STUDY. OF GEOMETRIC STIFFNESS MATRIX FOR 3D BEAM ELEMENT FOR STATIC AND DYNAMIC ANALYSES

Abstract

Stable structures are in equilibrium in their deformed configuration. Therefore the equilibrium equation must be satisfied in the deformed configuration of the structure. This necessitates nonlinear analysis and consideration of geometric stiffness of structural elements. Fortunately the errors in satsfying equilibrium in the undeformed configuration of the structure are likely to be small. For this reason little emphasis has been given in finite element literature in developing the geometric stiffness of structural elements. This study seeks to address this laxity by attemping to develop the geometric stiffness of truss and beam elements. Toward this end, an effort has been made to derive elastic and geometric stiffness matrices for plane truss, plane -beam, space truss and space beam elements. The elastic stiffness matrix for the elements is derived by the use of matrix relating structure to global forces which. is advantageous for use on computers in storage and computation. The, geometric stiffness due to axial loads on elements is derived. The geometric stiffness matrix of space beam is derived by including the effects of torsion. The geometric stiffness due to effects of torsion can produce considerable effects in high deformable' structures like, piping systems, thin shells and many others. A brief review. of application of geometric stiffness matrix along with elastic stiffness matrix is also presented.