Transverse Flexure of a Semi-Infinite Thin Plate Containing an Infinite Row of Circular Holes

1959 ◽  
Vol 26 (4) ◽  
pp. 661-665
Author(s):  
O. Tamate
Keyword(s):  
Thin Plate ◽  
Infinite Plate ◽  
Mutual Interference ◽  
Thin Plates ◽  
Bending Moments ◽  
Circular Holes ◽  
Kirchhoff Theory

Abstract The problem of finding stress resultants in a semi-infinite plate under plain bending and containing an infinite row of equal and equally spaced circular holes is discussed on the basis of the Poisson-Kirchhoff theory of thin plates. A method of perturbation is adopted for the determination of parametric coefficients included in the solution. The maximum bending moments occurring on the rim of the hole across the minimum section are calculated for several cases and shown in graphs, from which the mutual interference of adjacent boundaries will be informed.

Transverse Flexure of a Thin Plate Containing Two Circular Holes

1959 ◽  
Vol 26 (1) ◽  
pp. 55-60
Author(s):  
O. Tamate
Keyword(s):  
Stress Concentration ◽  
Thin Plate ◽  
Elastic Plate ◽  
Equal Size ◽  
Thin Elastic Plate ◽  
Two Circular Holes ◽  
Circular Holes ◽  
Axes Of Symmetry ◽  
Kirchhoff Theory

Abstract The problem of finding stress resultants in a thin elastic plate containing two circular holes of equal size, under plain bending about the axes of symmetry, has been discussed on the basis of the Poisson-Kirchhoff theory. A method of perturbation is adopted for the determination of parametric coefficients involved in the solution. The factors of stress concentration are calculated and compared with the results available.

Green’s Functions for Infinite and Semi-infinite Anisotropic Thin Plates

2003 ◽  
Vol 70 (2) ◽  
pp. 260-267 ◽  
Author(s):  
Z.-Q. Cheng ◽  
J. N. Reddy
Keyword(s):  
Green's Functions ◽  
Green’S Functions ◽  
Infinite Plate ◽  
Fundamental Solutions ◽  
Thin Plates ◽  
Green Functions ◽  
Real Form ◽  
Concentrated Forces ◽  
Anisotropic Elastic ◽  
Kirchhoff Theory

This paper presents fundamental solutions of an anisotropic elastic thin plate within the context of the Kirchhoff theory. The plate material is inhomogeneous in the thickness direction. Two systems of problems with non-self-equilibrated loads are solved. The first is concerned with in-plane concentrated forces and moments and in-plane discontinuous displacements and slopes, and the second with transverse concentrated forces. Exact closed-form Green’s functions for infinite and semi-infinite plates are obtained using the recently established octet formalism by the authors for coupled stretching and bending deformations of a plate. The Green functions for an infinite plate and the surface Green functions for a semi-infinite plate are presented in a real form. The hoop stress resultants are also presented in a real form for a semi-infinite plate.

The Influence of Hyperbolic Notches on the Transverse Flexure of Elastic Plates

1940 ◽  
Vol 7 (2) ◽  
pp. A53-A56
Author(s):  
George H. Lee
Keyword(s):  
Infinite Plate ◽  
Bending Moment ◽  
Bending Moments ◽  
Elastic Plates ◽  
Transverse Bending ◽  
Narrow Section ◽  
Kirchhoff Theory

Abstract This paper considers the solution of the two problems of the infinite plate, with two symmetrically disposed hyperbolic notches, subjected to (a) transverse bending and (b) twisting. The transverse-bending moments and torsional couples are so applied that the narrow section between the notches transmits the bending moment or the torsional couple. Using the Poisson-Kirchhoff theory, finite expressions were obtained for the deflection and stress in each problem.

scholarly journals Determination of Natural Frequency and Mode Shape for Hollow Thin Plates

2019 ◽  
Vol 9 (1) ◽  
pp. 2601-2606
Keyword(s):  
Finite Element ◽  
Resonance Frequency ◽  
Natural Frequency ◽  
Thin Plate ◽  
Mode Shape ◽  
Hollow Structure ◽  
Thin Plates ◽  
Mode Behavior ◽  
Analysis Experiment

The determination of natural frequency and the mode shape of structures are important in characterizing the properties or behavior of the structures. The existing hollow in solid thin plate will change the vibration behavior in term of resonance frequency and mode behavior. A lot of structure consists of hollow space such as inner panel of car hood and bonnet. However, simplifying the model from hollow structure with solid thin plates only will resulting some difference in their vibration performance. This study begins with conducting modal analysis experiment using solid thin plate under free-free boundary condition. Next, the finite element methods were performing to compare with the experimental results. The average error of 3.96% was obtain when compared which provide a good confident level with the simulation result. Next, the study continued by finding the natural frequency and the mode shape for the thin plate under various position of hole, number of holes and shape of hole by using FEM software. Finally, finite element was also being carried out on the simplified design model of the inner panel car hood based from the real product and compared the resonance frequency from the model with some vibration reference sources. Through this study, it is found that the diversity of the hole position, the increasing number of holes and the change of the hole shape play a role in changing the natural frequencies of a thin plate. Since there is a lot of hollow thin plates in the car part, designing every parts are important to make sure the NVH quality is improve and not opposite of it.

