Large curvature analysis of two-dimensional linear elastic frames by direct stiffness method /|cJongaphonh Douanevanh

Abstract

This thesis presents an efficient semi-analytical technique based upon the co-rotational formulation and the direct stiffness strategy for large displacement and rotation analysis of two-dimensional, linearly elastic, extensible frames of general geometries and subjected to general loading conditions. The technique exploits the standard direct stiffness procedure to systematically set up the governing equations for the entire structure. In the formulation, a set of nonlinear differential equations derived from the exact curvature-displacement relationship is employed to construct an equivalent set of nonlinear algebraic equations governing the behavior of a straight prismatic member. Such governing equations are employed first to obtain the force-displacement relation and the corresponding gradient matrix for a member in its co-rotational coordinate system. Such basic results are then utilized along with the co-rotational approach to develop the exact element tangent stiffness matrix and the force-displacement relation for a generic member. The direct assembly algorithm is then used to obtain the exact tangent stiffness matrix and exact load residuals for the structure. These two components are essential in the solution procedure for a large system of nonlinear equations by Newton-Raphson iterative scheme. Several examples have been selected in the numerical experiments to verify both the formulation and implementation and it can be concluded that the proposed technique yields numerical results comparable to analytical solutions without refining the discretization.