Thin Plates and Shallow Cylindrical Shells Subjected to Hot Spots

1964 ◽  
Vol 31 (1) ◽  
pp. 79-82 ◽  
Author(s):  
A. Jahanshahi
Keyword(s):  
Plane Stress ◽  
Hot Spots ◽  
Cylindrical Shells ◽  
Equation Of Motion ◽  
Thin Plates ◽  
Lagrange’S Equation ◽  
Singular Functions

Using Lagrange’s equation of motion for thin plates, the equations of plane stress, and the equations for shallow cylindrical shells, the deformations of thin plates and cylindrical shells subjected to bending and plane hot spots are studied. The interrelation between different singular functions associated with these problems has been indicated also.

Some Notes on Singular Solutions and the Green’s Functions in the Theory of Plates and Shells

1964 ◽  
Vol 31 (3) ◽  
pp. 441-446 ◽  
Author(s):  
A. Jahanshahi
Keyword(s):  
Hot Spots ◽  
Green's Functions ◽  
Green’S Functions ◽  
Cylindrical Shells ◽  
Thin Plates ◽  
Singular Solutions ◽  
Theory Of Plates ◽  
Plates And Shells ◽  
Circular Cylindrical Shells

Singular solutions are constructed which generate the singularities for great many types of concentrated action on shallow spherical and cylindrical shells. Subsequently a technique is introduced to construct the Green’s functions for closed circular cylindrical shells. Also, the deformation of thin plates subjected to moving hot spots is discussed briefly.

Accurate Calculation of Stress Distributions in Multiholed Plates

1965 ◽  
Vol 87 (3) ◽  
pp. 331-335 ◽  
Author(s):  
L. E. Hulbert ◽  
F. W. Niedenfuhr
Keyword(s):  
Computer Program ◽  
Plane Stress ◽  
Symmetric Groups ◽  
Thin Plates ◽  
Stress Distributions ◽  
Accurate Calculation ◽  
Point Matching ◽  
Shallow Shells ◽  
Matching Technique ◽  
Stress Functions

This paper discusses the application of the point-matching technique in obtaining the solution of many problems involving multiholed thin plates undergoing generalized plane stress. The stress functions appropriate to plates with symmetric groups of holes are described. A large number of problems solved by a computer program are described and compared with published results. Problems are solved also for which there are no known published results. Two interesting new problems are discussed in detail. The results show the power and flexibility of the technique. The extension of the methods to permit the solution of problems in the deflection of thin, multiholed plates and shallow shells is discussed.

Free vibration characteristics of delaminated composite pretwisted stiffened cylindrical shell

2017 ◽  
Vol 232 (4) ◽  
pp. 595-611 ◽  
Author(s):  
Mrutyunjay Rout ◽  
Sasank Shekhara Hota ◽  
Amit Karmakar
Keyword(s):  
Free Vibration ◽  
Dynamic Equilibrium ◽  
Twist Angle ◽  
Cylindrical Shells ◽  
Shell Element ◽  
Vibration Characteristics ◽  
Mode Shapes ◽  
Iteration Algorithm ◽  
Lagrange’S Equation ◽  
Benchmark Solutions

Effects of delamination on free vibration characteristics of laminated stiffened cylindrical shells with pretwist are analyzed by finite element method. The investigation is carried out using an eight-noded quadratic isoparametric shell element, which incorporates the transverse shear deformation and rotary inertia along with a three-noded beam element for the stiffener. The multipoint constraint algorithm has been included to guarantee the compatibility of deformation, equilibrium of resultant forces, and moments at delamination crack tip. The general dynamic equilibrium equation is derived from Lagrange’s equation of motion for moderate rotational speeds for which the Coriolis effect is neglected. The standard eigenvalue problem is solved utilizing QR iteration algorithm. The accuracy of the present formulation is validated with benchmark solutions is available in the literature. The present work concerns about the effects of delamination, fiber orientation, twist angle, stiffener depth-to-shell thickness ratio, and rotational speed on the fundamental frequency of shallow cylindrical shells with stiffener. Representative mode shapes for some typical case of the stiffened shell for different twist angles and rotational speeds are also presented.

