scholarly journals PROBABLE CALCULATION OF BUILDING SEISMIC RESISTANCE ON KINEMATIC SUPPORT

2019 ◽  
Vol 45 (3) ◽  
pp. 194-211
Author(s):  
H. M. Muselemov ◽  
O. M. Ustarkhanov ◽  
A. K. Yusupov
Keyword(s):  
Cauchy Problem ◽  
Numerical Experiments ◽  
Seismic Stability ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Strong Earthquakes ◽  
Method Of Calculation ◽  
Earthquake Resistant ◽  
The Cauchy Problem ◽  
Stochastic Cauchy Problem

Objectives. The article reflects the results of the numerical analysis of the earthquake-resistant building on kinematic supports. To this end, the problem is reduced to solving the nonlinear stochastic Cauchy problem. The solution is constructed by the method of successive approximations. The probabilistic characteristics of the oscillation of the building are determined without the use of linearization techniques. An algorithm for solving this problem, which allows to perform numerical experiments on a computer to study the operation of a earthquake-resistant building on kinematic sup-ports, is given.Method. The acceleration of the earth's surface during an earthquake is represented as a non-stationary random Gaussian process. This approach is now generally accepted and beyond doubt. The study of vibrations of the building on kinematic supports under the influence of strong earthquakes is reduced to the solution of the stochastic nonlinear Cauchy equation. This equation is solved by iteration. The acceleration of the earth's surface is a function of three random variables. The required probability is represented as a triple integral, which is calculated using a computer.Result. The basic information about the considered kinematic supports is given. The Cauchy problem is formulated for the case of oscillations of a earthquake-resistant building on kinematic supports under the influence of strong earthquakes. The algorithm allowing to solve this equation is described in detail. The probability of finding the movements of the building within certain limits is represented as a triple integral. The results of numerical experiments carried out on a computer are given. The corresponding graphs are constructed using real accelerograms of strong earthquakes that occurred in the cities of Taft (USA) and Gazli (Uzbekistan).Conclusion. This article describes the method of calculation of earthquake-resistant buildings on kinematic supports, using the data of real strong earthquakes. Based on the results of numerical experiments conducted on a computer, graphs of the reliability of seismic stability of the building in earthquakes. The constructed algorithm and the developed technique can be used in the calculation and design of earthquake-resistant buildings both on conventional supports and on kinematic supports.

First Order Partial Functional Differential Equations with Unbounded Delay

2003 ◽  
Vol 10 (3) ◽  
pp. 509-530
Author(s):  
Z. Kamont ◽  
S. Kozieł
Keyword(s):  
Differential Equations ◽  
Integral Functional ◽  
Functional Differential Equations ◽  
Generalized Solutions ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
First Order ◽  
Unbounded Delay ◽  
The Cauchy Problem ◽  
Functional Differential

Abstract The phase space for nonlinear hyperbolic functional differential equations with unbounded delay is constructed. The set of axioms for generalized solutions of initial problems is presented. A theorem on the existence and continuous dependence upon initial data is given. The Cauchy problem is transformed into a system of integral functional equations. The existence of solutions of this system is proved by the method of successive approximations and by using theorems on integral inequalities. Examples of phase spaces are given.

scholarly journals An Integral Equations Method for the Cauchy Problem Connected with the Helmholtz Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Yao Sun ◽  
Deyue Zhang
Keyword(s):  
Cauchy Problem ◽  
Approximate Solution ◽  
Helmholtz Equation ◽  
Numerical Method ◽  
Integral Equations ◽  
Regularization Method ◽  
Numerical Experiments ◽  
Suitable Choice ◽  
Convergence And Stability ◽  
The Cauchy Problem

We are concerned with the Cauchy problem connected with the Helmholtz equation. We propose a numerical method, which is based on the Helmholtz representation, for obtaining an approximate solution to the problem, and then we analyze the convergence and stability with a suitable choice of regularization method. Numerical experiments are also presented to show the effectiveness of our method.

scholarly journals Analysis of Dirichlet–Robin Iterations for Solving the Cauchy Problem for Elliptic Equations

2020 ◽  
Author(s):  
Pauline Achieng ◽  
Fredrik Berntsson ◽  
Jennifer Chepkorir ◽  
Vladimir Kozlov
Keyword(s):  
Cauchy Problem ◽  
Boundary Conditions ◽  
Helmholtz Equation ◽  
Iterative Algorithm ◽  
Elliptic Equations ◽  
Numerical Experiments ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
General Elliptic ◽  
The Cauchy Problem

Abstract The Cauchy problem for general elliptic equations of second order is considered. In a previous paper (Berntsson et al. in Inverse Probl Sci Eng 26(7):1062–1078, 2018), it was suggested that the alternating iterative algorithm suggested by Kozlov and Maz’ya can be convergent, even for large wavenumbers $$k^2$$ k 2 , in the Helmholtz equation, if the Neumann boundary conditions are replaced by Robin conditions. In this paper, we provide a proof that shows that the Dirichlet–Robin alternating algorithm is indeed convergent for general elliptic operators provided that the parameters in the Robin conditions are chosen appropriately. We also give numerical experiments intended to investigate the precise behaviour of the algorithm for different values of $$k^2$$ k 2 in the Helmholtz equation. In particular, we show how the speed of the convergence depends on the choice of Robin parameters.

scholarly journals On the Cauchy Problem of a Quasilinear Degenerate Parabolic Equation

2009 ◽  
Vol 2009 ◽  
pp. 1-12
Author(s):  
Zongqi Liang ◽  
Huashui Zhan
Keyword(s):  
Cauchy Problem ◽  
Parabolic Equation ◽  
Classical Solution ◽  
Finite Time ◽  
Numerical Experiments ◽  
Degenerate Parabolic Equation ◽  
Blow Up ◽  
Strong Solutions ◽  
The Cauchy Problem ◽  
Degenerate Parabolic

By Oleinik's line method, we study the existence and the uniqueness of the classical solution of the Cauchy problem for the following equation in[0,T]×R2:∂xxu+u∂yu−∂tu=f(⋅,u), provided thatTis suitable small. Results of numerical experiments are reported to demonstrate that the strong solutions of the above equation may blow up in finite time.

Cauchy Problem for Equations with Fractional Differentiation Bessel Operator in the Space of Temperate Distributions

2003 ◽  
Vol 8 (1) ◽  
pp. 61-75
Author(s):  
V. Litovchenko
Keyword(s):  
Functional Analysis ◽  
Cauchy Problem ◽  
Fundamental Solution ◽  
Initial Function ◽  
Well Posedness ◽  
Fractional Differentiation ◽  
Basic Tool ◽  
Conjugate Space ◽  
Analysis Technique ◽  
The Cauchy Problem

The well-posedness of the Cauchy problem, mentioned in title, is studied. The main result means that the solution of this problem is usual C∞ - function on the space argument, if the initial function is a real functional on the conjugate space to the space, containing the fundamental solution of the corresponding problem. The basic tool for the proof is the functional analysis technique.

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