Direct stiffness method

About: Direct stiffness method is a research topic. Over the lifetime, 2584 publications have been published within this topic receiving 53131 citations.

Identification of Stiffness Reductions Using Natural Frequencies

Abstract: A technique is presented for the identification of localized reductions in the stiffness of a structure using natural frequency measurements. The sensitivities of the eigenvalues to localized changes in the stiffness have been developed as a set of underdetermined equations. These equations have been used as the constraints in an optimization problem, which minimizes one of three criteria: (1) the changes in the element stiffnesses; (2) the norm of the changes to the global stiffness matrix; or (3) the residuals of the eigenvalue problem. An additional constraint, which forces the stiffness to always decrease due to damage, places the optimization problem in the realm of nonlinear programming. The overall formulation has provided a useful method to identify damage with a small number of measured natural frequencies. Ten to 90% localized reduction in stiffness was successfully identified in a 10-story, two-bay steel frame. The method was verified using test data from an aluminum, cantilever beam.

Analysis of Axisymmetrical Shells by the Direct Stiffness Method

Abstract: A method for the structural analysis of shells of revolution, composed of materials with orthotropic properties, is discussed. The development is based on the direct stiffness method. A truncated cone element is introduced to take advantage of symmetry. Derivations of the stiffness and stress matrices for the truncated cone element are given. Several examples are solved on the digital computing machine using a program that is based on the truncated cone element. The results are compared to other theoretical results, and the correlation is excellent. Extension of the technique to handle linear unsymmetric deformation and nonlinear symmetric deformation is discussed.

Derivation of a new stiffness matrix for helically armoured cables considering tension and torsion

Abstract: A new element stiffness matrix is derived for straight cable elements subjected to tension and torsion The cross-section of a cable, which may consist of many different structural components, is treated in the following as a single composite element The derivation is quite general; consequently, the results can be used for a broad category of cable configurations Individual helical armourning wires, for instance, may have unique geometric and material properties In addition, no limit is placed on the number of wire layers Furthermore, compressibility of the central core element can also be considered The equations of equilibrium are first derived to include ‘internal’ geometric non-linearties produced by large deformations (axial elongation and rotatioin) of a straight cable element These equations are then linearized in a consistent manner to give a liner stiffness matrix Linear elasticity is assumed throughout Excellent agreement with experimental results for two different cables validates the correctness of the analysis