Analysis of Clamped Rectangular Plates

1940 ◽  
Vol 7 (4) ◽  
pp. A139-A142
Author(s):  
Dana Young
Keyword(s):  
Middle Surface ◽  
Lateral Loading ◽  
Thin Plates ◽  
Superposition Method ◽  
Rectangular Plates ◽  
Lagrange’S Equation

Abstract This paper attempts to solve the problem of the bending action of rectangular plates clamped at all four edges and subjected to lateral loading. Analytical in nature, the author’s investigation is based upon the ordinary theory of bending of thin plates as treated in Lagrange’s equation of the middle surface. The superposition method is used and applied to a number of loadings not hitherto studied.

Spectral Fatigue Analysis of Plate Surface Hot-Spots: A Practical Solution to the Stress Direction Issue

2020 ◽  
Author(s):  
Fabien Bigot ◽  
Stéphanie Mougin
Keyword(s):  
Finite Element ◽  
Spectral Analysis ◽  
Fatigue Strength ◽  
Plane Stress ◽  
Hot Spots ◽  
Fatigue Analysis ◽  
Multiaxial Fatigue ◽  
The Other ◽  
Plate Surface ◽  
Practical Solution

Abstract Spectral Fatigue Analysis using coupled hydrodynamics and finite element models has now become a common practice for the fatigue strength assessment of offshore units, with established procedures given in Classification Rules. However, users are facing a practical issue that is almost never mentioned in the procedures. Indeed, many fatigue hot-spots are located on a plate surface, as opposed to plate edges. For such hot-spots, the finite element model results are the three components of the plane-stress stress tensor. Therefore, the outcome of the Spectral Fatigue Analysis is a set of three transfer functions (RAOs). On the other hand, our industry’s practice regarding the fatigue strength model is still the proven « design S-N curve » approach in combination with the Palmgren-Miner’s damage summation. As a consequence, today the engineer is left with no clear instruction about the proper way how to close this gap between the three stress RAOs on the one hand, and the single stress S-N curve on the other hand. If any advice is given, it is most often to consider the principal stresses, tentatively extending to spectral analysis the classification rule load cases approach. However, principal stress determination is a non-linear procedure that is not compatible with spectral analysis in frequency domain. Turning the spectral results into time domain to overcome this limitation is extremely costly and is not straightforward. Of course, a rational solution to this issue would be the adoption of a multiaxial fatigue damage criteria in lieu of the uniaxial S-N curve. But until such a multiaxial fatigue criteria is widely accepted in our industry, users have to square the circle, and force their stress tensor RAOs into the existing rule criteria. In this paper, a practical solution to reconcile plane stress results and conventional S-N curve criterion in spectral fatigue is proposed: the “facet approach “.

Hydroelastic Vibrations of Flat Plates Related to Trailing Edge Geometry

1961 ◽  
Vol 83 (4) ◽  
pp. 671-678 ◽  
Author(s):  
G. H. Toebes ◽  
P. S. Eagleson
Keyword(s):  
Leading Edge ◽  
Equation Of Motion ◽  
Thin Plates ◽  
Comprehensive Treatment ◽  
Angle Of Incidence ◽  
Flat Plates ◽  
Trailing Edge ◽  
Edge Geometry ◽  
Vortex Induced Vibrations ◽  
Hydroelastic Vibrations

Vortex-induced vibrations of thin flat plates are studied as a function of trailing edge geometry. In an effort to extend the analysis to a more comprehensive treatment than that provided by the common vortex model, the vibrations are considered as hydroelastic phenomena. An equation of motion is formulated. From a qualitative analysis of this nonlinear equation some expected features of its solution are set forth. A detailed experimental determination is made of the amplitude spectra of various thin plates mounted at zero mean angle of incidence in the test section of a water tunnel and suspended by a torsion spring through their leading edge. The effects of trailing edge geometry and elastic properties of plate support are explored. Data analysis gives interesting confirmation of the formulated equation of motion. The vibration is shown to become self-excited and the degree of two dimensionality of the wake is deduced to be determinative in regard to the severity of the vibration.

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