A numerical method for static or dynamic stiffness matrix of non-uniform members resting on variable elastic foundations

Girgin, Z. Canan; Girgin, Konuralp

doi:10.1016/j.engstruct.2005.04.005

Cited by 9 publications

(5 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The element has three degrees of freedom at each node: translations in the nodal x and y directions and rotation about the nodal z-axis. The obtained result of stability analysis of case c is compared with the buckling load evaluated by matrices solution proposed by Girgin and Girgin [27] whereas, in the case of tapered column, the linear buckling load acquired by present method is verified with results obtained by numerical method proposed by Soltani et al [28]. The relative errors ( (%)  ) between the results of present study and the abovementioned methods are also calculated.…”

Section: -1 Examplesupporting

confidence: 58%

Elastic stability of columns with variable flexural rigidity under arbitrary axial load using the finite difference method

Soltani

Sistani

2017

NMCE

View full text Add to dashboard Cite

In this paper, the finite difference method (FDM) is applied to investigate the stability analysis and buckling load of columns with variable flexural rigidity, different boundary conditions and subjected to variable axial loads. Between various mathematical techniques adopted to solve the equilibrium equation, the finite difference method, especially in its explicit formulation, requires a minimum of computing stages. This numerical method is therefore one of the most suitable and fast approaches for engineering applications where the exact solution is very difficult to obtain. The main idea of this method is to replace all the derivatives presented in the governing equilibrium equation and boundary condition equations with the corresponding forward, central and backward second order finite difference expressions. The critical buckling loads are finally determined by solving the eigenvalue problem of the obtained algebraic system resulting from FDM expansions. In order to illustrate the correctness and performance of FDM, several numerical examples are presented. The results are compared with finite element results using Ansys software and other available numerical and analytical solutions. The competency and efficiency of the method is then declared.

show abstract

Section: -1 Examplesupporting

confidence: 58%

Elastic stability of columns with variable flexural rigidity under arbitrary axial load using the finite difference method

Soltani

Sistani

2017

NMCE

View full text Add to dashboard Cite

show abstract

Section: -1 Examplesupporting

confidence: 53%

Application of discretization error estimators in stepped column buckling problems

Souza¹,

Fernandes²,

Anflor³

et al. 2021

RIMNI

View full text Add to dashboard Cite

In order to reduce the discretization error, in this paper, Richardson’s Extrapolation and Convergence Error Estimator were used to investigating the buckling problem convergence. The main objective was to verify the convergence order of the stepped column problem and to define a consistent moment of inertia at the point of variation of the cross-section. The variable of interest was the critical buckling load obtained by the Finite Difference Method. The convergent solution obtained errors less than 10-8, and this work showed that the best solution is not defined by excessive mesh refinement, but by the solution convergence analysis.

show abstract

“…Wang et al (2005) presented a paper for comprehensive review of state-of-art on the analysis of beams and plates resting on elastic foundations considering the interaction of between structure and supporting soil media. Z. C. Girgin and K. Girgin (2005) represented the numerical method focusing non-uniform beam-columns on resting on variable one-or two-parameter elastic foundations or supported by no foundation; a variable iterative algorithm is developed for computer application of the method. Z. C. Girgin and K. Girgin (2006) proposed a generalized numerical method for non-uniform Timoshenko beam-columns subjected to several effects through a unified approach based on the Mohr method.…”

Section: Introductionmentioning

confidence: 99%

Simplified formulations for the determination of rotational spring constants in rigid spread footings resting on tensionless soil

Girgin

2017

Journal of Civil Engineering and Management

View full text Add to dashboard Cite

In spread footings, the rotational spring constants, which represent the soil-structure interaction, play an important role in the structural analysis and design. To assign the behaviour of soil, which is generally represented via Winkler-type tensionless springs, necessitates time consuming iterative computing procedures in practice. In this study, a straightforward approach is proposed for the soil-structure interaction of rigid spread footings especially subjected to excessive eccentric loading. By considering the uplift of footing, the rotational spring constants of those type footings under axial load and biaxial bending are easily attained through the proposed simplified formulations. Since these formulations enable manual calculation, iterative computer efforts are not required. The formulations under consideration can be applicable to symmetric and non-symmetric rigid spread footings. The numerical results of this study are verified with SAP2000.

show abstract

A numerical method for static or dynamic stiffness matrix of non-uniform members resting on variable elastic foundations

Cited by 9 publications

References 25 publications

Elastic stability of columns with variable flexural rigidity under arbitrary axial load using the finite difference method

Elastic stability of columns with variable flexural rigidity under arbitrary axial load using the finite difference method

Application of discretization error estimators in stepped column buckling problems

Simplified formulations for the determination of rotational spring constants in rigid spread footings resting on tensionless soil

Contact Info

Product

Resources

About