Three‐Dimensional and Shell‐Theory Analysis for Axisymmetric Vibrations of Orthotropic Shells

1966 ◽  
Vol 39 (3) ◽  
pp. 549-555 ◽  
Author(s):  
I. Mirsky
Keyword(s):  
Shell Theory ◽  
Three Dimensional ◽  
Theory Analysis ◽  
Orthotropic Shells

Three-Dimensional and Shell-Theory Analysis of Elastic Waves in a Hollow Sphere: Part 1—Analytical Foundation

1969 ◽  
Vol 36 (3) ◽  
pp. 431-439 ◽  
Author(s):  
A. H. Shah ◽  
C. V. Ramkrishnan ◽  
S. K. Datta
Keyword(s):  
Elastic Waves ◽  
Shell Theory ◽  
Three Dimensional ◽  
Frequency Equation ◽  
Wave Number ◽  
Normal Strain ◽  
Theory Analysis ◽  
Analytical Foundation ◽  
Transverse Normal Strain ◽  
Approximate Equations

In Part 1 of this paper an exact analysis of the nonaxisymmetric wave propagation in a hollow elastic sphere is presented. It is found that the characteristic frequency equation is independent of the longitudinal wave number. Approximate equations for thin shells and membranes are derived by way of asymptotic expansions. In general, the vibrations fall into two distinct classes, one of which is equivoluminal. Also included in the paper is a six-mode shell theory in which the effects of transverse normal strain are included. A technique due to van der Neut is used to separate the governing partial differential equations whereby two frequency equations corresponding to the two classes of vibrations are obtained.

To the theory analysis of tightness of tank of pressure testing

2019 ◽  
Vol 5 (4) ◽  
pp. 129-142
Author(s):  
Vladislav Sh. Shagapov ◽  
Ismagilyan G. Khusainov ◽  
Emiliya V. Galiakbarova ◽  
Zulfya R. Khakimova
Keyword(s):  
Relaxation Time ◽  
Three Dimensional ◽  
Petroleum Products ◽  
Technical Condition ◽  
Excess Pressure ◽  
Soil Parameters ◽  
Theory Analysis ◽  
Pressure Testing ◽  
Tank Pressure ◽  
Over Time

This article studies the process of relaxation of the pressure in a tank with the damaged area of the wall after pressure-testing. The authors use different methods for the diagnosis of the technical condition of objects of petroleum products storage. Pressure testing is one of nondestructive methods. The rate of pressure decrease is characteristic of the system tightness. This article studies the cases of ground and underground location of the tank. Pressure testing involves excess pressure inside of a tank and observing its decrease. Over time, one can assess the integrity of the system. This has required creating mathematical models to account the filtration of the liquid depending on the location of the tank. The results include the analytical solution of the task and the formulas for describing the dependence of the relaxation time of pressure in the tank from the liquid and soil parameters, geometry of the tank, and the damaged portion of the wall. The two- and three-dimensional cases of liquids filtration for the case of underground location of the tank were considered. The results of some numerical calculations of the dependence of reduction time and the time of half-life pressure from the area of the damaged portion of the wall were shown. The obtained solutions allow assessing the extent of the damaged area by the pressure testing with known values of tank, liquid, and soil.

scholarly journals Alternative derivation of the higher-order constitutive model for six-parameter elastic shells

2021 ◽  
Vol 72 (2) ◽  
Author(s):  
Mircea Bîrsan
Keyword(s):  
Energy Density ◽  
Constitutive Model ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Shell Theory ◽  
Constitutive Relations ◽  
Three Dimensional ◽  
Classical Shell Theory ◽  
Three Dimensional Elasticity ◽  
General Method

AbstractIn this paper, we present a general method to derive the explicit constitutive relations for isotropic elastic 6-parameter shells made from a Cosserat material. The dimensional reduction procedure extends the methods of the classical shell theory to the case of Cosserat shells. Starting from the three-dimensional Cosserat parent model, we perform the integration over the thickness and obtain a consistent shell model of order $$ O(h^5) $$ O ( h 5 ) with respect to the shell thickness h. We derive the explicit form of the strain energy density for 6-parameter (Cosserat) shells, in which the constitutive coefficients are expressed in terms of the three-dimensional elasticity constants and depend on the initial curvature of the shell. The obtained form of the shell strain energy density is compared with other previous variants from the literature, and the advantages of our constitutive model are discussed.

