NATURAL FREQUENCIES OF VIBRATION OF LAYERED HOLLOW SPHERES USING EXACT THREE-DIMENSIONAL ELASTICITY EQUATIONS

1996 ◽  
Vol 195 (1) ◽  
pp. 155-162 ◽  
Author(s):  
H. Jiang ◽  
P.G. Young ◽  
S.M. Dickinson
Keyword(s):  
Natural Frequencies ◽  
Hollow Spheres ◽  
Three Dimensional ◽  
Elasticity Equations ◽  
Three Dimensional Elasticity

Elasticity solution for thick laminated anisotropic cylindrical panels under dynamic load

2002 ◽  
Vol 216 (3) ◽  
pp. 315-322 ◽  
Author(s):  
A Alibiglu ◽  
M Shakeri ◽  
M R Eslami
Keyword(s):  
Differential Equations ◽  
Dynamic Load ◽  
Three Dimensional ◽  
Variable Coefficients ◽  
Cylindrical Panel ◽  
Great Length ◽  
Elasticity Equations ◽  
Shell Panel ◽  
Asymmetric Load ◽  
Three Dimensional Elasticity

The dynamic response of an axisymmetric arbitrary laminated anisotropic cylindrical panel subjected to asymmetric load is studied on the basis of three-dimensional elasticity equations. The shell panel has a great length and is simply supported at both edges. The highly coupled partial differential equations (PDEs) are reduced to ordinary differential equations (ODEs) with variable coefficients by means of trigonometric function expansion in circumferential directions. The resulting OPEs are solved by Galerkin's finite element method. Numerical examples are presented for 45°/-45° and 45°/-45°/45° laminations under dynamic load. Finally, the results are compared with published results.

Three-Dimensional Analysis of an Elastic Plate-Cylinder Intersection by the Boundary-Point-Least-Squares Technique

1977 ◽  
Vol 99 (1) ◽  
pp. 17-25 ◽  
Author(s):  
D. Redekop
Keyword(s):  
Boundary Conditions ◽  
Least Squares ◽  
Boundary Point ◽  
Shell Theory ◽  
Three Dimensional ◽  
Middle Part ◽  
Elasticity Equations ◽  
Three Dimensional Elasticity ◽  
Tension Loading ◽  
Theoretical Results

The boundary-point-least-squares technique is applied to the axisymmetric three-dimensional elasticity problem of a hollow circular cylinder normally intersecting with a perforated flat plate. The geometry of the intersection is partitioned into three parts. Boundary conditions on the middle part and continuity conditions between adjacent parts are satisfied using the numerical boundary-point-least-squares technique while the governing elasticity equations and all other boundary conditions are satisfied exactly. Sample theoretical results are presented for the case of axisymmetric radial tension loading on the plate. The results compare favorably with previously published experimental data and provide supplementary data to theoretical results obtained using existing shell theory solutions.

Elastohydrodynamic Studies of Three-Lobe Journal Bearings with Non-Newtonian Lubricants

1991 ◽  
Vol 205 (6) ◽  
pp. 379-388 ◽  
Author(s):  
K C Goyal ◽  
R Sinhasan
Keyword(s):  
Journal Bearing ◽  
Dynamic Performance ◽  
Three Dimensional ◽  
Performance Characteristics ◽  
Continuity Equations ◽  
Viscosity Term ◽  
Elasticity Equations ◽  
Wide Range ◽  
Deformation Coefficient ◽  
Three Dimensional Elasticity

A computer aided elastohydrodynamic study of the three-lobe journal bearing with non-Newtonian lubricants is presented for the static and dynamic performance characteristics. The three-dimensional momentum and continuity equations in cylindrical coordinates governing the flow of Newtonian lubricants in the clearance space of a three-lobe journal bearing have been solved using the finite element method. The non-Newtonian effect is introduced by modifying the viscosity term for the model iteratively. Three-dimensional elasticity equations are solved to obtain deformations in the bearing shell. Static and dynamic performance characteristics are presented for a wide range of values of non-dimensional load, deformation coefficient and non-linearity factor.

scholarly journals Partial-mixed special finite element for the analysis of multilayer composites and FGM

2012 ◽  
Author(s):  
Orlando Andrianarison ◽  
Ayech Benjeddou
Keyword(s):  
Finite Element ◽  
Three Dimensional ◽  
Hamiltonian Formalism ◽  
Single Layer ◽  
Static Problem ◽  
Functionally Graded ◽  
Elasticity Equations ◽  
Graded Material ◽  
Transverse Stresses ◽  
Three Dimensional Elasticity

A partial-mixed special finite element (FE) is proposed for the static analysis of multilayer composite and functionally graded material plates. Using the Hamiltonian formalism, the three-dimensional elasticity equations are first reformulated so that a partial-mixed variational formulation, retaining as primary variables the translational displacements augmented with the transverse stresses only, is obtained; this allows, in particular, a straightforward fulfilment of the multilayer interfaces continuity conditions. After an only in-plane FE discretisation, the static problem is then reduced, for a single layer, to a Hamiltonian eigenvalue problem that is solved analytically, through the layer thickness, using the symplectic formalism; the multilayer solution is finally reached via the state-space method and the propagator matrix concept. The performance, in convergence and accuracy, of the proposed approach, applied to representative examples, is shown to be very satisfactory.