Determination of collapse moment of different angled pipe bends with initial geometric imperfection subjected to in-plane bending moments

2021 ◽  
pp. 095440622199640
Author(s):  
Manish Kumar ◽  
Pronab Roy ◽  
Kallol Khan
Keyword(s):  
Finite Element ◽  
Cross Section ◽  
Circular Cross Section ◽  
Initial Imperfection ◽  
Bend Angle ◽  
Bending Moments ◽  
Element Analysis ◽  
Geometric Imperfection ◽  
Initial Geometric Imperfection

From the recent literature, it is revealed that pipe bend geometry deviates from the circular cross-section due to pipe bending process for any bend angle, and this deviation in the cross-section is defined as the initial geometric imperfection. This paper focuses on the determination of collapse moment of different angled pipe bends incorporated with initial geometric imperfection subjected to in-plane closing and opening bending moments. The three-dimensional finite element analysis is accounted for geometric as well as material nonlinearities. Python scripting is implemented for modeling the pipe bends with initial geometry imperfection. The twice-elastic-slope method is adopted to determine the collapse moments. From the results, it is observed that initial imperfection has significant impact on the collapse moment of pipe bends. It can be concluded that the effect of initial imperfection decreases with the decrease in bend angle from 150∘ to 45∘. Based on the finite element results, a simple collapse moment equation is proposed to predict the collapse moment for more accurate cross-section of the different angled pipe bends.

Stress Concentration Factors in Auxetic Rods and Plates

2013 ◽  
Vol 394 ◽  
pp. 134-139 ◽  
Author(s):  
Teik Cheng Lim
Keyword(s):  
Stress Concentration ◽  
Circumferential Stress ◽  
Axial Direction ◽  
Thin Plates ◽  
Auxetic Materials ◽  
Circular Holes ◽  
Concentration Factors ◽  
Stress Concentration Factors ◽  
Future Work ◽  
Poissons Ratio

Auxetic materials are solids that possess negative Poissons ratio. Although rare, such materials do occur naturally and also have been artificially produced. Due to their unique properties, auxetic materials have been extensively investigated for load bearing applications including in biomedical engineering and aircraft structures. This paper considers the effect of Poissons ratio on the stress concentration factors on rods with hyperbolic groove and large thin plates with circular holes and rigid inclusions. Results reveal that the use of auxetic materials is useful for reducing stress concentration in the maximum circumferential stress of the rods with grooves, and in plates with circular holes and rigid inclusions. However, the use of auxetic materials increases the stress concentration in the axial direction of the rod. Therefore a procedure to accurately select and/or design materials with precise negative Poissons ratio for optimal design is suggested for future work.

High Frequency Ultrasonic Measurements

1988 ◽  
Vol 21 (5) ◽  
pp. 133-136
Author(s):  
N Zarsav
Keyword(s):  
High Frequency ◽  
Polymer Coating ◽  
Steel Sheet ◽  
Lamb Waves ◽  
Thin Plates ◽  
Design Features ◽  
Degree Of Cure ◽  
Double Probe ◽  
Ultrasonic Measurements

The use of high frequency ultrasonic Lamb waves to measure the thickness of thin plates and foils, is discussed and the feasibility of their application to the determination of the degree of cure of polymer coating on coated tin plated steel sheet (as used by the food can industry) is evaluated. The paper also discusses briefly the design features of the purpose built precision double probe ultrasonic goniometer used to carry out these measurements.

Reinforced Circular Holes in Bending With Shear

1953 ◽  
Vol 20 (2) ◽  
pp. 279-285
Author(s):  
S. R. Heller
Keyword(s):  
Stress Distribution ◽  
Arbitrary Shape ◽  
Theoretical Solution ◽  
Bead Type ◽  
Circular Holes ◽  
Radial Thickness ◽  
Bending With Shear ◽  
The Web

Abstract The object of this paper is the determination of the effect of the reinforcement of circular holes on the stress distribution in the webs of beams subjected to bending with shear. A theoretical solution for a bead-type reinforcement, i.e., small radial thickness, is developed. The stress distribution in the web for arbitrary shape reinforcement is based on the work of Reissner and Morduchow (1). The theory developed is valid provided the diameter of the hole does not exceed one fourth of the depth of the beam.

Some Unexpected Results in the Stress Calculation Around Multiple Holes in an Isotropic Plate Under In-Plane-Loads

2014 ◽  
Author(s):  
Ghazi H. Asmar ◽  
Elie A. Chakar ◽  
Toni G. Jabbour
Keyword(s):  
Finite Element ◽  
Isotropic Plate ◽  
Potential Method ◽  
The Finite Element Method ◽  
Close Proximity ◽  
Complex Fourier Series ◽  
Circular Holes ◽  
Complex Potential Method ◽  
Multiple Holes

The Schwarz alternating method, along with Muskhelishvili’s complex potential method, is used to calculate the stresses around non-intersecting circular holes in an infinite isotropic plate subjected to in-plane loads at infinity. The holes may have any size and may be disposed in any manner in the plate, and the loading may be in any direction. Complex Fourier series, whose coefficients are calculated using numerical integration, are incorporated within a Mathematica program for the determination of the tangential stress around any of the holes. The stress values obtained are then compared to published results in the literature and to results obtained using the finite element method. It is found that part of the results generated by the authors do not agree with some of the published ones, specifically, those pertaining to the locations and magnitudes of certain maximum stresses occurring around the contour of holes in a plate containing two holes at close proximity to each other. This is despite the fact that the results from the present authors’ procedure have been verified several times by finite element calculations. The object of this paper is to present and discuss the results calculated using the authors’ method and to underline the discrepancy mentioned above.

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