Analytical Solutions for the Lateral-Torsional Buckling of Serpentine Interconnects in Stretchable Electronics

2020 ◽  
Vol 87 (8) ◽  
Author(s):  
Peng Feng ◽  
Jianghong Yuan ◽  
Yin Huang ◽  
Xiangyu Li
Keyword(s):  
Aspect Ratio ◽  
Scaling Laws ◽  
Strong Dependence ◽  
Asymptotic Properties ◽  
Stretchable Electronics ◽  
Lateral Torsional Buckling ◽  
Torsional Buckling ◽  
Element Analysis ◽  
Buckling Modes ◽  
End Conditions

Abstract Serpentine interconnects, as an integral part of island-bridge layouts, enable extremely large reversible deformation under the action of mechanical loads and are thus widely used in the emerging new field of stretchable electronics. In this paper, the lateral-torsional buckling is analytically studied for a simplified S-shaped serpentine structure that consists of five straight components rigidly connected at point joints. Simple analytic scaling laws between the dimensionless critical buckling load and the aspect ratio of the serpentine structure are newly derived and uniformly expressed in terms of generalized hypergeometric series for various types of boundary conditions, which can serve as the benchmark of numerical simulations. These scaling laws, fully verified by finite element analysis, may well capture the implied connection between stretching- and compression-induced buckling, the strong dependence of buckling modes on end conditions, and the monotonic/asymptotic properties of the critical load with respect to the aspect ratio of serpentine structures.

Mechanics of Buckled Kirigami Membranes for Stretchable Interconnects in Island-Bridge Structures

2020 ◽  
Vol 87 (5) ◽  
Author(s):  
Ruitao Tang ◽  
Haoran Fu
Keyword(s):  
Scaling Laws ◽  
High Surface ◽  
Design Guidelines ◽  
Stretchable Electronics ◽  
Postbuckling Behavior ◽  
Critical Height ◽  
Element Analysis ◽  
Bridge Structures ◽  
Stretchable Interconnects ◽  
Novel Design

Abstract Island-bridge structures incorporated with kirigami membranes emerge as a novel design strategy for flexible/stretchable electronics, taking advantages of large stretchability, high-surface filling ratio and low resistance. However, it is hard to determine the mechanical properties of this design due to its complex geometries and nonlinear deformation configuration, thereby limiting its further applications. In this paper, we present a model for the postbuckling behavior of kirigami membranes through a combination of theoretical modeling, finite element analysis, and experiments. Scaling laws for elastic stretchability are developed, showing good agreement with numerical results and experimental images. Investigations on the critical height of post array are conducted to ensure the boundary condition of the kirigami membranes in the analytical model. These results can serve as design guidelines for kirigami structures and facilitate their applications in flexible/stretchable electronics.

Lateral-torsional buckling capacity of Hybrid Double-I-Box Beams: A numerical approach

2018 ◽  
Vol 22 (3) ◽  
pp. 641-655 ◽  
Author(s):  
MS Deepak ◽  
VM Shanthi
Keyword(s):  
Finite Element ◽  
Numerical Approach ◽  
Lateral Torsional Buckling ◽  
Torsional Buckling ◽  
Lateral Buckling ◽  
Element Analysis ◽  
Section Modulus ◽  
Parameter Ratio ◽  
Box Beams ◽  
Hot Rolled

In this article, a parametric study on the lateral-torsional buckling performance of thin-walled cold-formed steel Hybrid Double-I-Box Beams through numerical analyses has been presented. These built-up beams have distinctive cross-section geometry; the presence of more section modulus at the flanges provides high resistance to flexural bending and the closed-box portion offers high stiffness to resist torsion and lateral buckling. Therefore, these beams can be used for longer spans. The nonlinear finite element analysis was performed using ABAQUS software. All the beams were modelled as ideal finite element models adopting simply supported boundary conditions and loads were applied as end moments. To acquire a large number of data, three varying parameters were considered namely, hybrid parameter ratio, that is, yield strength of flange steel to web steel (1.0, 1.3, 1.5 and 1.7); ratio of breadth to depth of the beam (4/6, 5/6, 6/6 and 7/6); and length of the beam (1.0, 2.5, 5.0, 10, 15, 20, 30, 40, 50 and 60 in m). The thickness of both the flanges and the webs were 2.5 mm. All these parameters alter the overall slenderness of the members. It is shown that at larger spans, Hybrid Double-I-Box Beams experience lateral buckling. The results obtained from the numerical studies were plotted on nondimensional moment versus nondimensional slenderness graph. These results were compared with the predictions using effective width method design rules specified in Euro codes EN 3-1-3 and buckling curve-d of EN 3-1-1, which was originally adopted lateral-torsional buckling capacities of hot-rolled steel ‘I’ sections, and the adequacy is checked. It was found that Hybrid Double-I-Box Beams has higher lateral-torsional buckling capacity than common ‘I’ or box sections. Hence, a new simplified design equation was proposed for determining lateral-torsional buckling capacity of Hybrid Double-I-Box Beams.

