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.

Stiffness of Reinforced Concrete Frame Members for Seismic Analysis

Abstract: Effective stiffness assumption in the modeling of reinforced concrete (RC) frame members is important for seismic design because it directly affects the building periods and dynamic response, particularly deflection and internal force distribution. Different opinions about the magnitude and governing parameters of effective stiffness persist in different national codes and literature. In this paper, parameters governing the effective stiffness of RC frame members are identified and their relative influence is determined using the three-component approach. Based on parametric study, lower-bound and upper-bound estimates of effective stiffness for the normal range of parameters in RC frame buildings are obtained and verified with experimental results. Various effective stiffness relationships and equations available in literature are also compared. Separate models for the effective stiffness of normal-strength and high-strength concrete members are proposed. The models can be used for the design of buildings without excessive computational effort.

Stress analysis of flat plates with shear using explicit stiffness matrix

Abstract: An explicit expression for the stiffness matrix is worked out for a triangular plate bending element considering the effect of transverse shear deformation. The element has twelve nodes on the sides and four nodes internal to it. The formulation is displacement type and the use of area co-ordinates makes it possible to obtain the shape functions explicitly. Separate polynomials are assumed for transverse displacement and rotations. To obtain the element stiffness matrix no matrix inversion or numerical integration need be carried out and only a few matrix multiplications of low order are necessary. The element, which is initially of thirty five degrees of freedom, can be reduced to a thirty degrees of freedom one by condensation of the internal nodes. An interesting feature of the element developed is that the values of nodal moments computed at a node point, considering different elements surrounding the node, do not vary significantly. Thus the nodal moments can be obtained directly at node points. Also, the element does not give rise to any inconvenience like locking, even for very thin plates. The straightforward approach in formation of the element stiffness will cut down the storage space considerably and will also call for less CPU time, thus making the use of the element well suited to low capacity computers. A number of plate bending problems have been worked out using the present element for different thickness to side ratios and a comparison has been made with the available results. Good accuracy has been observed in all cases, even for a small number of elements.

The buckling mode extracted from the LDLT‐decomposed large‐order stiffness matrix

Abstract: The present study proposes an innovated eigenanalysis-free idea to extract the buckling mode only from the LDLT-decomposed stiffness matrix in large-scale bifurcation analysis. The computational cost for extracting the critical eigenvector is negligible, because the decomposition of the stiffness matrix will continually be repeated during path-tracing to solve the stiffness equations. A numerical example is computed to illustrate that the proposed idea is tough enough even for multiple bifurcation. Copyright © 2002 John Wiley & Sons, Ltd.