Graph Theoretical Methods for improving The conditioning of Flexibility Matrix of Structures

Document Type : پژوهشی

Authors

• farzad Dizaji
• mostafa Khanzadi

10.22067/civil.v22i1.9032

Abstract

In addition to reducing the size and time of analyses, reduction of analytical errors is one of the most important considerations in ideal analysis of skeletal structures by computer. Appropriate matrixes with more zeros (sparse), well structure, and well condition are helpful for this aim. Therefore, an optimizing problem with multiple objectives will be considered.The objective of this research is reducing the analytical errors such as rounding errors in flexibility matrixes of skeletal structures by performing more constant and proper algorithm. These errors increase in special structures with unsuitable flexibility matrixes; the structures with different stiffnesses are one of the most prevalent examples for this case.Use of weak elements leads into high non-diagonal terms in flexibility matrix, which result in analytical errors. In numerical analysis, ill-condition of a matrix is soluble by movement or substitution of the rows; then specification and implementation of these changes before forming the flexibility matrix has been studied. By identifying cycle bases with specific qualities, simple typological and algebraic properties have been used basically in analyses for this purpose. In conclusion, stiffness matrixes with optimally condition number are obtainable and analytical errors reduce.

Keywords

• Graph Theory Methods
• Force Method
• Well Conditioning of Structural Matrices

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