scholarly journals Effect of Eccentric Lateral Bracing Stiffness on Lateral Torsional Buckling Resistance of Wooden Beams

2018 ◽  
Vol 18 (02) ◽  
pp. 1850027 ◽  
Author(s):  
Ye Hu ◽  
Magdi Mohareb ◽  
Ghasan Doudak
Keyword(s):  
Threshold Value ◽  
Point Load ◽  
Symmetric Mode ◽  
Lateral Torsional Buckling ◽  
Torsional Buckling ◽  
Buckling Modes ◽  
Buckling Resistance ◽  
Load Height ◽  
Lateral Bracing ◽  
Critical Moments

An energy-based solution is developed for the lateral torsional buckling (LTB) analysis of wooden beams with flexible mid-span lateral bracing offset from section mid-height and subjected to uniformly distributed or mid-span point load. The study shows that such beams are prone to two potential buckling modes; symmetric or anti-symmetric. The symmetric mode is shown to govern the capacity of the beam for low bracing stiffness while the anti-symmetric mode governs the capacity when the bracing stiffness exceeds a threshold value. Using the present formulation, the threshold bracing stiffness required to suppress the symmetric mode and maximize the critical moments is directly obtained by solving a special eigenvalue problem in the unknown bracing stiffness. The technique thus eliminates the need for trial and error in standard solutions. A parametric study is conducted to investigate the effect of bracing height, load height, and bracing stiffness on the critical moments. A large database of runs is generated and used to develop simple expressions for determining the threshold bracing stiffness required to maximize the elastic LTB resistance.

Analytical Solutions of Lateral–Torsional Buckling of Castellated Beams

2016 ◽  
Vol 16 (08) ◽  
pp. 1550044 ◽  
Author(s):  
Boksun Kim ◽  
Long-Yuan Li ◽  
Ashley Edmonds
Keyword(s):  
Analytical Solutions ◽  
Bottom Flange ◽  
Lateral Torsional Buckling ◽  
Torsional Buckling ◽  
Element Analysis ◽  
Web Openings ◽  
Total Potential ◽  
Numerical Studies ◽  
Shear Buckling ◽  
Critical Moments

The majority of the existing literature on the lateral stability of castellated beams deals with experimental and/or numerical studies. This paper presents a comprehensive analytical study of the lateral–torsional buckling of simply supported castellated beams subject to pure bending and/or a uniformly distributed load. Using the principle of total potential energy, analytical expressions for the critical buckling moments and loads are derived and applied for various beam lengths. The three different locations of the applied load are used: At the top flange, shear center and bottom flange. The results show that the influence of web openings on the critical buckling moments and loads are mainly due to the reduction of the torsional constant caused by the web openings. Web shear effects and web shear buckling become important only when the beam is short and the flange is wide. The critical moments and loads will be overestimated or underestimated if the full or reduced section properties are used. The accurate critical moment or load should be calculated based on the average torsional constant of the full and reduced sections rather than simply taking the average of the critical moments or loads calculated from the full and reduced section properties. The present analytical solutions are verified using 3D finite element analysis results.

scholarly journals STUDI EKSPERIMENTAL KUAT LENTUR BAJA PROFIL I KOMPAK SIMETRIS GANDA BERDASARKAN RSNI 03-1729-201X

1970 ◽  
Vol 6 (2) ◽  
pp. 99-105
Author(s):  
Redaksi Tim Jurnal
Keyword(s):  
Flexural Strength ◽  
Cross Section ◽  
Experimental Testing ◽  
Point Load ◽  
National Standard ◽  
Lateral Torsional Buckling ◽  
Torsional Buckling ◽  
Element Analysis ◽  
Long Span ◽  
The Stability

The danger of buckling and instability structures easily occurs on the steel beam structure, it will make the structure fails before it reaches the cross section ultimate capacity.In that case the strength of a beam is not only determined by cross-section ultimate capacity. The instability of the structure causes lateral torsional buckling eventhough there is no torque on the beam. There is one way to support the stability of the beam; by installing lateral support on its side. This research is intended to obtain information about flexural strength by comparing the theoretical results based on SNI 03-1729-2002 and (Indonesian National Standard Draft) RSNI 03-1729.1- 201x with the results of experimental testing and finite element analysis results (using the ABAQUS program). The flexural specimens which are studied are in the long-span with a length of 3.3 meters span test. The loading uses three-point load system. The results of the test show information that flexural strength for the long-span specimen from experimental test results has the smallest difference of 33.18% of the theoretical result. As for analysis with FEM also hasthe same difference of 33.18% with the experimental results. Failure that occurs for long-span specimen is due to lateral torsional buckling failures.

scholarly journals BEHAVIOUR OF PARALLEL GIRDERS STABILISED WITH U‐FRAMES

2010 ◽  
Vol 16 (2) ◽  
pp. 197-202 ◽  
Author(s):  
Kuldeep Virdi ◽  
Walid Azzi
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Buckling Analysis ◽  
Effective Length ◽  
Ultimate Capacity ◽  
Lateral Torsional Buckling ◽  
Torsional Buckling ◽  
Element Analysis ◽  
Key Factor ◽  
The Stability

Lateral torsional buckling is a key factor in the design of steel girders. Stability can be enhanced by cross‐bracing, reducing the effective length and thus increasing the ultimate capacity. U‐frames are an option often used to brace the girders, when designing through type of bridges and where overhead bracing is not practical. This paper investigates the effect of the U‐frame spacing on the stability of the parallel girders. Eigenvalue buckling analysis was undertaken with four different spacings of the U‐frames. Results were extracted from finite element analysis, interpreted and conclusions drawn. Santrauka Projektuojant plienines sijas šoninis sukamasis klupumas yra svarbiausias veiksnys. Pastovumas gali būti padidintas skersiniais ryšiais, mažinančiais veikiamaji ilgi ir padidinančiais ribine galia. U‐formiai remai yra dažna priemone sijoms išramstyti, kai projektuojami tiltai, kuriu laikančiosios konstrukcijos yra virš pakloto, o viršutiniai ryšiai yra nepraktiški. Šiame straipsnyje nagrinejamas U‐formiu remu tarpatramio poveikis lygiagrečiuju siju pastovumui. Tikravertis klupumo skaičiavimas buvo atliktas esant keturiems skirtingiems U‐formiu remu tarpatramiams. Aptarti rezultatai, gauti apskaičiavus baigtinius elementus, padarytos išvados.

scholarly journals Analisis Nonlinier Tekuk Torsi Lateral pada Balok Baja Cellular

2020 ◽  
Vol 25 (2) ◽  
pp. 141
Author(s):  
Benny Gunawan Hung ◽  
Bambang Suryoatmono
Keyword(s):  
Circular Opening ◽  
Lateral Deformation ◽  
Maximum Difference ◽  
Lateral Torsional Buckling ◽  
Torsional Buckling ◽  
Buckling Modes ◽  
Critical Moment ◽  
Design Guide ◽  
Simple Support ◽  
The Web

One of many buckling modes that could occur on the beam is lateral-torsional buckling. Lateral torsional buckling could result in lateral deformation and torsion of section. In the AISC 360-16 Spesification, an equation is provided to calculate lateral-torsional buckling critical moment of prismatic I section beam. For cellular beams (I section beam with circular openings), AISC Design Guide 31 states that the lateral-torsional buckling critical moment should be checked in accordance with AISC Specification using gross section properties. With this assumption, thus, the design guide ignores the existence of circular opening on the web, which can cause a reduction of lateral-torsional buckling critical moment. In this study, lateral-torsional buckling analysis on cellular beam with simple support loaded by distributed transversal load has been done - the analysis utilized finite element based software. From the analysis, the critical moment is lower than AISC 360-16 critical moment with the assumption of prismatic I section beam, with the maximum difference percentage of 43,58%. Based on this study, a correction factor has been obtained to estimate the critical moment of cellular beams by using equation on AISC 360-16. 

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