Buckling of non-uniform beams by a direct functional perturbation method

Totry, Essam; Altus, Eli; Proskura, Aleksey

doi:10.1016/j.probengmech.2006.08.002

Cited by 14 publications

(7 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Exact, closed-form solutions for w and β are not generally available, although solutions to equation (2) have been calculated for a few special cases. 14–19 A number of analytical approaches have been used to obtain approximate solutions, including a functional perturbation method involving convolutions of ζ with Green’s functions, 20 application of the variational iteration method (VIM), 12,21,22 homotopy analysis 23 or by assuming a power series solution to w and generating linear relations to identify coefficients. 13,15…”

Section: Methodsmentioning

confidence: 99%

“…Exact, closed-form solutions for w and are not generally available, although solutions to equation (2) have been calculated for a few special cases. [14][15][16][17][18][19] A number of analytical approaches have been used to obtain approximate solutions, including a functional perturbation method involving convolutions of with Green's functions, 20 application of the variational iteration method (VIM), 12,21,22 homotopy analysis 23 or by assuming a power series solution to w and generating linear relations to identify coefficients. 13,15 Numerical approaches other than FEM have been used to investigate column buckling, such as the boundary element 24 and differential quadrature 25 Representation of the buckling problem for a textile fabric against skin, where the fiber length has been normalized to the unit length, and the fiber is subject to a normalized force, , by the skin, with buckling occurring if this force is greater than or equal to the normalized critical buckling load, cr , of the fiber.…”

Section: Solution Approaches Alternative To Femmentioning

confidence: 99%

See 1 more Smart Citation

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

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.

show abstract

Section: Methodsmentioning

confidence: 99%

Section: Solution Approaches Alternative To Femmentioning

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

“…As can be seen from the literature survey mentioned, there are several studies consisting of buckling analyses of the FG beams. In addition, there are various method for buckling analysis, such as localized differential quadrature method [7] semi-inverse method [8], functional perturbation method [9], variational iteration method [10], homotopy perturbation method [11], integral-equation approach [12], and exact dynamic stiffness method [13] etc. In the study presented, the mechanical buckling behavior of multi-layered functionally graded beams in the axial direction was investigated under clamped-clamped (C-C) boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

Investigation of Effects of Layer Positions on Mechanical Buckling Behavior of Axially Layered Functionally Graded Beams

Evran¹

2019

Pamukkale J Eng Sci

View full text Add to dashboard Cite

ÖzThe aim of this research is to examine the mechanical buckling behavior of multi-layered functionally graded beams in the axial direction. Numerical buckling analyses were performed using finite element software called ANSYS. Each beam configuration is suggested to be three layers prepared using various percent volume fractions of Zirconia (ZrO2) and Aluminum (Al) materials. The levels of layers and layer positions of the beams were evaluated according to Taguchi's L9 (3 3 ) orthogonal array technique. Layers were determined as control factor and so nine numerical analyses were performed under clampedclamped boundary conditions. The first mode shapes of the axially layered functionally graded beams were demonstrated in order to detect the most affected layers as visually. Analysis of signal-to-noise ratio was applied to obtain the optimum levels of layers. Analysis of Variance (ANOVA) was employed to solve the layers with significant impacts and their percent contributions on numerical results. The maximum buckling load was determined using various positions of layers with the optimum levels obtained based on Taguchi methodology.Bu araştırmanın amacı eksenel yönde çoklu tabakalı fonksiyonel derecelendirilmiş kirişlerin mekanik burkulma davranışlarını incelemektir. Sayısal burkulma analizleri ANSYS olarak bilinen sonlu elemanlar yazılımı kullanılarak gerçekleştirilmiştir. Her kiriş konfigürasyonu Zirkonyum (ZrO2) ve Alüminyum (Al) malzemelerinin değişik yüzde hacim fraksiyonları kullanılarak hazırlanmış üç tabaka olarak önerilmiştir. Tabaka seviyeleri ve kirişlerin tabaka pozisyonları Taguchi L9 (3 3 ) ortogonal dizi tekniğine göre incelenmiştir. Tabakalar kontrol faktörleri olarak değerlendirildi ve böylece dokuz sayısal analiz tutulu-tutulu sınır şartları altında gerçekleştirildi. Görsel olarak en çok etkilenen tabakaları tespit etmek için eksenel yönde tabakalı olarak fonksiyonel derecelendirilirmiş kirişlerin birinci mod şekilleri gösterildi. Tabakaların optimum seviyelerini elde edebilmek için sinyal-gürültü oran analizi kullanıldı. Sayısal sonuçlar üzerinde önemli etkilere sahip tabakalar ve onların yüzde katkı oranlarını çözmek için Varyans Analizi (ANOVA) uygulandı. En yüksek burkulma yükü Taguchi metodolojisine bağlı elde edilen optimum seviyeli tabakaların değişik pozisyonları kullanılarak karar verildi.

show abstract

“…The solution of natural frequencies and mode shapes of non-homogeneous rods and beams was studied based on the FPM in 2007 [14]. Also in the same year the buckling load of heterogeneous columns has been found by applying the FPM directly to the buckling differential equation in [18]. The FPM is generalized in [19] for solving eigenvalue functional differential equations in 2008.…”

Section: Introductionmentioning

confidence: 99%

A new approximation method to solve boundary value problems by using functional perturbation concepts

Pourghanbar

Ranjbar

2018

B Soc Paran Mat

View full text Add to dashboard Cite

Functional perturbation method (FPM) is presented for the solution of differential equations with boundary conditions. Some properties of FPM are utilized to reduce the differential equation with variable coefficients to the equations with constant coefficients. The FPM can be applied directly for many types of differential equations. The exact solution is obtained by only the first term of the Frechet series for polynomial cases. Four examples are included to demonstrate the method.

show abstract

Buckling of non-uniform beams by a direct functional perturbation method

Cited by 14 publications

References 15 publications

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

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

Investigation of Effects of Layer Positions on Mechanical Buckling Behavior of Axially Layered Functionally Graded Beams

A new approximation method to solve boundary value problems by using functional perturbation concepts

Contact Info

Product

Resources

About