Stress Distribution and Displacements on the Electromechanical Shield of a Superconducting Generator After a Three-Phase Fault

1978 ◽  
Vol 100 (4) ◽  
pp. 630-636 ◽  
Author(s):  
N. G. Dagalakis ◽  
J. L. Kirtley
Keyword(s):  
Approximate Solution ◽  
Stress Distribution ◽  
Three Dimensional ◽  
Open Circuit ◽  
Thick Wall ◽  
Two Dimensional ◽  
Elasticity Equations ◽  
Three Phase ◽  
Three Dimensional Elasticity ◽  
Resultant Stress

We assume that there is a cylindrical electromechanical shield between the armature and the field windings of a superconducting generator. The maximum shield load after an open circuit three-phase fault is derived. The resultant stress distribution and displacements are calculated for two cases: for the case of a thick wall long shield, where two dimensional plane strain conditions are assumed away from the two end supports, and for the case of the moderately thick to thin shield wall, where an approximate solution is derived which approximately satisfies the three dimensional elasticity equations and the end boundary conditions. The solution was applied to 2-pole and 4-pole machine designs.

Three-Dimensional Analysis of the Free Vibration of Thick Rectangular Plates With Depressions, Grooves or Cut-Outs

1996 ◽  
Vol 118 (2) ◽  
pp. 184-189 ◽  
Author(s):  
P. G. Young ◽  
J. Yuan ◽  
S. M. Dickinson
Keyword(s):  
Kinetic Energy ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Dimensional Analysis ◽  
Thick Plate ◽  
Three Dimensional ◽  
Rectangular Plates ◽  
Algebraic Polynomials ◽  
Elasticity Equations ◽  
Three Dimensional Elasticity

A solution is presented for the free vibration of very thick rectangular plates with depressions, grooves or cut-outs using three-dimensional elasticity equations in Cartesian coordinates. Simple algebraic polynomials which satisfy the boundary conditions of the plate are used as trial functions in a Ritz approach. The plate is modelled as a parallelepiped, and the inclusions are treated quite straightforwardly by subtracting the contribution to the strain and kinetic energy expressions of the volume removed, before minimizing the functional. The approach is demonstrated by considering a number of square thick plate cases, including a plate with a cylindrical groove, a shallow depression or a cylindrical cut-out.

Beam Theory and Its Suitability for the Analysis of Pipes

1991 ◽  
Vol 113 (2) ◽  
pp. 291-296
Author(s):  
H. Fan ◽  
G. E. O. Widera ◽  
P. Afshari
Keyword(s):  
Asymptotic Expansion ◽  
Boundary Conditions ◽  
Cross Section ◽  
Three Dimensional ◽  
Beam Theory ◽  
Arbitrary Cross Section ◽  
Elasticity Equations ◽  
Expansion Technique ◽  
Three Dimensional Elasticity ◽  
Benchmark Solutions

The use of the asymptotic expansion technique when applied to the three-dimensional elasticity equations is outlined and used to demonstrate the development of an asymptotic beam theory and associated boundary conditions. The formulation thus obtained holds for arbitrary cross section shapes and is applied here to pipes. It can be used to provide benchmark solutions to test the suitability of engineering beam and shell theories.

Solution of the Elastohydrodynamic Finite Journal Bearing Problem

1973 ◽  
Vol 95 (3) ◽  
pp. 342-351 ◽  
Author(s):  
K. P. Oh ◽  
K. H. Huebner
Keyword(s):  
Reynolds Equation ◽  
Journal Bearing ◽  
Three Dimensional ◽  
Solution Procedure ◽  
Iteration Scheme ◽  
Bearing Material ◽  
Constant Property ◽  
Elasticity Equations ◽  
Minimum Film Thickness ◽  
Three Dimensional Elasticity

Finite-element techniques are applied to solve the elastohydrodynamic finite journal bearing problem. Reynolds’ equation for the fluid film and the three-dimensional elasticity equations for the bearing housing are solved simultaneously using a unique iteration scheme. The analysis yields the pressure distribution and the displacement distribution which satisfy the elastohydrodynamic requirements of realistic three-dimensional bearing geometries. From these distributions, important information such as the stresses in the bearing material and the minimum film thickness in the lubricant can be calculated. In the calculations it is assumed that the bearing operates with a constant-property lubricant and a linearly elastic bearing material. The solution procedure is applied to a typical problem and numerical results are presented.

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