On Immobile Kinematic Chains and a Fallacious Matrix Analysis

Kuznetsov, E. N.

doi:10.1115/1.3176051

Cited by 7 publications

(7 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As shown by Tarnai and Szabo [16], Calladine and Pellegrino [14] and Kuznetsov [15] arrive to the identical conclusion that if a state of self-stress or combination of multiple states (when they exist) can impart positive stiffness to all mechanisms in the assembly, then the mechanisms are first-order infinitesimal and the structure can be stabilized through prestress.…”

Section: Introductionmentioning

confidence: 88%

“…Kinematically indeterminate systems containing only first-order infinitesimal mechanisms that can be stabilized through prestress are usually referred as 'prestress-stable' [13]. Methods to evaluate whether a kinematically indeterminate system is prestress-stable have been proposed, among others, by Calladine and Pellegrino [14], Kuznetsov [15] and Tarnai and Szabo [16].…”

Section: Introductionmentioning

confidence: 99%

“…Through appropriate prestress, the product forces can equilibrate the load that has excited the mechanism, which otherwise could not be taken by the structure in its original configuration. In [15], another prestress stability criterion was formulated based on kinematic constraint functions and virtual displacements. Tarnai and Szabo [16] unified and proved equivalence of the prestress stability criteria given in [14] and [15] through the formulation of a more general theory based on stationarity of the Hellinger-Reissner variational principle.…”

Section: Introductionmentioning

confidence: 99%

“…This criterion involves to verify the positive definiteness of a quadratic form which contains the mechanisms modes, and the self-stress states. Although the works in [14,15,16] gave general criteria for prestress stability, they did not offer a general and efficient numerical procedure to obtain an appropriate prestress when the structure has multiple self-stress states.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Extended integrated force method for the analysis of prestress-stable statically and kinematically indeterminate structures

Wang

Senatore

2020

International Journal of Solids and Structures

View full text Add to dashboard Cite

This paper presents a new force method to predict the structural response of statically and kinematically indeterminate systems that can be stabilized through prestress, i.e. prestressstable structures. This new force method, here named Extended Integrated Force Method (IFME), extends the existing Integrated Force Method (IFM) which is only applicable to the analysis of kinematically determinate systems. The product force concept is adopted and incorporated into the IFME to model the effect of infinitesimal mechanisms. This makes the IFME capable of dealing with cases in which the external loads contain components that cannot be taken by the system in its initial configuration. As the original IFM, the IFME bypasses the well-known concept of redundant forces and basis determinant structure of the Standard Force Method (SFM) by taking the internal forces as the independent variables which are obtained simultaneously. A proof is provided to show that, when the product force is not included in the formulation, the IFME reduces to the IFM for kinematically determinate systems and it also reduces to another force method based on singular value decomposition of the equilibrium matrix which is here named SVD-FM. Compared to the better known Displacement Method (DM), the IFME is a suitable alternative and it offers a deeper insight into the structure response which is decoupled into an extensional and an inextensional part for prestress-stable kinematically indeterminate systems. Numerical examples are carried out to test accuracy and effectiveness of the IFME on kinematically indeterminate structures with multiple self-stress states and mechanism modes. Application of the IFME to active structural control of kinematically indeterminate systems is also discussed through a numerical example.

show abstract

Section: Introductionmentioning

confidence: 88%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Extended integrated force method for the analysis of prestress-stable statically and kinematically indeterminate structures

Wang

Senatore

2020

International Journal of Solids and Structures

View full text Add to dashboard Cite

show abstract

“…A determination criterion for these systems was primarily developed by Pellegrino and Calladine (1986). Consequent discussions about this criterion (Kuznetsov, 1989;Calladine and Pellegrino, 1991) stimulated improvement of the criterion to the eventual form:…”

Section: Prestressed Mechanismmentioning

confidence: 99%