Multi-scale iteration method for efficiently solving state of large-scale nonlinear random structure system

Abstract

The invention discloses a multi-scale iteration method for efficiently solving a state of a large-scale nonlinear random structure system. The method comprises the following steps: establishing a moment function equation of a state response of the nonlinear random structure system; establishing an enclosed moment function equation of the state response by a Gauss truncation technology; establishing a multi-scale discrete interval within a time domain; and iteratively solving the enclosed moment function equation of the state response within the multi-scale interval by a Runge-Kutta method to obtain a statistical characteristic of the state response of the nonlinear random structure system finally. Through adoption of the multi-scale iteration method, simultaneous solving of three random differential equations can be avoided; a large quantity of computer storage resources are saved; and the computation efficiency is increased greatly. Moreover, iteration times can be adjusted automatically through error control and initial value setting, so that accelerated convergence of a solving process is realized. An efficient solving method is provided for state analysis of the large-scale nonlinear random structure system, and the method has an actual engineering application value.

Description

technical field [0001] The invention is mainly applicable to the efficient calculation of the statistical characteristics of the state response of a large-scale nonlinear random structure system, and specifically relates to a multi-scale iterative method for efficiently solving the state of a large-scale nonlinear random structure system. Background technique [0002] Earthquakes, wind loads and sea waves are common environmental loads. Under long-term environmental loads, the dynamic response of man-made structures will affect the function and safety of the structure. Therefore, the dynamic response analysis of structures under environmental loads is particularly important. Since environmental loads are usually treated as stochastic processes, it is necessary to establish and solve stochastic differential equations during dynamic response analysis. [0003] The Fokker-Planck-Kolmogorov (FPK) method is widely used to establish differential equations for nonlinear stochasti...

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Problems solved by technology

Although the application of the FPK method is promoted by means of the random averaging method and filtering method, there are still two disadvantages in this method: on the one hand, the external random excitation must be a delta-related random process or can be expressed as a white noise filter; on the other hand, the method Increased the number of states in the system

However, the vast majority of theoretical studies have neglected the improvement of the numerical solution efficiency of the moment function equation

Obviously, inefficient numerical solution algorithms will lead to difficulties in the practical application of nonlinear dynamic response analysis methods, especially for large-scale nonlinear stochastic structural systems

In addition, delta-related stochastic excitation is often used to establish the moment function equation of nonlinear systems, but this stochastic process cannot accurately describe the characteristics of environmental loads

In fact, Qiu Zhiping has studied the dynamical system affected by environmental loads and pointed out that it is very effective to use the direct probability method to establish the moment function equation of the state response. However, this research work is only applicable to linear stochastic structural system problems

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