A modular modeling approach for investigating wool critical buckling from biologically variable along-fiber microstructure

2020 ◽  
pp. 004051752094461
Author(s):  
Indrakumar Vetharaniam ◽  
Jeffrey E Plowman ◽  
Peter Brorens ◽  
Duane Harland
Keyword(s):  
Cross Sections ◽  
Cortical Cell ◽  
Numerical Approach ◽  
Buckling Load ◽  
Cell Type ◽  
Fiber Morphology ◽  
Arbitrary Length ◽  
Critical Buckling Load ◽  
Modeling Approach ◽  
Fiber Microstructure

Mammalian hair fibers are internally sophisticated. We introduce a modeling approach aimed at use in research that derives value from understanding how microstructural organization generates effects at the macroscopic level in the context of natural biological variation. Critical buckling load is solved using a numerical approach applied to a modular fiber microstructure model where fibers of arbitrary length are made up of snippets composed of serial cross-sections at 25 micrometer intervals. As an example, the model is applied to investigate how much effect changes to single microstructural properties (fiber ellipticity, cortical cell type distribution and cell type proportion) have on critical buckling load in the context of prickle. Potential uses and key weak areas in our knowledge of wool fiber morphology and biophysics are discussed.

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

2017 ◽  
Vol 88 (9) ◽  
pp. 1002-1012 ◽  
Author(s):  
Indrakumar Vetharaniam ◽  
Surinder Tandon ◽  
Jeffrey E Plowman ◽  
Duane P Harland
Keyword(s):  
High Throughput ◽  
Analytical Methods ◽  
Numerical Approach ◽  
Buckling Load ◽  
Fiber Morphology ◽  
Mathematical Methods ◽  
High Throughput Analysis ◽  
Critical Buckling Load ◽  
Computationally Intensive ◽  
Fabric Surface

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.

scholarly journals Buckling of nanobeams and nanorods with cracks

2019 ◽  
Author(s):  
Hina Arif ◽  
Jaan Lellep
Keyword(s):  
Cross Sections ◽  
Nonlocal Theory ◽  
Theory Of Elasticity ◽  
Buckling Load ◽  
Buckling Loads ◽  
Critical Buckling Load ◽  
Piecewise Constant ◽  
Cracklike Defects ◽  
General Method

Buckling of nanobeams and nanorods is treated with the help of the nonlocal theory of elasticity. The nanobeams under consideration have piecewise constant dimensions of cross sections and are weakened with cracks or cracklike defects emanating at the re-entrant corners of steps. A general method for determination of critical buckling loads of stepped nanobeams with cracks is developed. The influence of defects on the critical buckling load is evaluated numerically and compared with similar results of other researchers.

Strongest Columns and Isoperimetric Inequalities for Eigenvalues

1962 ◽  
Vol 29 (1) ◽  
pp. 159-164 ◽  
Author(s):  
I. Tadjbakhsh ◽  
J. B. Keller
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Ordinary Differential Equations ◽  
Cross Sections ◽  
Isoperimetric Inequalities ◽  
Second Order ◽  
Buckling Load ◽  
The Other ◽  
Critical Buckling Load ◽  
Various Boundary Conditions

We consider the problem of determining what shape column has the largest critical buckling load of all columns of given length and volume. This problem was previously solved for a column hinged (pinned) at both ends. We solve it for columns clamped at one end and clamped, hinged, or free at the other end, assuming that all cross sections of the column are similar and similarly oriented. We also prove that the column previously obtained in the hinged-hinged case is actually strongest and not merely stationary. Graphs of the areas of the strongest columns as functions of distance along the columns are given for the various cases. The results are also expressed as isoperimetric inequalities for eigenvalues of second-order ordinary differential equations with various boundary conditions. Certain additional inequalities of this type are also obtained.

Designing pinhole vacancies in graphene towards functionalization: Effects on critical buckling load

2017 ◽  
Vol 103 ◽  
pp. 343-357 ◽  
Author(s):  
S.K. Georgantzinos ◽  
S. Markolefas ◽  
G.I. Giannopoulos ◽  
D.E. Katsareas ◽  
N.K. Anifantis
Keyword(s):  
Buckling Load ◽  
Critical Buckling Load

scholarly journals Nonlocal vibration and buckling of two-dimensional layered quasicrystal nanoplates embedded in an elastic medium

2021 ◽  
Author(s):  
Tuoya Sun ◽  
Junhong Guo ◽  
E. Pan
Keyword(s):  
Elastic Medium ◽  
Vibration Frequency ◽  
Surrounding Medium ◽  
Nonlocal Parameter ◽  
Buckling Load ◽  
Width Ratio ◽  
Two Dimensional ◽  
Coating Materials ◽  
Decagonal Quasicrystal ◽  
Critical Buckling Load

