Saint-Venant–Picard–Banach Method for Integrating Thin-Walled System Equations of the Theory of Elasticity

2020 ◽  
Vol 55 (7) ◽  
pp. 1042-1050
Author(s):  
E. M. Zveryaev
Keyword(s):  
Theory Of Elasticity ◽  
System Equations ◽  
Thin Walled

scholarly journals INFLUENCE OF CREEP CONCRETE ON SPACE STABILITY THIN-WALLED DOME COVERINGS

2021 ◽  
Vol 1 (24) ◽  
Author(s):  
Ekaterina Prokshits ◽  
Sergey Gridnev ◽  
Olga Sotnikova ◽  
Iana Zolotukhina
Keyword(s):  
Theory Of Elasticity ◽  
Deformation Condition ◽  
Software Systems ◽  
Geometrical Parameters ◽  
Loss Of Stability ◽  
Construction Mechanics ◽  
Body Construction ◽  
Calculation Results ◽  
Load Action ◽  
Thin Walled

The task was set, due to the capabilities of modern software systems, to assess the effect of the increase in inelastic deformations under prolonged load action on the loss of stability of thin-walled dome coverings. The study of the dependences of the forms of the loss of stability of dome covering from creep concrete that will help further with optimization calculations when determining of the most influencing parameters of designs. Calculation results of thin-walled concrete dome roof of circular outline under the influence of operational loadings with use of two modern program complexes are given in article. It is investigated intense and deformation condition of dome coverings as a part of construction from position of forecasting of possible forms of loss of stability, with use of opportunities of the final and element «MidasCivil» computer system. In work provisions of the theory of elasticity, mechanics of deformation of solid body, construction mechanics and also methods of mathematical modeling based on application of finite element method are used. The received results give the chance to rationally select geometrical parameters and material of design and also to set structural strength safety factors at the solution of problems of stability of different covers taking into account possible creep of material.

scholarly journals NUMERICAL STUDIES OF THE INFLUENCE OF THE PARAMETERS OF THIN-SHELL DOME STRUCTURE ON THEIR OPTIMIZATION FROM THE POSITION OF SPATIAL STABILITY

2021 ◽  
pp. 6-18
Author(s):  
S. Yu. Gridnev ◽  
O. A. Sotnikova ◽  
E. E. Prokshits
Keyword(s):  
Finite Element ◽  
Theory Of Elasticity ◽  
Topological Optimization ◽  
Design System ◽  
Sound Design ◽  
Construction Design ◽  
Construction Mechanics ◽  
Dome Structure ◽  
Deformation Mechanics ◽  
Thin Walled

Statement of the problem. The task was to evaluate the influence of the parameters of thin-walled dome coatings using the capabilities of modern software complexes. The method of optimization of dome covering structures with selection of criteria and parameters of the task has been improved. Results. The article presents the results of refinement and testing of the methodology for addressing the problem of optimizing dome structures with the choice of criteria and parameters of the optimization problem using the capabilities of the Topological Optimization module of the finite-element computational complex MidasCivil. The objective function was considered dependent on the thickness of the dome, the modulus of elasticity of the Poisson coefficient of the material. The study employs the positions of the theory of elasticity, solid body deformation mechanics, construction mechanics, as well as mathematical modeling methods based on the use of the finite element method employing modern licensed finite-element computing complexes Midas Civil and the Ing + architectural and construction design system of the calculation module MicroFe. Conclusions. Using the methods of optimal (in particular, geometric) design, the most affecting parameters of thin-walled dome coatings and their combinations were identified. This will allow us to design the most rational, economical and architectural-expressive dome structures as well as to make sound design decisions.

FINE GRIT TREATMENT OF RANGY PLATES

2021 ◽  
Vol 2021 (9) ◽  
pp. 15-22
Author(s):  
Vladimir Scriabin
Keyword(s):  
Experimental Studies ◽  
Theory Of Elasticity ◽  
Theoretical Research ◽  
Kinematic Parameters ◽  
Engineering Technology ◽  
Abrasive Particles ◽  
Finishing Process ◽  
Abrasive Finishing ◽  
Thin Walled ◽  
The Relationship

The features of the final machining of thin-walled plates are given. The calculation scheme for the kinematic parameters of abrasive finishing of thin-walled easily deformable plates and the mathematical dependence for calculating the pressure on the lapping faceplates with the processed parts are determined. The aim of the work is to obtain an analytical dependence that establishes the relationship between the operating parameters and the conditions of the abrasive finishing process with the roughness of the working surface of the plates. The task, which the article is devoted to solve is theoretical and experimental studies of the influence of technological modes and conditions of abrasive finishing of plates with complex relative movement of parts and lapping on the roughness of the treated surfaces, as well as in the development of a methodology for determining rational modes and conditions of surface treatment of thin-walled plates. Theoretical research was carried out on the basis of the main provisions of mechanical engineering technology, grinding theory, theoretical mechanics, theory of elasticity and plasticity, probability theory and mathematical statistics. Experimental studies have been carried out according to standard methods in production and laboratory conditions using certified control and measuring equipment. The obtained data were processed using computer technology and presented in the form of empirical dependencies that are convenient for practical application. The originality of the work consists in obtaining mathematical dependencies for calculating the kinematic parameters and parameters of the contact interaction of abrasive particles with the treated surfaces of the plates, which allow determining the rational values of the ratio of the speeds of movement of the plates and lapping.

