BUCKLING ANALYSIS OF LINE CONTINUUM WITH NEW MATRICES OF STIFFNESS AND GEOMETRY

C.N Okoli, J.C. Ezeh, O.M. Ibearugbulem

Abstract: This research work present buckling analysis of line continuum with new matrices of elastic stiffness and geometric stiffness. The stiffness matrices were developed using energy variational principle. Two deformable nodes were considered at the centre and at the two ends of the continuum which brings the number of deformable node to six. The six term Taylor McLaurin’s shape function was substituted into strain energy equation and the result functional was minimized, resulting in a 6 x 6 stiffness matrix used herein. The six term shape function is also substituted into the geometric work equation and minimized to obtain 6 x 6 geometric stiffness matrix for buckling analysis. The two matrices were employed, as well as traditional 4 x 4 matrices in classical buckling analysis of four line continua. The results from the new 6 x 6 matrices of stiffness and geometry were very close to exact results, with average percentage difference of 2.33% from exact result. Whereas those from the traditional 4 x 4 matrices and 5 x 5 matrices differed from exact results, with average percentage difference of 23.73% and 2.55% respectively. Thus the newly developed 6 x 6 matrices of stiffness and geometry are suitable for classical buckling analysis of line continuum

Keywords: 6x6 stiffness system; buckling; geometry; line continuum; variational principle; deformable node; shape function; classical; numerical; analysis; beam

DOI: https://doi.org/10.15623/ijret.2014.0303044