Elasticity Solutions for Thick-Wall Submersible Spheres

1974 ◽  
Vol 96 (4) ◽  
pp. 1136-1140
Author(s):  
F. J. Dzialo
Keyword(s):  
Hydrostatic Pressure ◽  
Infinite Series ◽  
Legendre Polynomials ◽  
Buoyancy Force ◽  
Potential Functions ◽  
Thick Wall ◽  
Arbitrary Boundary ◽  
Numerical Example ◽  
Body Forces ◽  
Elasticity Solutions

Elasticity solutions utilizing the classical Boussinesq potential functions for thick-wall submersible spheres are developed. The solutions provide field stresses and strains, which consider the effect of gravity body forces, and arbitrary boundary loadings. The boundary loadings may be due to a nonuniform hydrostatic pressure, hull equipment, ballast, and can be expressed as an infinite series of Legendre polynomials. A numerical example which considers a nonuniform hydrostatic pressure and an arbitrary counter-buoyancy force applied at the inner boundary is given. Field stresses and strains are presented for various shell thicknesses and hydrostatic pressures.

scholarly journals Anchoring Energy for Nematic Liquid Crystals an Analysis of the Proposed Forms

1984 ◽  
Vol 39 (11) ◽  
pp. 1066-1076 ◽  
Author(s):  
G. Barbero ◽  
N. V. Madhusudana ◽  
G. Durand
Keyword(s):  
Liquid Crystal ◽  
Infinite Series ◽  
Tilt Angle ◽  
Legendre Polynomials ◽  
Fourier Expansion ◽  
Easy Axis ◽  
Practical Interest ◽  
Surface Anchoring ◽  
Functional Forms ◽  
Anchoring Energy

We analyze the proposed functional forms describing the surface anchoring energy of MBBA nematic liquid crystal. Measurements of the surface torque versus tilt angle suggest that the simple cosinus-square form is not adequate for MBBA. The generalized form in an infinite series in cosinus-square is not useful since the set of functions is not orthogonal. Analyses using the orthogonal Legendre polynomials and Fourier expansion are given. Finally we analyse the data in terms of small tilt angles compared to the easy axis, and very far from it, which are the two limits of practical interest.

Non-linear influence of hydrostatic pressure on the yielding of asymmetric anisotropic sheet metals

2016 ◽  
Vol 23 (2) ◽  
pp. 159-180
Author(s):  
Farzad Moayyedian ◽  
Mehran Kadkhodayan
Keyword(s):  
Hydrostatic Pressure ◽  
Potential Functions ◽  
Face Centered Cubic ◽  
Sheet Metals ◽  
Strength Differential ◽  
Plastic Potential ◽  
Yield Functions ◽  
Non Linear ◽  
Data Points ◽  
Face Centered

The objective of the current research is the investigation into possible non-linear influence of hydrostatic pressure on yielding of asymmetric (exhibiting the so-called “strength-differential effect”) anisotropic sheet metals. To reach this aim, two yield functions are developed, called here “non-linear pressure sensitive criteria I and II,” (NPC-1 and NPC-2). In addition, the non-associated flow rules are employed for these new criteria. The yield functions are defined as non-linearly dependent on hydrostatic pressure, while the plastic potential functions are introduced to be pressure insensitive. To calibrate these criteria, the yield functions need 10 directional experimental yield stresses and the plastic potential functions need eight Lankford coefficients data points. Four well-known anisotropic sheet metals with different structures, namely AA 2008-T4, a Face Centered Cubic material (FCC), AA 2090-T3, a Face Centered Cubic material (FCC), AZ31, a hexagonal closed packed material (HCP) and high-purity [Formula: see text]-titanium (HCP) are considered as case studies. Finally, it is observed that NPC-1 and NPC-2 are more successful than previous criteria in anticipating directional strength and mechanical properties.

Proper Inclusion of Interiorly Applied Loads With Beam Theory

2012 ◽  
Vol 80 (1) ◽  
Author(s):  
Jimmy C. Ho ◽  
Wenbin Yu ◽  
Dewey H. Hodges
Keyword(s):  
Asymptotic Method ◽  
Beam Theory ◽  
Elliptic Cylinder ◽  
Conventional Approach ◽  
Body Forces ◽  
Variational Asymptotic ◽  
Variational Asymptotic Method ◽  
Elasticity Solutions ◽  
Precise Distribution

An error is introduced by the conventional approach of applying beam theory in the presence of interiorly applied loads. This error arises from neglecting the influence of the precise distribution of surface tractions and body forces on the warping displacements. This paper intends to show that beam theory is capable of accounting for this influence on warping and accomplishes this by the variational asymptotic method. Correlations between elasticity solutions and beam solutions provide not only validations of beam solutions, but also illustrate the resulting errors from the conventional approach. Correlations are provided here for an isotropic parallelepiped undergoing pure extensional deformations and for an isotropic elliptic cylinder undergoing pure torsional deformations.

