A new approach for buckling analysis of axially functionally graded beams

Rychlewska, Jowita

doi:10.17512/jamcm.2015.2.10

Cited by 2 publications

(2 citation statements)

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“…Alternative approaches involve the numerical solution of equation (2) (or equivalent first-order formulations involving tangent angles and displacements) with an iterative search to find unknown initial values and buckling load. 26–28 Rychlewska 29 used a piecewise, exponential approximation of ζ, generating an eigenvalue problem incorporating continuity conditions across segments.…”

Section: Methodsmentioning

confidence: 99%

Investigating mathematical methods for high-throughput prediction of the critical buckling load of non-uniform wool fibers

Vetharaniam

Tandon

Plowman

et al. 2017

Textile Research Journal

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The sensation of prickle from textile garments is directly related to the force that a fiber protruding from the fabric surface can exert on the skin without buckling – its critical buckling load (CBL). Finite element modeling (FEM) has previously been used in the literature to predict CBLs for a set of 25 fibers with different along-fiber morphology. With a view to high-throughput analysis of fibers, we investigated two analytical methods that were potentially faster and less computationally intensive than FEM and applied them to calculate CBLs for the same set of fibers. In addition, we tested a numerical integration and gradient search (NIGS) method that we developed by adapting a previously published, non-FEM, numerical approach. The analytical methods that we tested were either inadequately formulated or prone to instability. Our NIGS method was more reliable that the analytical methods (but slower to compute), and its results appeared more accurate than the published FEM results, based on an inconsistency metric that we developed. The published FEM results and the NIGS predictions agreed within 5% for 60% of the fibers, and within 10% for 72% of the fibers (with differences ranging from 0.4% to 19.1%) and generally showed qualitative agreement on the response of CBL to fiber shape, with some notable exceptions. The response of CBL to dimensional variation was complex. This, and the inconsistency between methods, highlights the need for caution when analyzing complicated biological structures, such as wool, and the value of verifying the reliability of any predictions from any approach.

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Section: Methodsmentioning

confidence: 99%

Investigating mathematical methods for high-throughput prediction of the critical buckling load of non-uniform wool fibers

Vetharaniam

Tandon

Plowman

et al. 2017

Textile Research Journal

View full text Add to dashboard Cite

show abstract

“…The result is that the vibration problem of beams were and are the subject of the work of many authors [1][2][3][4][5][6][7][8][9][10][11]. In order to solve the linear boundary problems, the authors applied various methods, like the Green's function method [1,2], the Lagrange multiplier formalism [3,4], FEM [5,6] or others [7,8].…”

Section: Introductionmentioning

confidence: 99%