Direct Integration of Elastic Thin Shallow Shell’s Governing Equations and Lower Order Method

1987 ◽  
pp. 38-42
Author(s):  
Fan Jashen
Keyword(s):  
Lower Order ◽  
Direct Integration ◽  
Order Method ◽  
Governing Equations

Variational Analysis of Sloshing in Spherical Industrial Vessels Under Earthquake Loading

2006 ◽  
Author(s):  
L. A. Patkas ◽  
S. A. Karamanos
Keyword(s):  
Variational Formulation ◽  
Variational Analysis ◽  
Velocity Potential ◽  
Time Function ◽  
Direct Integration ◽  
Governing Equations ◽  
Dynamic Excitation ◽  
Spatial Function ◽  
Linear Differential ◽  
Ordinary Linear Differential Equations

A variational formulation is developed for calculating liquid sloshing effects on the dynamic response of spherical containers under external dynamic excitation. The velocity potential is expressed in a series form, where each term is the product of a time function and the associated spatial function. Because of the configuration of the containers, the associated spatial functions are non-orthogonal, and the problem is not separable and results in a system of coupled non-homogeneous ordinary linear differential equations, which is solved numerically. The solution can be obtained through either direct integration or modal analysis. Sloshing frequencies and masses are calculated rigorously for arbitrary liquid height, and convergence of the solution is thoroughly examined. Particular emphasis is given on the cases of half-full spheres, where explicit expressions for the coefficients of the governing equations are derived. Furthermore, the behavior of nearly-full and nearly-empty vessels is briefly discussed.

scholarly journals Direct integration method in three-dimensional elasticity and thermoelasticity problems for inhomogeneous transversely isotropic solids: governing equations in terms of stresses

2019 ◽  
pp. 102-105
Author(s):  
R. M. Kushnir ◽  
Y. V. Tokovyy ◽  
D. S. Boiko
Keyword(s):  
Stress Tensor ◽  
Integral Equations ◽  
Integration Method ◽  
Separation Of Variables ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Solution Technique ◽  
Direct Integration ◽  
Governing Equations ◽  
Direct Integration Method

An efficient technique for thermoelastic analysis of inhomogeneous anisotropic solids is suggested within the framework of three-dimensional formulation. By making use of the direct integration method, a system of governing equations is derived in order to solve three-dimensional problems of elasticity and thermoelasticity for transversely isotropic inhomogeneous solids with elastic and thermo-physical properties represented by differentiable functions of the variable in the direction that is transversal to the plane of isotropy. By implementing the relevant separation of variables, the obtained equations can be uncoupled and reduced to second-kind integral equations for individual stress-tensor components and the total stress, which represents the trace of the stress tensor. The latter equations can be attempted by any of the numerical, analyticalnumerical, or analytical means available for the solution of the second-kind integral equations. In order to construct the solutions in an explicit form, an advanced solution technique can be developed on the basis of the resolvent-kernel method implying the series representation by the recurring kernels, computed iteratively by the original kernel of an integral equation.

MHD Free Convective Flow Past a Vertical Porous Plate in a Porous Medium in the Presence of Soret and Dofour Effects

2018 ◽  
Vol 6 (8) ◽  
pp. 429
Author(s):  
Y. Hari Krishna ◽  
G Kamala ◽  
M.V. Ramana Murthy ◽  
D Bhagyya
Keyword(s):  
Convective Flow ◽  
Porous Plate ◽  
Order Method ◽  
Governing Equations ◽  
Free Convective Flow ◽  
Shooting Technique ◽  
Vertical Porous Plate ◽  
Flow Past ◽  
Fourth Order Method ◽  
Transfer Flow

A steady MHD free convective heat and mass transfer flow past a semi-infinite vertical porous plate in the presence of Soret and Dofour effects has been studied in this paper. The governing equations are solved numerically by Runge – Kutta fourth order method along with shooting technique. The effect of various governing parameters for velocity, temperature, concentration; skin-friction, Nusselt number and Sherwood number are also obtained. The effects of various parameters have been shown numerically and discussed graphically.

scholarly journals REDUCTION OF PLANE THERMOELASTICITY PROBLEM IN INHOMOGENEOUS STRIP TO INTEGRAL VOLTERRA TYPE EQUATION

2005 ◽  
Vol 12 (1) ◽  
pp. 91-100 ◽  
Author(s):  
Yu. V. Tokovyy ◽  
A. V. Rychahivskyy
Keyword(s):  
Fourier Transforms ◽  
Type Equation ◽  
Thermoelasticity Problem ◽  
Direct Integration ◽  
Governing Equations ◽  
Volterra Type ◽  
Simple Iteration ◽  
Method Of Simple Iteration

We have developed a method for analytical solving of the plane thermoelasticity problem in terms of stresses for a strip, which is infinite with respect to width. To derive the governing equations, we have used a method of direct integration of differential equilibrium and compatibility equations. Reducing the governing equations to the integral Volterra type equation of the second kind, we have solved it in Fourier transforms by applying a method of simple iteration. Straipsnyje vystomas analizinio sprendinio metodas nehomogeninio strypo termoelastiškumo uždaviniui strypo itempimams rasti, kai strypo ilgis yra begalinis pločio atžvilgiu. Pagrindines lygtys išvedamos naudojant diferencialines pusiausvyros ir suderinamumo lygtis ir tiesiogini integravima. Suvedus pagrindines lygtis i antrojo tipo Volterra integraline lygti, naudojant Furje transformacija, ji sprendžiama paprastosios iteracijos metodu.