Continuity of Cylindrical Shells Subjected to the Uniformly Distributed Longitudinal Surface Loads

1965 ◽  
Vol 87 (2) ◽  
pp. 115-123
Author(s):  
Jeng C. Shang
Keyword(s):  
Cylindrical Shell ◽  
Hydrostatic Pressure ◽  
Loading Condition ◽  
Abrupt Change ◽  
Constant Pressure ◽  
Cylindrical Shells ◽  
Plate Thickness ◽  
Numerical Example ◽  
Surface Loads

The continuity problems in the cylindrical shells due to abrupt change in geometry, plate thickness, or loading condition are discussed. In order to illustrate the method of determining the membrane stresses and the secondary stresses caused by the discontinuity in geometry, plate thickness, or loading, a numerical example is also presented for a cylindrical shell subjected to (a) constant pressure; (b) hydrostatic pressure; and (c) partial loading.

Research on Thick-Wall Columnar Pressure Vessel with Auto-Frettage

2010 ◽  
Vol 156-157 ◽  
pp. 969-972
Author(s):  
Qing Hua Cao
Keyword(s):  
Shear Strength ◽  
Pressure Vessel ◽  
Bauschinger Effect ◽  
Thick Wall ◽  
Operating Pressure ◽  
Strength Theory ◽  
Numerical Example ◽  
The Relationship ◽  
Designing Method ◽  
Optimal Radius

The theoretic formula for the optimal radius of elastic-plastic junction in auto-frettage thick-wall columnar pressure vessel was deduced. on the basis of the twin shear strength theory, the relationship between the allowable maximal operating pressure for the pressure vessel and yield was analyzed,Bauschinger effect to reverse yield with auto-engaged vessel was investigated, The procedure was illustrated with the help of numerical example and the results show the reliability of the designing method.

Natural Convection in Binary Gases Due to Horizontal Thermal and Solutal Gradients

1991 ◽  
Vol 113 (1) ◽  
pp. 141-147 ◽  
Author(s):  
J. A. Weaver ◽  
R. Viskanta
Keyword(s):  
Natural Convection ◽  
Unsteady Flow ◽  
Buoyancy Force ◽  
Measured Temperature ◽  
Concentration Gradients ◽  
Thermal Buoyancy ◽  
Smoke Flow ◽  
Numerical Predictions ◽  
Body Forces ◽  
Thermal Buoyancy Force

The influence of augmenting and opposing thermal and solutal buoyancy forces on natural convection of binary gases due to horizontal temperature and concentration gradients is examined through comparison of smoke flow visualization and measured temperature and concentration distributions with numerical predictions. The observed flow at the cold wall was unsteady for opposing body forces. The same basic flow structure was observed, but the unsteady flow intensifies as the opposing solutal buoyancy force increases as compared to the thermal buoyancy force. Comparison of predicted and measured temperatures and concentrations is fair overall, but the steady-state analytical model fails to predict the unsteady flow and heat and mass transport for opposing body forces.

A Method for Obtaining Stresses and Displacements in Thick Cylindrical Shells Under Arbitrary Boundary Conditions

1973 ◽  
Vol 40 (1) ◽  
pp. 221-226 ◽  
Author(s):  
E. B. Golub ◽  
F. Romano
Keyword(s):  
Stress State ◽  
Variational Principle ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Cylindrical Shells ◽  
Present Theory ◽  
Bending Stress ◽  
Arbitrary Boundary ◽  
Elasticity Solutions ◽  
Circular Cylindrical Shells

This paper presents a means for obtaining both the stress and displacement states which appear in thick, circular, cylindrical shells under arbitrary load and boundary conditions. The governing differential equations and the associated boundary conditions are obtained by utilizing Reissner’s variational principle [6], the assumed form of the stress state containing, in addition to terms corresponding to conventional membrane and bending stress resultants, supplementary sets of self-equilibrating stress resultants. Comparison of results obtained from known elasticity solutions shows that the present theory accurately yields solutions for shells with radius-thickness ratios of the order of 3.0. Numerically computed here, for comparison purposes, is the axisymmetric, periodically spaced, band load problem of Klosner and Levine.

Hydrostatic force exerted on a submerged surface

2018 ◽  
Author(s):  
Marcel Escudier
Keyword(s):  
Hydrostatic Pressure ◽  
Buoyancy Force ◽  
Vertical Plane ◽  
Vertical Component ◽  
Horizontal Component ◽  
Curved Surface ◽  
Hydrostatic Force ◽  
Floating Object ◽  
Floating Objects ◽  
Metacentric Height

In this chapter it is shown how to calculate the force which arises due to the hydrostatic pressure distributed over a submerged surface or object. The vertical component of force is shown to be equal in magnitude to the weight of fluid which would occupy the volume directly above the surface and to act vertically downwards through the centroid of this volume. For a curved surface, the magnitude of the horizontal component of the hydrostatic force is shown to equal the hydrostatic force on the projection of the surface onto a vertical plane. This force is equal to the product of the area of the surface and the pressure at its centroid. The buoyancy force exerted on a submerged or floating object is shown to equal the weight of the fluid displaced by the object (Archimedes’ principle) and to act vertically upwards through the centroid of the displaced fluid. Stability of floating objects is discussed and the concept of metacentric height introduced.

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