear analysis [2], and the solutions have also been obtained for some non-linear prob• lems [3]. However, much research is now underway to solve the problems of the continuum mechanics and to improve the finite element formulations as well as numerical integration procedures and computer program implementation. In the field of structural mechanics, the analyses of beam and frame structures are of great importance. With the fast development of computational technology, and the importance of the beam and frame structures in practical