Eine Plattform für die Wissenschaft: Bauingenieurwesen, Architektur und Urbanistik
Eine Plattform für die Wissenschaft: Bauingenieurwesen, Architektur und Urbanistik
Numerical methodfor solving dynamic problems of the theory of elasticity in the polar coordinate system similar to the finiteelement method Численный метод решения динамических задач теории упругости в полярной системе координат типа метода конечных элементов
The authors consider a dynamic problem solving procedure based on the theory of elasticity in the Cartesian coordinate system. This method consists in the development of the pattern of numerical solutions to dynamic elastic problems within any coordinate system and, in particular, in the polar coordinate system. Numerical solutions of dynamic problems within the theory of elasticity are the most accurate ones, if the boundaries of the areas under consideration coincide with the coordinate lines of the selected coordinate system.The first order linear system of differential equations is converted into an implicit difference scheme. The implicit scheme is transformed into the explicit method of numerical solutions. Using the Galerkin method, the authors obtain formulas for the calculation of both the points of the computational domain and the boundary points.Difference ratios similar to those obtained for a discrete rectangular grid and derived in this paper are suitable to design any geometry, which fact significantly increases the value of the methods considered in this paper.As a test case, the problem of diffraction of a longitudinal wave in a circular cavity, where maximum stresses are obtained analytically, was considered by the authors. The proposed method demonstrated sufficient accuracy of calculations and convergence of numerical solutions, depending on the size of discrete steps. The problem of diffraction of longitudinal waves in a circular cavity was taken for example; however, the proposed method is applicable to any problems within any computational domain.The polar coordinate system is the best one for any research into the diffraction of plane longitudinal waves in a circular cavity, since the boundaries of the computational domain coincide with the coordinate lines of the selected system.
Рассмотрен метод построения схемы решения динамических задач теории упругости в полярной системе координат. Получен численный метод, который определяет с одинаковой точностью значения скоростей и напряжений и точно выполняет заданные граничные условия. В качестве тестового примера рассмотрена задача о дифракции продольной волны на круглом отверстии. Произведена оценка точности и сходимости численного решения в зависимости от величины дискретного шага по координатам и времени.
Numerical methodfor solving dynamic problems of the theory of elasticity in the polar coordinate system similar to the finiteelement method Численный метод решения динамических задач теории упругости в полярной системе координат типа метода конечных элементов
The authors consider a dynamic problem solving procedure based on the theory of elasticity in the Cartesian coordinate system. This method consists in the development of the pattern of numerical solutions to dynamic elastic problems within any coordinate system and, in particular, in the polar coordinate system. Numerical solutions of dynamic problems within the theory of elasticity are the most accurate ones, if the boundaries of the areas under consideration coincide with the coordinate lines of the selected coordinate system.The first order linear system of differential equations is converted into an implicit difference scheme. The implicit scheme is transformed into the explicit method of numerical solutions. Using the Galerkin method, the authors obtain formulas for the calculation of both the points of the computational domain and the boundary points.Difference ratios similar to those obtained for a discrete rectangular grid and derived in this paper are suitable to design any geometry, which fact significantly increases the value of the methods considered in this paper.As a test case, the problem of diffraction of a longitudinal wave in a circular cavity, where maximum stresses are obtained analytically, was considered by the authors. The proposed method demonstrated sufficient accuracy of calculations and convergence of numerical solutions, depending on the size of discrete steps. The problem of diffraction of longitudinal waves in a circular cavity was taken for example; however, the proposed method is applicable to any problems within any computational domain.The polar coordinate system is the best one for any research into the diffraction of plane longitudinal waves in a circular cavity, since the boundaries of the computational domain coincide with the coordinate lines of the selected system.
Рассмотрен метод построения схемы решения динамических задач теории упругости в полярной системе координат. Получен численный метод, который определяет с одинаковой точностью значения скоростей и напряжений и точно выполняет заданные граничные условия. В качестве тестового примера рассмотрена задача о дифракции продольной волны на круглом отверстии. Произведена оценка точности и сходимости численного решения в зависимости от величины дискретного шага по координатам и времени.
Numerical methodfor solving dynamic problems of the theory of elasticity in the polar coordinate system similar to the finiteelement method Численный метод решения динамических задач теории упругости в полярной системе координат типа метода конечных элементов
Nemchinov Vladimir Valentinovich (Autor:in) / Musayev Vyacheslav Kadyr ogly (Autor:in)
2013
Aufsatz (Zeitschrift)
Elektronische Ressource
Unbekannt
finite-difference derivative , double-layer scheme , diffraction of longitudinal waves , circular cavity contour stress , numerical modeling , finite element method , polar coordinate system , конечно-разностная производная , двухслойная по времени схема , дифракция продольной волны , круговая полость , контурные напряжения , численное моделирование , метод конечных элементов , полярная система координат , Architecture , NA1-9428 , Construction industry , HD9715-9717.5
Metadata by DOAJ is licensed under CC BY-SA 1.0
Методические возможности решения изобретательских задач в архитектуре и строительстве
| DOAJ | 2024
| DOAJ | 2019
Метод освоенного объема в интеллектуальной системе управления строительными проектами
| DOAJ | 2022