A general solution technique for electroelastic fields in piezoelectric bodies with D ∞ symmetry in cylindrical coordinates

2016 ◽  
Vol 62 (1) ◽  
pp. 29-41 ◽  
Author(s):  
Masayuki Ishihara ◽  
Yoshihiro Ootao ◽  
Yoshitaka Kameo
Keyword(s):  
General Solution ◽  
Solution Technique ◽  
Cylindrical Coordinates ◽  
Electroelastic Fields

Validation of a Thermal Spreading/Constriction Resistance Model for a Convectively Cooled Plate With an Applied Heat Flux

2008 ◽  
Author(s):  
P. Y. C. Lee ◽  
W. H. Leong
Keyword(s):  
Heat Flux ◽  
General Solution ◽  
Neumann Boundary ◽  
Solution Technique ◽  
Two Dimensional ◽  
Experimental Heat ◽  
Experimental Heat Transfer ◽  
Present Solution ◽  
Resistance Model ◽  
Dimensional Boundary

A thermal resistance model of a two-dimensional boundary value problem (BVP) that is commonly found in engineering/experimental heat transfer is presented. The problem consists of two different convectively cooled sub-sections along one boundary, and a heat flux distribution imposed on a portion of another (opposite) boundary, coupled with adiabatic conditions (Neumann boundary conditions) along the remaining boundaries under steady-state conditions. In solving this BVP, the solution technique is highlighted. Consistent with theory, the solution to this problem depends on two Biot numbers, dimensionless heat flux and other dimensionless geometric parameters related to the problem. The present solution is an exact general solution to an existing two-dimensional problem found in literature, and as a special case, the general solution reduces exactly to the existing solution. Also, the present model is validated by comparing the present solution with measured data, and in terms of a temperature difference between two locations on the plate, the analytical solution is well within the experimental error of 0.03 K.

The “Weighted Composite Life” Problem

1982 ◽  
Vol 104 (4) ◽  
pp. 844-848 ◽  
Author(s):  
M. A. Townsend
Keyword(s):  
General Solution ◽  
Solution Technique ◽  
Problem Class

A problem class is identified and characterized: The problem is to optimally select variables of a multi-segment activity or design where there is an overall limiting constraint. A number of problems have been individually solved, but it is shown that a wide variety of practical problems can be formulated thusly and that a general solution technique is effective.

The Role of VLBI in the Establishment of Coordinate Systems

1975 ◽  
Vol 26 ◽  
pp. 293-295 ◽  
Author(s):  
I. Zhongolovitch
Keyword(s):  
General Solution ◽  
Future Development ◽  
Rational Approach ◽  
Radio Telescopes ◽  
Coordinate Systems ◽  
Tectonic Plates ◽  
Astronomical Observations ◽  
Optical Instruments ◽  
Fundamental Polyhedron

Considering the future development and general solution of the problem under consideration and also the high precision attainable by astronomical observations, the following procedure may be the most rational approach:1. On the main tectonic plates of the Earth’s crust, powerful movable radio telescopes should be mounted at the same points where standard optical instruments are installed. There should be two stations separated by a distance of about 6 to 8000 kilometers on each plate. Thus, we obtain a fundamental polyhedron embracing the whole Earth with about 10 to 12 apexes, and with its sides represented by VLBI.

The limit state of concrete and reinforced concrete rods at complex and longitudinal-transverse bending

2020 ◽  
pp. 60-73
Author(s):  
Yu V Nemirovskii ◽  
S V Tikhonov
Keyword(s):  
General Solution ◽  
Least Squares ◽  
Nonlinear Differential Equations ◽  
Limit State ◽  
Algebraic Equations ◽  
Method Of Least Squares ◽  
Elasticity Limit ◽  
Limit Values ◽  
Symbolic Calculations ◽  
Deformation Diagrams

The work considers rods with a constant cross-section. The deformation law of each layer of the rod is adopted as an approximation by a polynomial of the second order. The method of determining the coefficients of the indicated polynomial and the limit deformations under compression and tension of the material of each layer is described with the presence of three traditional characteristics: modulus of elasticity, limit stresses at compression and tension. On the basis of deformation diagrams of the concrete grades B10, B30, B50 under tension and compression, these coefficients are determined by the method of least squares. The deformation diagrams of these concrete grades are compared on the basis of the approximations obtained by the limit values and the method of least squares, and it is found that these diagrams approximate quite well the real deformation diagrams at deformations close to the limit. The main problem in this work is to determine if the rod is able withstand the applied loads, before intensive cracking processes in concrete. So as a criterion of the conditional limit state this work adopts the maximum permissible deformation value under tension or compression corresponding to the points of transition to a falling branch on the deformation diagram level in one or more layers of the rod. The Kirchhoff-Lyav classical kinematic hypotheses are assumed to be valid for the rod deformation. The cases of statically determinable and statically indeterminable problems of bend of the rod are considered. It is shown that in the case of statically determinable loadings, the general solution of the problem comes to solving a system of three nonlinear algebraic equations which roots can be obtained with the necessary accuracy using the well-developed methods of computational mathematics. The general solution of the problem for statically indeterminable problems is reduced to obtaining a solution to a system of three nonlinear differential equations for three functions - deformation and curvatures. The Bubnov-Galerkin method is used to approximate the solution of this equation on the segment along the length of the rod, and specific examples of its application to the Maple system of symbolic calculations are considered.

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