AbstractA mathematical model for nonlocal vibration and buckling of embedded two-dimensional (2D) decagonal quasicrystal (QC) layered nanoplates is proposed. The Pasternak-type foundation is used to simulate the interaction between the nanoplates and the elastic medium. The exact solutions of the nonlocal vibration frequency and buckling critical load of the 2D decagonal QC layered nanoplates are obtained by solving the eigensystem and using the propagator matrix method. The present three-dimensional (3D) exact solution can predict correctly the nature frequencies and critical loads of the nanoplates as compared with previous thin-plate and medium-thick-plate theories. Numerical examples are provided to display the effects of the quasiperiodic direction, length-to-width ratio, thickness of the nanoplates, nonlocal parameter, stacking sequence, and medium elasticity on the vibration frequency and critical buckling load of the 2D decagonal QC nanoplates. The results show that the effects of the quasiperiodic direction on the vibration frequency and critical buckling load depend on the length-to-width ratio of the nanoplates. The thickness of the nanoplate and the elasticity of the surrounding medium can be adjusted for optimal frequency and critical buckling load of the nanoplate. This feature is useful since the frequency and critical buckling load of the 2D decagonal QCs as coating materials of plate structures can now be tuned as one desire.

Effect of Fiber Orientation on the Critical Buckling Load of Symmetric Composite Laminated Plates

2012 ◽  
Vol 629 ◽  
pp. 95-99 ◽  
Author(s):  
N. Hamani ◽  
D. Ouinas ◽  
N. Taghezout ◽  
M. Sahnoun ◽  
J. Viña
Keyword(s):  
Fiber Orientation ◽  
Composite Plates ◽  
Laminated Plates ◽  
Buckling Load ◽  
The Finite Element Method ◽  
Notch Radius ◽  
Critical Buckling Load ◽  
Buckling Strength ◽  
Degree Of Anisotropy ◽  
Circular Notch

In this study, a buckling analysis is performed on rectangular composite plates with single and double circular notch using the finite element method. Laminated plates of carbon/bismaleimde (IM7/5250-4) are ordered symmetrically as follows [(θ/-θ)2]S. The buckling strength of symmetric laminated plates subjected to uniaxial compression is highlighted as a function of the fibers orientations. The results show that whatever the notch radius, the buckling load is almost stable. Increasing the degree of anisotropy significantly improves critical buckling load.

Deformation of Perforated Aluminium Plates under In-Plane Compressive Loading

2016 ◽  
Vol 710 ◽  
pp. 357-362
Author(s):  
Irene Scheperboer ◽  
Evangelos Efthymiou ◽  
Johan Maljaars
Keyword(s):  
Research Work ◽  
Compressive Loading ◽  
Local Buckling ◽  
Buckling Load ◽  
Structural Behaviour ◽  
Critical Buckling Load ◽  
Out Of Plane ◽  
The Difference ◽  
Ultimate Resistance ◽  
Multiple Holes

Aluminium plates containing a single hole or multiple holes in a row are recently becoming very popular among architects and consultant engineers in many constructional applications, due to their reduced weight, as well as facilitating ventilation and light penetration of the buildings. However, there are still uncertainties concerning their structural behaviour, preventing them from wider utilization. In the present paper, local buckling phenomenon of perforated aluminium plates has been studied using the finite element method. For the purposes of the research work, plates with simply supported edges in the out-of-plane direction and subjected to uniaxial compression are examined. In view of perforations, circular cut-outs and the total cut-out size has been varied between 5 and 40% of the total plate area. Moreover, different perforation patterns have been investigated, from a single, central cut-out to a more refined pattern consisting of up to 25 holes equally distributed over the plate. Regarding the material characteristics, several aluminium alloys are considered and compared to steel grade A36 on plates of different slenderness. For each case the critical (Euler) buckling load and the ultimate resistance has been determined.A study into the boundary conditions of the plate showed that the restrictions at the edges parallel to the load direction have a large influence on the critical buckling load. Restraining the top or bottom edge does not significantly influence the resistance of the plate.The results showed that the ultimate resistance of aluminium plates containing multiple holes occurs at considerably larger out-of-plane displacement as that of full plates. For very large total cut-out, a plate containing a central hole has a larger resistance than a plate with equal cut-out percentage but with multiple holes. The strength and deformation in the post-critical regime, i.e. the difference between the critical buckling load and the ultimate resistance, differs significantly for different number of holes and cut-out percentage.

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