Tangent stiffness matrix

About: Tangent stiffness matrix is a research topic. Over the lifetime, 1031 publications have been published within this topic receiving 21140 citations.

Non‐linear earthquake‐response analysis of long‐span cable‐stayed bridges: Applications

Abstract: The dynamic non-linear behaviour of three-dimensional long-span cable-stayed bridges under seismic loadings is studied. The cases of multiple-support as well as uniform seismic excitations of these long and flexible structures are considered. Different sources of non-linearity for such bridges are included in the analysis, as outlined in the companion paper. In this accompanying analysis a tangent stiffness iterative procedure is utilized to estimate the non-linear seismic response. Numerical examples are presented in which a comparison between a linear earthquake-response analysis (based on the utilization of the tangent stiffness matrix of the bridge at the dead-load deformed state which is obtained from the geometry of the bridge under gravity load conditions) and a non-linear earthquake response analysis using the step-by-integration procedure is made. In these examples two three-dimensional bridge models representing recent and future trends in cable-stayed bridge design are utilized. The study sheds some light on the salient features of the seismic analysis and design of these long contemporary bridges. In addition, parameters affecting the seismic response of these bridges are discussed: other factors considered are non-linearity, uniformity and spatial variation of ground motion inputs and structural configuration.

Modeling of wave propagation in layered piezoelectric media by a recursive asymptotic method

Abstract: In this paper, a simple asymptotic method to compute wave propagation in a multilayered general anisotropic piezoelectric medium is discussed. The method is based on explicit second and higher order asymptotic representations of the transfer and stiffness matrices for a thin piezoelectric layer. Different orders of the asymptotic expansion are obtained using Pade approximation of the transfer matrix exponent. The total transfer and stiffness matrices for thick layers or multilayers are calculated with high precision by subdividing them into thin sublayers and combining recursively the thin layer transfer and stiffness matrices. The rate of convergence to the exact solution is the same for both transfer and stiffness matrices; however, it is shown that the growth rate of the round-off error with the number of recursive operations for the stiffness matrix is twice that for the transfer matrix; and the stiffness matrix method has better performance for a thick layer. To combine the advantages of both methods, a hybrid method which uses the transfer matrix for the thin layer and the stiffness matrix for the thick layer is proposed. It is shown that the hybrid method has the same stability as the stiffness matrix method and the same round-off error as the transfer matrix method. The method converges to the exact transfer/stiffness matrices essentially with the precision of the computer round-off error. To apply the method to a semispace substrate, the substrate was replaced by an artificial perfect matching layer. The computational results for such an equivalent system are identical with those for the actual system. In our computational experiments, we have found that the advantage of the asymptotic method is its simplicity and efficiency.