POSTULATION AND BUILDING OF A NUMERICAL ALGORITHM FOR SOLVING THE PROBLEMS OF THE DYNAMICS OF THE THEORY OF CONICAL SHELLS IN NONORTHOGONAL COORDINATE SYSTEM

The paper presents the formulation and numerical algorithm for solving problems of the dynamics of the theory of conical shells in a non-orthogonal coordinate system. The object of the study are conical shells, the equations of which are represented in non-orthogonal coordinate system. Purpose of the work is to formulate and construct a numerical algorithm for solving the problems of the dynamics of conical shells in a non-orthogonal coordinate system. The methods of research include the basic principles of the theory of shells to Tymoshenko's type and numerical methods. The formulation of problems and a numerical algorithm for studying the dynamic behavior of conical shells in a non-orthogonal coordinate system are considered. The results obtained in the work can be used in the design of elements of shell structures in the rocket, aircraft and shipbuilding industries. KEYWORDS: CONIC SHELL, DYNAMIC PROCESSES, NON-ORTHOGONAL COORDINATE SYSTEM, NUMERICAL METHODS

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Shock loading of fixed flexible thread and orthotropic elastic membrane

Proceedings of the Mavlyutov Institute of Mechanics ◽

10.21662/uim2003.1.003 ◽

2003 ◽

Vol 3 ◽

pp. 52-59

Author(s):

S.S. Komarov ◽

N.Yu. Tsvileneva ◽

N.I. Miskaktin

Keyword(s):

Numerical Methods ◽

Dynamic Loading ◽

Elastic Deformation ◽

Numerical Algorithm ◽

Shock Loading ◽

Elastic Membrane ◽

Wave Dynamics ◽

Elastic Membranes ◽

Pneumatic Structures

The main problems of the wave dynamics of flexible filaments and elastic membranes are solved. The reliability of the numerical algorithm proposed by the authors for calculating the elastic deformation of pneumatic structures under dynamic loading is confirmed when compared with the results of known studies obtained by analytical and numerical methods.

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Block Adjustment of Airborne Imagery in Geocentric Orthogonal Coordinate System

2009 International Conference on Information Engineering and Computer Science ◽

10.1109/iciecs.2009.5366589 ◽

2009 ◽

Cited By ~ 2

Author(s):

Chunquan Cheng ◽

Kazhong Deng ◽

Jixian Zhang ◽

Li Zhang

Keyword(s):

Coordinate System ◽

Orthogonal Coordinate System

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Three‐component sonde orientation in a deviated well

Geophysics ◽

10.1190/1.1442786 ◽

1990 ◽

Vol 55 (10) ◽

pp. 1386-1388 ◽

Cited By ~ 15

Author(s):

M. Becquey ◽

M. Dubesset

Keyword(s):

Hydraulic Fracturing ◽

Coordinate System ◽

Vertical Plane ◽

Vertical Axis ◽

Horizontal Axis ◽

Orthogonal Coordinate System ◽

Coordinate Rotation ◽

Orthogonal Components ◽

Particle Velocities

In well seismics, when operating with a three‐component tool, particle velocities are measured in the sonde coordinate system but are often needed in other systems (e.g., source‐bound or geographic). When the well is vertical, a change from the three orthogonal components of the sonde to another orthogonal coordinate system can be performed through one rotation around the vertical axis and, if necessary, another one around a horizontal axis (Hardage, 1983). If the well is deviated, the change of coordinate system remains easy in the case when the source is located at the vertical of the sonde, or in the case when the source stands in the vertical plane defined by the local well axis. In the general case (offset VSPs or walkaways) or when looking for unknown sources (such as microseismic emissions induced by hydraulic fracturing), coordinate rotation may still be performed, provided that we first get back to a situation in which one of the axes is vertical.

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Legendre Spectral Collocation Technique for Advection Dispersion Equations Included Riesz Fractional

Fractal and Fractional ◽

10.3390/fractalfract6010009 ◽

2021 ◽

Vol 6 (1) ◽

pp. 9

Author(s):

Mohamed M. Al-Shomrani ◽

Mohamed A. Abdelkawy

Keyword(s):

Numerical Methods ◽

Numerical Algorithm ◽

Spectral Collocation ◽

Theoretical Formulation ◽

Numerical Examples ◽

Dispersion Equations ◽

Advection Dispersion ◽

Collocation Technique ◽

Collocation Approach

The advection–dispersion equations have gotten a lot of theoretical attention. The difficulty in dealing with these problems stems from the fact that there is no perfect answer and that tackling them using local numerical methods is tough. The Riesz fractional advection–dispersion equations are quantitatively studied in this research. The numerical methodology is based on the collocation approach and a simple numerical algorithm. To show the technique’s performance and competency, a comprehensive theoretical formulation is provided, along with numerical examples.

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Building of a space form of the flexible inextensible one-layer conic shell

Nexo Revista Científica ◽

10.5377/nexo.v34i01.11326 ◽

2021 ◽

Vol 34 (01) ◽

pp. 489-503

Author(s):

Marina V. Byrdina ◽

Mikhail F. Mitsik ◽

Lema A. Bekmurzaev ◽

Svetlana V. Kurenova ◽

Anastasiya A. Movchun

Keyword(s):

Strain State ◽

Space Form ◽

Shell Structures ◽

Stress And Strain ◽

Thin Wall ◽

Linear Deformation ◽

Program Module ◽

Gravitational Forces ◽

Conic Shell ◽

Elastic Forces

The paper covers the visualization of a volume-space form of the flexible inextensible one-layer shell that is represented in the stress and strain state appearing during fastening the shell on the upper edge and its free location below the fastening border in the field of gravitational and elastic forces of the material. With no account taken of the gravitational forces, the shell is a right circular flattened cone. A developed program module can be used in designing and calculating the thin-wall shell structures during their non-linear deformation and their visualization. Visualization of the space form of the shell structure can be used for simulating various products, for instance, the cone antennae or the textile products, flexible elastic shells in the hydraulic engineering, etc.

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Engineering Analysis Methods for Hydraulic Shell Structures with Infill

Solid State Phenomena ◽

10.4028/www.scientific.net/ssp.265.779 ◽

2017 ◽

Vol 265 ◽

pp. 779-784

Author(s):

N.Ya. Tsimbelman ◽

T.I. Chernova ◽

T.E. Shalaya

Keyword(s):

Thin Shell ◽

Design Theory ◽

Engineering Students ◽

Civil Engineering ◽

State Of The Art ◽

Shell Structures ◽

Engineering Analysis ◽

History Of Development ◽

History Of ◽

Theory Of Shells

The article examines the history of development and state-of-the-art of the design theory of structures of filled shells delivered in “Civil Engineering” specialist, MSc, and postgraduate engineering disciplines courses. The analysis of the engineering design methods based on the theory of shells propositions has been performed. Structural numerical model field of application expansion has been proved. The obtained parameters and proposed methods can be used in numerical simulations using finite element method to analyze and design the thin shell structures with soil infill. The propositions reflecting state-of-the-art of the design theory of the structures under consideration have been set; their place in the logic of delivering engineering disciplines taught to civil engineering students has been designated.

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