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Математическое моделирование поверхностных волн напряжений в задаче Лэмба при воздействии в виде функции Хевисайда

Математическое моделирование поверхностных волн напряжений в задаче Лэмба при воздействии в виде функции Хевисайда

Abstract

Provides information on the numerical modeling of longitudinal, transverse and surface waves on the free surface of an elastic half-plane. Given the change in elastic contour stresses on the free surface of the half plane. For the solution of two-dimensional non-stationary dynamical problems of the mathematical theory of elasticity with initial and boundary conditions using the finite element method in movements. The problem is solved by a method of capturing, without isolation gaps. Applied homogeneous algorithm. Using the finite element method in displacements, a linear problem with initial and boundary conditions has led to the linear Cauchy problem. Provides a bit of information on numerical simulation of elastic stress waves in elastic half-plane when focused vertical exposure in the form of Heaviside functions. Shows the variation of elastic contour stresses on the free surface of the half plane.

Приводится информация о численном моделировании продольных, поперечных и поверхностных волн на свободной поверхности упругой полуплоскости. Приводится изменение упругого контурного напряжения на свободной поверхности полуплоскости. Для решения двумерной нестационарной динамической задачи математической теории упругости с начальными и граничными условиями используем метод конечных элементов в перемещениях. Задача решается методом сквозного счета, без выделения разрывов. Применяется однородный алгоритм. С помощью метода конечных элементов в перемещениях, линейную задачу с начальными и граничными условиями привели к линейной задаче Коши. Приводится некоторая информация о численном моделировании упругих волн напряжений в упругой полуплоскости при сосредоточенном вертикальном воздействии в виде функции Хевисайда. Показано изменение упругого контурного напряжения на свободной поверхности полуплоскости.

Keywords

НЕСТАЦИОНАРНЫЕ ВОЛНЫ, ЧИСЛЕННЫЙ МЕТОД, ПЕРЕМЕЩЕНИЕ, СКОРОСТЬ ПЕРЕМЕЩЕНИЙ, УСКОРЕНИЕ, НАПРЯЖЕНИЕ, ТЕОРИЯ УПРУГОСТИ, КРАЕВАЯ ЗАДАЧА, ЗАДАЧА С НАЧАЛЬНЫМИ УСЛОВИЯМИ, ЗАДАЧА КОШИ, МЕТОДИКА, АЛГОРИТМ, ОДНОРОДНЫЙ АЛГОРИТМ, КОМПЛЕКС ПРОГРАММ, ПРОДОЛЬНАЯ ВОЛНА, ПОПЕРЕЧНАЯ ВОЛНА, КОНИЧЕСКАЯ ВОЛНА, ВОЛНА РЕЛЕЯ, ПОВЕРХНОСТНАЯ ВОЛНА, ЗАДАЧА ЛЭМБА, СОСРЕДОТОЧЕННОЕ ВЕРТИКАЛЬНОЕ ВОЗДЕЙСТВИЕ, ФУНКЦИЯ В ВИДЕ ХЕВИСАЙДА, УПРУГАЯ ПОЛУПЛОСКОСТЬ, НАПРЯЖЕНИЯ НА СВОБОДНОЙ ПОВЕРХНОСТИ

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
gold