Theory of matrix structural analysis

On derivation of timoshenko beam stiffness equation

This paper deals with the free vibration of Timoshenko columns with attached masses having rotary inertia. The support of the model is elastically restrained against rotation. The concept of fixity factor is used to define the stiffness of the elastic connection relative to that of the column. The governing equation of the column elements is solved by applying the separation of variables method in the transfer matrix method (TMM) algorithm. The same problems are solved, also, by finite element method (FEM) algorithm in which the matrices in equation of motion are obtained for Timoshenko column, and the results are compared with the ones of TMM. The comparison graphs are presented in numerical analysis to show the effectiveness of the considered methods, and it is resulted that FEM gives closer results to TMM.

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Free vibration analysis of elastically supported Timoshenko columns with attached masses by transfer matrix and finite element methods

Polymer composite materials reinforced by continuous fibers have excellent in-plane strength but are usually weak against delamination. The current study has provided a FEM model with using carbon nanotubes to improve the interlaminar fracture properties of composites. A full 3-D multiscale finite element model consisting of a carbon nanotube, inter-phase, surrounding polymer and cohesive layer was built using ANSYS commercial package. The cohesive layer was constructed using cohesive zone method (CZM), which is a commonly used method to investigate delamination analysis. The inter-phase region was represented by van der Waals interactions. In addition, the critical energy release rates of mode-I delamination (GIC) were characterized for nanocomposite specimens and for those with pure resin. Significant improvement in GIC was consistently observed.

Effect of CNT on the Delamination Resistance of Composites

The solution of the equality constrained least squares problem is considered $\min _{x \in R^n } ||f - Ex||_2 $ subject to $Cx = g$ is considered. It is shown that for well-conditioned or moderately ill-conditioned problems of this form, the deferred correction procedure of Van Loan [SIAM J. Numer. Anal., 22 (1985), pp. 851–864] can be made to converge in two iterations.The implementation suggestions due to Barlow [SIAM.J. Numer. Anal., 25 (1988), pp. 1340–1358] are modified to obtain a more robust strategy. This modification was discovered in numerical experiments to verify the quick convergence proven in this paper. The new implementation seems to always obtain the predicted convergence behavior.

Theory of matrix structural analysis

Citations

On derivation of timoshenko beam stiffness equation

Free vibration analysis of elastically supported Timoshenko columns with attached masses by transfer matrix and finite element methods

Effect of CNT on the Delamination Resistance of Composites

A note on deferred correction for equality constrained least squares problems

Computer analysis of rigid frames

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