Iterative solution of large structures

Behravesh, A.; Kaveh, A.

doi:10.1016/0045-7949(90)90347-5

Cited by 2 publications

(3 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Behravesh and Kaveh (Behravesh and Kaveh, 1990) explained the relationship between moment distribution and Kani methods and a numerical iterative procedure, and showed that the calculation trends in these two methods are similar to the Jacobi iteration procedure that has been used to solve the equations of classical displacement. The Jacobi iteration approach in both methods is converged, if the stiffness matrix is diagonally dominant.…”

Section: Latin American Journal Of Solids and Structures 12 (2015) 25mentioning

confidence: 98%

“…If the magnitude of the diagonal entry in each row exceeds the sum of the magnitudes of the non-diagonal entries in that row, the matrix is called diagonally-dominant. In fact, matrix A is strictly diagonally dominant if (Behravesh and Kaveh, 1990;Datta, 2010). Where, a ୧୨ denotes the entry in the ith row and jth column.…”

Section: The Jacobi Schemementioning

confidence: 99%

“…In addition, the Gaspar Kani's method (Kani, 1957) which is used in structural analysis, uses iterative procedures to solve the slope deflection equations system (Behravesh and Kaveh, 1990). In the moment distribution method, the unknowns (end moments of structural members) are obtained through performing iteration on their changes (increments), whereas in the Kani method, the iteration procedure is applied on the unknowns themselves.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A New Jacobi-based Iterative Method for the Classical Analysis of Structures

Mirfallah

Bozorgnasab

2015

Lat. Am. j. solids struct.

View full text Add to dashboard Cite

Traditionally, classical methods of structural analysis such as slope-deflection and moment distribution methods (Cross method) are used for primary analysis of structures and also controlling the results of computer programs. The main objective of this paper is to introduce a new method for classical computing and extending it to a matrix formulation. The proposed approach, named the "Slope Distribution Method (SDM)", is based on a Jacobi iterative procedure, in which without forming the system of linear equations, structural displacement values are obtained. Also, to make the method applicable and to use it in computer softwares, the matrix formulation of the approach is developed, where there is no need for iterative procedures and the nodal rotations are obtained through solving only one matrix equation. The SDM is able to analyze frames with non-vertical columns and those with nodal vertical displacement. Whereas current analysis softwares have some elimination for the analysis of non-prismatic members, the proposed method can be applied to analyze structures with any non-prismatic member. The SDM process is also developed for the analysis of dual lateral load resisting systems (moment resisting frames with other lateral load resisting elements such as bracings and shear walls). The advantages of the method over previous ones and also, its accuracy and reliability are presented through the article.

show abstract

Section: Latin American Journal Of Solids and Structures 12 (2015) 25mentioning

confidence: 98%

Section: The Jacobi Schemementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation