scholarly journals Low-frequency sinusoids for enhanced shear buckling performance of thin plates

2021 ◽  
Vol 177 ◽  
pp. 106475
Author(s):  
Peter Y. Wang ◽  
Maria E.M. Garlock ◽  
Ted P. Zoli ◽  
Spencer E. Quiel
Keyword(s):  
Low Frequency ◽  
Thin Plates ◽  
Shear Buckling

Low-Frequency Sine Webs for Improved Shear Buckling Performance of Plate Girders

2019 ◽  
Author(s):  
Peter Y. Wang ◽  
Maria E. Garlock ◽  
Theodore P. Zoli ◽  
Spencer E. Quiel
Keyword(s):  
Fatigue Cracks ◽  
Low Frequency ◽  
Robotic Welding ◽  
Plate Girders ◽  
Material Efficiency ◽  
Corrugated Webs ◽  
Shear Buckling ◽  
Elastic Shear ◽  
Traditional Strategy ◽  
The Web

<p>Steel plate girders are used extensively in buildings and bridges. Given shear rarely governs, minimizing web thickness is desirable. However, web slenderness can enable shear buckling and fatigue problems. The traditional strategy is to use welded transverse stiffeners; yet transversely-stiffened girders are prone to fatigue cracks and difficult to fabricate at high slenderness ratios. Thus, AASHTO currently limits web slenderness to 150. Alternatively, corrugated web girders overcome these deficiencies but require robotic welding for the web-to-flange weld. Corrugated webs are also limited to small web thicknesses (6mm or less) and girder depths (less than 1.5m) given web forming limits. The authors propose an alternative web geometry, introducing low-frequency sinusoids (LFS) in the web along its length. The LFS web can be welded to the flanges using semi-automatic weld techniques currently employed by bridge fabricators. The reduced web curvature allows for a wider array of web forming techniques with much larger plate thicknesses. In a finite element study, web geometric properties such as sinusoidal frequency and amplitude are varied. Results demonstrate a significant increase in the elastic shear buckling load and ultimate strength using a wavelength equal to the depth of the girder. The results of this study show promise for improved girder durability paired with material efficiency, demonstrating that a web product with constant amplitude and wavelength could work for various girder depths up to 3m and above.</p>

Bloch–Floquet bending waves in perforated thin plates

2007 ◽  
Vol 463 (2086) ◽  
pp. 2505-2518 ◽  
Author(s):  
A.B Movchan ◽  
N.V Movchan ◽  
R.C McPhedran
Keyword(s):  
Plane Waves ◽  
Low Frequency ◽  
Free Edge ◽  
Multipole Expansion ◽  
Thin Plates ◽  
Band Diagram ◽  
Single Defect ◽  
Bending Waves ◽  
Zero Radius ◽  
Square Array

This paper presents a mathematical model describing propagation of bending waves in a perforated thin plate. It is assumed that the holes are circular and form a doubly periodic square array. A spectral problem for the biharmonic operator is formulated in a unit cell containing a single defect, and its analytical solution is constructed using a multipole method. The overall system for the coefficients in the multipole expansion is then solved numerically. We generate dispersion diagrams for the two cases where the boundaries of holes are either clamped or free. We show that in the clamped case, there is a total low-frequency band gap in the limit of inclusions of zero radius, and give a simple formula describing the corresponding band diagram in this limit. We show that in the free-edge case, the band diagram of the vibrating plate is much closer to that of plane waves in a uniform plate than for the clamped case.

scholarly journals On the Shear Buckling of Clamped Narrow Rectangular Orthotropic Plates

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Seyed Rasoul Atashipour ◽  
Ulf Arne Girhammar
Keyword(s):  
Closed Form ◽  
Plate Theory ◽  
Exact Analytical Solution ◽  
Differential Quadrature Method ◽  
Thin Plates ◽  
Orthotropic Plates ◽  
Classical Plate Theory ◽  
Aspect Ratios ◽  
Wide Range ◽  
Shear Buckling

This paper deals with stability analysis of clamped rectangular orthotropic thin plates subjected to uniformly distributed shear load around the edges. Due to the nature of this problem, it is impossible to present mathematically exact analytical solution for the governing differential equations. Consequently, all existing studies in the literature have been performed by means of different numerical approaches. Here, a closed-form approach is presented for simple and fast prediction of the critical buckling load of clamped narrow rectangular orthotropic thin plates. Next, a practical modification factor is proposed to extend the validity of the obtained results for a wide range of plate aspect ratios. To demonstrate the efficiency and reliability of the proposed closed-form formulas, an accurate computational code is developed based on the classical plate theory (CPT) by means of differential quadrature method (DQM) for comparison purposes. Moreover, several finite element (FE) simulations are performed via ANSYS software. It is shown that simplicity, high accuracy, and rapid prediction of the critical load for different values of the plate aspect ratio and for a wide range of effective geometric and mechanical parameters are the main advantages of the proposed closed-form formulas over other existing studies in the literature for the same problem.

Symmetric low-frequency feature-guided ultrasonic waves in thin plates with transverse bends

Ultrasonics ◽  
2015 ◽  
Vol 56 ◽  
pp. 232-242 ◽  
Author(s):  
Abilasha Ramdhas ◽  
Roson Kumar Pattanayak ◽  
Krishnan Balasubramaniam ◽  
Prabhu Rajagopal
Keyword(s):  
Low Frequency ◽  
Ultrasonic Waves ◽  
Thin Plates ◽  
Guided Ultrasonic Waves ◽  
Frequency Feature

scholarly journals A Review of Skin Buckling Theory in Composite Members

2016 ◽  
Vol 846 ◽  
pp. 312-317
Author(s):  
Jiang Hui Dong ◽  
Xing Ma ◽  
Julie E. Mills ◽  
Zhu Ge Yan
Keyword(s):  
Infinite Plate ◽  
Buckling Analysis ◽  
Thin Plates ◽  
Filler Material ◽  
Future Research ◽  
Plate Model ◽  
Fe Method ◽  
Foundation Model ◽  
Shear Buckling ◽  
Post Buckling

This paper provides a comprehensive review of various methods used for skin buckling analysis in composite components. The skin buckling phenomenon is one of the governing criteria in composite design. It is a kind of contact buckling in which partial sections of skin buckle away from the filler material. In general, the problem can be modelled as a thin plate (skin) in unilateral contact with elastic medium (filler material). The theoretical analysis of contact buckling is complicated due to the nonlinearity arising from changing contact regions. To simplify the calculations, the filler material was usually modelled as a tensionless elastic foundation. The skin buckling coefficient varies in terms of the relative foundation stiffness factors. Because the Eigen-value method is not applicable to nonlinear systems, the finite element (FE) method was usually employed for post-buckling analysis, while initial buckling performance was investigated through analytical or semi-analytical methods such as rigid foundation model, infinite plate model and finite plate model. The compressive buckling and shear buckling problems for thin plates resting on tensionless foundations have been solved successfully. However, there are still urgent needs for future research on the topic. For example, the load carrying capacity of the buckling plates needs to be formulated for practical application. Complicated problems with complex loadings and/or corrugated skins need further investigation as well.

Eddy Current Flows Around Cracks in Thin Plates for Nondestructive Testing

1982 ◽  
Vol 49 (2) ◽  
pp. 389-395 ◽  
Author(s):  
S. Mukherjee ◽  
M. A. Morjaria ◽  
F. C. Moon
Keyword(s):  
Current Density ◽  
Eddy Current ◽  
Eddy Currents ◽  
Low Frequency ◽  
Numerical Results ◽  
Thin Plates ◽  
Line Integral ◽  
Faraday’S Law ◽  
Induced Currents ◽  
Current Flows

The boundary element method is used to calculate the induced electric current flow around cracks in thin conducting plates. A low frequency approximation leads to a Poisson equation for the current density potential or stream function. A kernel is used which produces the correct singularity at the crack tip. The boundary condition on the crack, derived from Faraday’s law, requires the line integral of the current density around the crack to be zero. Numerical results for induced currents due to a circular induction coil ore given. These results show that hot spots, due to Joule heating, can occur at the tips of the crack. Comparison of numerical results with infrared scanning experiments of eddy currents in a cracked plate are given. It is hoped that the numerical method presented here will provide a tool to simulate both new and conventional nondestructive eddy current testing techniques.

SHEAR BUCKLING OF THIN PLATES WITH CONSTANT IN-PLANE STRESSES

2007 ◽  
Vol 07 (02) ◽  
pp. 179-192 ◽  
Author(s):  
IGOR SHUFRIN ◽  
MOSHE EISENBERGER
Keyword(s):  
Shear Loading ◽  
Buckling Load ◽  
Thin Plates ◽  
Rectangular Plates ◽  
Kantorovich Method ◽  
Plane Shear ◽  
Buckling Loads ◽  
Extended Kantorovich Method ◽  
Tension And Compression ◽  
Shear Buckling

This work presents highly accurate numerical calculations of the buckling loads for thin elastic rectangular plates with known constant in-plane stresses, and in-plane shear loading that is increased until the critical load is obtained and the plate losses its stability. The solutions are obtained using the multi-term extended Kantorovich method. The solution is sought as the sum of multiplications of two one-dimensional functions. In this method a solution is assumed in one direction of the plate, and this enables transformation of the partial differential equation of the plate equilibrium into a system of ordinary differential equations. These equations are solved exactly by the exact element method, and an approximate buckling load is obtained. In the second step, the derived solution is now taken as the assumed solution in one direction, and the process is repeated to find an improved buckling load. This process converges with a small number of solution cycles. For shear buckling this process can only be used if two or more terms are taken in the expansion of the solution. Many examples are given for shear buckling loads for various cases of tension and compression bi-directional loading.

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