Theory Analysis of FBG Characteristics under 3D Homogeneous Stress Field

2012 ◽  
Vol 499 ◽  
pp. 213-217
Author(s):  
Zhao Xia Wu ◽  
Hui Fang Zhang ◽  
Jun Wei Wang ◽  
Li Fu Wang
Keyword(s):  
Three Dimensional ◽  
Transverse Force ◽  
Reflection Spectra ◽  
Theory Analysis ◽  
Center Wavelength ◽  
Leading Role ◽  
Wavelength Sensitivity ◽  
Homogeneous Stress ◽  
The Difference ◽  
Sensing Characteristics

FBG sensing characteristics and model under three-dimensional stress are studyed in this paper. Theory analysis indicates that the reflection spectra of FBG is gradually splitted into two resonance peaks with the increase of the load and the two resonance peaks have a linear relation to the load. The difference of the wavelength sensitivity of the two directions of FBG is much less than the conditions of FBG only under transverse force, that is to say, the axial force plays a leading role in the shift amount of center wavelength.

Three-Dimensional Vibration Analysis of Thick, Complete Conical Shells

2004 ◽  
Vol 71 (4) ◽  
pp. 502-507 ◽  
Author(s):  
Jae-Hoon Kang ◽  
Arthur W. Leissa
Keyword(s):  
Present Method ◽  
Shell Theory ◽  
Ritz Method ◽  
Three Dimensional ◽  
Mode Shapes ◽  
Algebraic Polynomials ◽  
Shells Of Revolution ◽  
Conical Shells ◽  
Thin Shell Theory ◽  
Time Periodic

A three-dimensional (3D) method of analysis is presented for determining the free vibration frequencies and mode shapes of thick, complete (not truncated) conical shells of revolution. Unlike conventional shell theories, which are mathematically two-dimensional (2D), the present method is based upon the 3D dynamic equations of elasticity. Displacement components ur,uz, and uθ in the radial, axial, and circumferential directions, respectively, are taken to be sinusoidal in time, periodic in θ, and algebraic polynomials in the r and z-directions. Potential (strain) and kinetic energies of the conical shells are formulated, the Ritz method is used to solve the eigenvalue problem, thus yielding upper bound values of the frequencies by minimizing the frequencies. As the degree of the polynomials is increased, frequencies converge to the exact values. Convergence to four-digit exactitude is demonstrated for the first five frequencies of the conical shells. Novel numerical results are presented for thick, complete conical shells of revolution based upon the 3D theory. Comparisons are also made between the frequencies from the present 3D Ritz method and a 2D thin shell theory.

On a Laminated Orthotropic Shell Theory Including Transverse Shear Deformation

1972 ◽  
Vol 39 (4) ◽  
pp. 1091-1097 ◽  
Author(s):  
S. B. Dong ◽  
F. K. W. Tso
Keyword(s):  
Shear Deformation ◽  
Transverse Shear ◽  
Shell Theory ◽  
Orthotropic Shell ◽  
Plane Waves ◽  
Present Theory ◽  
Transverse Shear Deformation ◽  
Correction Factors ◽  
Natural Oscillations ◽  
Orthotropic Shells

A constitutive relation for laminated orthotropic shells which includes transverse shear deformation is presented. This relation involves composite correction factors k112, k222 which are determined from an analysis of plane waves in a plate with the same layered construction. The range of applicability of the present theory and the quantitative effect of transverse shear deformation are evinced in a problem concerned with the natural oscillations of a three-layered freely supported cylinder.

