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Mathematical Modeling of Stresses Under Unsteady Wave Action in Geo-Objects
The article considers mathematical modeling of unsteady plane, diffraction, surface, and flexural waves in various complex-shaped objects. To solve this problem, the research uses the wave equation of solid mechanics. Based on the finite element method, a technique, an algorithm, and a software system for solving linear unsteady dynamic problems of the theory of elasticity have been developed. The Fortran-90 programming language was used to design the software system. The area under study is divided by the space and time coordinates into linear finite elements. An explicit two-layer scheme is obtained. The article proposes a quasiregular approach to solving a system of linear second-order ordinary differential equations in displacements with initial conditions and to the approximation of the area under study. The technique is based on the following schemes: point, line, and plane. The study makes comparison with the results of both analytical and experimental methods, as well as considers the problem of the plane longitudinal elastic wave action on a free circular hole. The article also deals with the problem of the plane longitudinal elastic wave action on a reinforced circular hole and the problem of the seismic unsteady wave action on concrete dams with a foundation (the Kurpsay and Koyna dams) under the influence of a plane longitudinal elastic wave. Flexural waves predominate in the considered seismic dam safety problems. The performed investigation of the unsteady wave stress state shows that the numerical simulation results correspond to the post-earthquake damage patterns observed in the Koyna Dam. The research solves the problem of mathematical modeling of unsteady elastic stress waves in a half-plane with an air-filled cavity (the width/height ratio is one to ten) under seismic action as well as for a localized explosive loading in the triangular pulse form (Dirac delta function).
Mathematical Modeling of Stresses Under Unsteady Wave Action in Geo-Objects
The article considers mathematical modeling of unsteady plane, diffraction, surface, and flexural waves in various complex-shaped objects. To solve this problem, the research uses the wave equation of solid mechanics. Based on the finite element method, a technique, an algorithm, and a software system for solving linear unsteady dynamic problems of the theory of elasticity have been developed. The Fortran-90 programming language was used to design the software system. The area under study is divided by the space and time coordinates into linear finite elements. An explicit two-layer scheme is obtained. The article proposes a quasiregular approach to solving a system of linear second-order ordinary differential equations in displacements with initial conditions and to the approximation of the area under study. The technique is based on the following schemes: point, line, and plane. The study makes comparison with the results of both analytical and experimental methods, as well as considers the problem of the plane longitudinal elastic wave action on a free circular hole. The article also deals with the problem of the plane longitudinal elastic wave action on a reinforced circular hole and the problem of the seismic unsteady wave action on concrete dams with a foundation (the Kurpsay and Koyna dams) under the influence of a plane longitudinal elastic wave. Flexural waves predominate in the considered seismic dam safety problems. The performed investigation of the unsteady wave stress state shows that the numerical simulation results correspond to the post-earthquake damage patterns observed in the Koyna Dam. The research solves the problem of mathematical modeling of unsteady elastic stress waves in a half-plane with an air-filled cavity (the width/height ratio is one to ten) under seismic action as well as for a localized explosive loading in the triangular pulse form (Dirac delta function).
Mathematical Modeling of Stresses Under Unsteady Wave Action in Geo-Objects
Power Technol Eng
Musayev, V. K. (author)
Power Technology and Engineering ; 57 ; 351-364
2023-09-01
14 pages
Article (Journal)
Electronic Resource
English
computer simulation , longitudinal waves , elastic wave diffraction , surface wave , flexural waves , algorithm , software system , dynamic photoelasticity , fringe pattern , numerical method verification , contour stress , circular hole , reinforced hole , Koyna Dam , Kurpsay Dam , vertical cavity , elastic half-plane Energy , Energy Systems , Power Electronics, Electrical Machines and Networks , Renewable and Green Energy , Geoengineering, Foundations, Hydraulics
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