Numerical Method for Solving the Problems of the Building Structures Dynamics with a Mobile Massive Load

Abstract:

The article considers the modeling of dynamic processes in buildings and structures. A general formulation of the dynamic problem of a massive load motion on a massive structure is considered. The equation of motion is obtained in the form of a finite element method. The equations solving is performed using direct methods of integrating dynamic problems. Absolutely stable schemes of direct integration are constructed, where the system of solving equations is trivial and the matrix of the system is diagonal. Due to this, the complexity at the time step is as low as in explicit schemes. Therefore, the proposed methods can be considered as explicit absolutely stable schemes of direct integration of a dynamical problem with a variable in time mass. These recommendations are for estimating the accuracy of a numerical solution.

• Periodical: Materials Science Forum (Volume 931)
• Pages: 72-77
• DOI: https://doi.org/10.4028/www.scientific.net/MSF.931.72
• Online since: September 2018
• Authors: Leonid N. Panasyuk, Galina M. Kravchenko*, Vakhtang Matua
• Keywords: Acceleration, Direct Integration Scheme, Finite Element Method (FEM), Knot Displacement, Mass Matrix, Moving Massive Load, Spectral Radius, Speed, Stiffness Matrix, Structures Dynamics, Time Integration Step

References

[1] .

[1] Ju. N. RabotnovRabotnov, Ju N. Mehanika de formiruemono Mechanics of deformable solid, M.: Nauka , 1979. 650p. Nauka, Moscow, (1979).

[2] .

[2] A. F. Aleksandrov A. F., Potapov VD OsnovyAleksandrov, V.D. Potapov, Fundamentals of the elasticity, M.: Vysshaja High School, Moscow, (1990).

[3] .

[3] K. Деккер К., Вервер Я. Устойчивость методов Рунге-Кутта для жестких нелинейных дифференциальных уравнений.Dekker, Ya. Verver, Stability of Runge-Kutta methods for rigid nonlinear differential equations, Mir, MoscowМ. : Мир, 1988.-334с., (1988).

[4] .

[4] Gurtin ME VarionationalM.E. Gurtin, Varionational Principless for Liner Elastodynamic /- Arch. Principless for Liner Elastodynamic, Arch. Rat . Rat. Mech.-Anal, 1964, N 16.: PP.31-50. Mech.-Anal, 16 (1964) 31-50.

DOI: 10.1007/bf00248489

[5] .

[5] Batha KJ Finite Element Procedures K.J. Bath, Finite Element Procedures, Prentice Hall, KJ Baths.New Jersey, 1996. 10.12.

[6] .

[6] L.N. Panasyuk LN, Kravchenko GM Stability of direct circuits integrating the equations of motion in the simulation of the dynamics of destruction.-MATEC «Web of Conferences» 2017 Panasyuk, G.M. Kravchenko, Stability of direct circuits integrating the equations of motion in the simulation of the dynamics of destruction, MATEC. 129 (2017).

DOI: 10.1051/matecconf/201712905019

[7] .

[7] L.N. Panasuk LN, Kravchenko GM, Trufanova EV Researching design solutions for frames of buildings in case of increased seismic intensity in specific zones. Panasuk, G.M. Kravchenko, E.V. Trufanova, Researching design solutions for frames of buildings in the case of increased seismic intensity in specific zones, – Matec Web of Conferences. MATEC. 106 2017 №106, Импакт - фактор (2017).

DOI: 10.1051/matecconf/201710602027

[8] .

[8] L.N. Панасюк Л.Н. Panasyuk, Анализ точности явных устой чивых схем прямого интегрирования задачи динамики сооружений// Известия ВУЗов, естественные науки. Analysis of the accuracy of explicit stable schemes of direct integration of the problem of the dynamics of structures, News of Higher Educational Institutions. Natural Sciences. 1994 . 4 (1994).

[9] .

[9] L.N. Панасюк Л.Н. Panasyuk,О построении явных безусловно устойчивых схем прямого интегрирования задачи динамики сооружений// Известия ВУЗов, строительство. On the construction of explicitly unconditionally stable schemes of direct integration of the problem of the dynamics of structures, News of Higher Educational Institutions, construction. 1995. №10, C .35-40 10 (1995).

[10] .

[10] Панасюк Л.Н. L.N. Panasyuk, О концепции программных комплексов решения задач строительной механики на основе объектно-ориентированного программирования. On the concept of software complexes for solving the problems of construction mechanics on the basis of object-oriented programming, – Ростов н /Д.: РГАС, 1996. – 39с. RGAS, Rostov on Don, (1996).