Effect of truck position and multiple truck loading on response of long-span metal culverts

2014 ◽  
Vol 51 (2) ◽  
pp. 196-207 ◽  
Author(s):  
Tamer M. Elshimi ◽  
Richard W.I. Brachman ◽  
Ian D. Moore
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Shell Theory ◽  
Orthotropic Shell ◽  
Three Dimensional ◽  
Element Analysis ◽  
Long Span ◽  
Dimensional Finite Element ◽  
Current Design ◽  
Three Dimensional Finite Element

Long-span metal culverts have been used for almost 50 years as an economical alternative to short-span bridges. Current design methods are based on two-dimensional finite element analysis using beam theory to represent the structure, or three-dimensional analysis employing orthotropic shell theory. However, neither analysis has been used to investigate the most critical position for trucks at the surface of long-span metal culverts. This paper shows results of three-dimensional finite element analysis, employing orthotropic shell theory and explicitly modeling the geometry of corrugated plates for a specific box culvert tested using a fully loaded dump truck. The analysis was then extended to study the effect of truck position on the response of long-span box and arch culverts. The finite element models, employing orthotropic shell theory and explicitly modeling the geometry of corrugated plates, successfully produced the behaviour of the culvert under truck loading for different truck positions. Culvert deformations were calculated within 7%–13% of the measured values at different locations. The bending moment at the crown was within 4%–17% of the values calculated using the measured strains. If three-dimensional finite element analysis is used to design these culverts, two design trucks should be considered (current design considers a single design truck). The highest moment or thrust is obtained when the truck tandem axles are located above the crown of the culvert.

Bifurcation of Equilibrium in Thick Orthotropic Cylindrical Shells Under Axial Compression

1995 ◽  
Vol 62 (1) ◽  
pp. 43-52 ◽  
Author(s):  
G. A. Kardomateas
Keyword(s):  
Axial Compression ◽  
Orthotropic Material ◽  
Shell Theory ◽  
Three Dimensional ◽  
Theory Of Elasticity ◽  
Elasticity Solution ◽  
Timoshenko Theory ◽  
Cylinder Axis ◽  
Dimensional Theory ◽  
Nonshallow Shell

The bifurcation of equilibrium of an orthotropic thick cylindrical shell under axial compression is studied by an appropriate formulation based on the three-dimensional theory of elasticity. The results from this elasticity solution are compared with the critical loads predicted by the orthotropic Donnell and Timoshenko nonshallow shell formulations. As an example, the cases of an orthotropic material with stiffness constants typical of glass/epoxy and the reinforcing direction along the periphery or along the cylinder axis are considered. The bifurcation points from the Timoshenko formulation are always found to be closer to the elasticity predictions than the ones from the Donnell formulation. For both the orthotropic material cases and the isotropic one, the Timoshenko bifurcation point is lower than the elasticity one, which means that the Timoshenko formulation is conservative. The opposite is true for the Donnell shell theory, i.e., it predicts a critical load higher than the elasticity solution and therefore it is nonconservative. The degree of conservatism of the Timoshenko theory generally increases for thicker shells. Likewise, the Donnell theory becomes in general more nonconservative with thicker construction.

scholarly journals The Analysis and Calculation of DC Earth Electrode Electric Field Coupling with Thermal based on Shell Theory

2017 ◽  
Author(s):  
Jingli Li ◽  
Liying Guo ◽  
Peng Hu ◽  
Yuanbo Li ◽  
Yu Zhang ◽  
...  
Keyword(s):  
Electric Field ◽  
Thermal Field ◽  
Shell Theory ◽  
Three Dimensional ◽  
Dynamic Coupling ◽  
Electrode Structure ◽  
Electrical Field ◽  
Field Coupling ◽  
Dc Current ◽  
Earth Electrode

During HVDC earth return operation systems, a high magnitude current will be injected into soil through earth electrode, the potential on the surface would change widely and produce unfavorable effects on the AC systems around. This paper presents an effective finite element method (FEM) coupling electric field with thermal field to evaluate the electrical field induced by the injected DC current. Firstly, owe to the characteristic of FEM, this method can consider arbitrary soil and earth electrode structure. Secondly, by setting the electrical and thermal parameters of soil as a function of temperature at the same time, the dynamic coupling process of electric field and thermal field is simulated accurately. Thirdly, to deal with the singular point in FEM subdivision and the huge computation in traditional three-dimensional FEM, the FEM coupling 2-D earth electrode with 3-D soil based on "shell" theory is introduced. Finally, based on the suggested method, the effect of abnormal resistance region (ARR) near DC earth electrode on electric field distribution is analyzed.

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