Waves in lattices with imperfect junctions and localized defect modes

2008 ◽  
Vol 464 (2096) ◽  
pp. 2037-2054 ◽  
Author(s):  
V.V Zalipaev ◽  
A.B Movchan ◽  
I.S Jones
Keyword(s):  
Vibration Mode ◽  
Periodic Structures ◽  
Lattice Models ◽  
Theory Of Elasticity ◽  
Defect Modes ◽  
Thin Walled Structures ◽  
Discrete Lattices ◽  
Thin Walled ◽  
Type Boundary ◽  
Type Boundary Condition

A correspondence between continuum periodic structures and discrete lattices is well known in the theory of elasticity. Frequently, lattice models are the result of the discretization of continuous mechanical problems. In this paper, we discuss the discretization of two-dimensional square thin-walled structures. We consider the case when thin-walled bridges have defects in the vicinity of junctions. At these points, the displacement satisfies an effective Robin-type boundary condition. We study a defect vibration mode localized in the neighbourhood of the damaged junction. We analyse dispersion diagrams that show the existence of standing waves in a structure with periodically distributed defects.

NUMERICAL STUDIES OF THE INFLUENCE OF THE PARAMETERS OF THIN-SHELL DOME STRUCTURE ON THEIR OPTIMIZATION FROM THE POSITION OF SPATIAL STABILITY

2020 ◽  
pp. 11-21
Author(s):  
С. Ю. Гриднев ◽  
О. А. Сотникова ◽  
Е. Е. Прокшиц
Keyword(s):  
Finite Element ◽  
Theory Of Elasticity ◽  
Topological Optimization ◽  
Design System ◽  
Sound Design ◽  
Construction Design ◽  
Construction Mechanics ◽  
Dome Structure ◽  
Deformation Mechanics ◽  
Thin Walled

Постановка задачи. Необходимо оценить влияние параметров тонкостенных купольных покрытий с использованием возможностей современных программных комплексов. Также требуется усовершенствовать методику оптимизации конструкций купольного покрытия с выбором критериев и параметров задачи. Результаты. Приведены результаты уточнения и апробации методики решения задачи оптимизации купольных конструкций с выбором критерия и параметров задачи оптимизации с использованием возможностей модуля «Топологическая оптимизация» конечно-элементного вычислительного комплекса «MidasCivil». Целевую функцию считали зависимой от толщины купола, модуля упругости коэффициента Пуассона материала. Использованы положения теории упругости, механики деформирования твердого тела, строительной механики, а также методы математического моделирования, основанные на применении метода конечных элементов с использованием современных лицензированных конечно-элементных вычислительных комплексов «MidasCivil» и системы сквозного архитектурно-строительного проектирования Ing+ расчетного модуля MicroFe. Выводы. Использование методов оптимального (в частности, геометрического) проектирования выявляет наиболее влияющие параметры тонкостенных купольных покрытий и их комбинации. Это позволит создавать рациональные, экономичные и архитектурно-выразительные купольные конструкции, а также принимать обоснованные проектные решения. Statement of the problem. The task was to evaluate the influence of the parameters of thin-walled dome coatings using the capabilities of modern software complexes. The method of optimization of dome covering structures with selection of criteria and parameters of the task has been improved. Results. The article presents the results of refinement and testing of the methodology for addressing the problem of optimizing dome structures with the choice of criteria and parameters of the optimization problem using the capabilities of the Topological Optimization module of the finite-element computational complex "MidasCivil." The objective function was considered dependent on the thickness of the dome, the modulus of elasticity of the Poisson coefficient of the material. The study employs the positions of the theory of elasticity, solid body deformation mechanics, construction mechanics, as well as mathematical modeling methods based on the use of the finite element method employing modern licensed finite-element computing complexes "MidasCivil" and the Ing + architectural and construction design system of the calculation module MicroFe. Conclusions. Using the methods of optimal (in particular, geometric) design, the most affecting parameters of thin-walled dome coatings and their combinations were identified. This will allow one to design the most rational, economical and architectural-expressive dome structures as well as to make sound design decisions.

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