NONLINEAR VIBRATION OF A THREE-DIMENSIONAL MOVING GANTRY CRANE SUBJECTED TO A TRAVELLING TROLLEY HOISTING A SWINGING OBJECT

2010 ◽  
Vol 34 (3-4) ◽  
pp. 333-350 ◽  
Author(s):  
Davood Younesian ◽  
Elyas Ghafoori ◽  
Mehdi Sadeghpour
Keyword(s):  
Finite Element Method ◽  
Sensitivity Analysis ◽  
Nonlinear Vibration ◽  
Parametric Study ◽  
Three Dimensional ◽  
Gantry Crane ◽  
Direct Integration ◽  
Governing Equations ◽  
Nonlinear Responses ◽  
Linear And Nonlinear

Nonlinear vibration of a three-dimensional moving gantry crane carrying a trolley hoisting a swinging object is studied in this paper. A finite element method is used to solve nonlinear coupled governing equations of the structure. A combinational technique (Newmark-Runge-Kutta) is employed for direct integration procedure. To develop a comprehensive parametric study and sensitivity analysis of the coupled nonlinear system, sequence of numerical simulations are carried out. Parametric study is directed to find out how different parameters like speed and acceleration of the trolley and gantry crane as well as the mass of the moving trolley and swinging object may affect the linear and nonlinear responses of the structure. It is found that the nonlinearity arises from large amplitude of three-dimensional motion of the swinging object.

Experiments with a Quadrupole Octopole Corrector in a STEM

1977 ◽  
Vol 35 ◽  
pp. 90-91 ◽  
Author(s):  
V. Beck
Keyword(s):  
Lower Order ◽  
Spherical Aberration ◽  
Mechanical Alignment

Recently a number of experiments have been carried out on a STEM which included a multipole corrector for primary spherical aberration. The results of these experiments indicate that the correction of primary spherical aberration with magnetic multipoles is beset with very serious difficulties related to hysteresis.The STEM and corrector have been described previously. In theory, the corrector should cancel primary spherical aberration so that other aberrations limit the resolution. For this instrument, secondary spherical aberration should limit the resolution to 1 A at 50 kV. A thorough study of misalignment aberrations was made. The result of the study indicates that the octopoles must be aligned to 1000 A. Since mechanical alignment cannot be done to this accuracy, trim coils were built into the corrector in order to achieve the required alignment electrically. The trim coils are arranged to excite all the lower order moments of an element.

Psychometric Definition of Rorschach Determinant Component Structure

1998 ◽  
Vol 14 (2) ◽  
pp. 116-123 ◽  
Author(s):  
Raymond M. Costello
Keyword(s):  
Lower Order ◽  
Three Dimensions ◽  
Comprehensive System ◽  
Empirical Examination ◽  
Component Structure ◽  
Exner's Comprehensive System ◽  
Factor Analytic ◽  
Confirmatory Factor ◽  
Components Analysis ◽  
Definition Of

This is an empirical examination of Experienced Stimulation (es) and Experience Actual (EA) from Exner's Comprehensive System (CS) for Rorschach's Test, spurred by Kleiger's theoretical critique. Principal components analysis, Cronbach's α, and inter-item correlational analyses were used to test whether 13 determinants used to code Rorschach responses (M, FM, m, CF+C, YF+Y, C'F+C', TF+T, VF+V, FC, FC', FV, FY, FT) are best represented as a one, two, or more-dimensional construct. The 13 determinants appear to reflect three dimensions, a “lower order” sensori-motor dimension (m + CF+C + YF+Y + C'F+C' + TF+T + VF+V) with a suggested label of Modified Experienced Stimulation (MES), a “higher order” sensori-motor dimension (FM + FV + FY + FT) with a suggested label of Modified Experience Potential (MEP), and a third sensori-motor dimension (M+FC+FC') for which the label of Modified Experience Actual (MEA) is suggested. These findings are consistent with Kleiger's arguments and could lead to a refinement of CS constructs by aggregating determinants along lines more theoretically congruous and more internally consistent. A RAMONA model with parameters specified was presented for replication attempts which use confirmatory factor analytic techniques.

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