OPTIMUM DESIGN BASED ON RELIABILITY IN STOCHASTIC STRUCTURE SYSTEMS

The optimum design method based on the reliability is presented to the stochastic structure systems （i. e., the sectional area, length, elastic module and strength of the structural member are random variables ） under the random loads. The sensitivity expression of system reliability index and the safety margins were presented in the stochastic structure systems. The optimum vector method was given. First, the expressions of the reliability index of the safety margins with the improved first-order second-moment and the stochastic finite element method were deduced, and then the expressions of the systemic failure probability by probabilistic network evaluation technique（PNET） method were obtained. After derivation calculus ,the expressions of the sensitivity analysis for the system reliability were obtained. Moreover, the optimum design with the optimum vector algorithm was undertaken. In the optimum iterative procedure, the gradient step and the optimum vector step were adopted to calculate. At the last, a numerical example was provided to illustrate that the method is efficient in the calculation, stably converges and fits the application in engineering.

Interval Analysis of the Finite Element Method for Stochastic Structures

A random parameter can be transformed into an interval number in the structural analysis with the concept of the confidence interval. Hence, analyses of uncertain structural systems can be used in the traditional FEM software. In some cases, the amount of solutions in stochastic structures is nearly as many as that in the traditional structural problems. In addition, a new method to evaluate the failure probability of structures is presented for the needs of the modern engineering design.

A NOTE ON THE STRUCTURE OF STOCHASTIC MATRICES

It is known that nearly uncoupled irreducible stochastic matrices must possess sub-dominant eigenvalues near λ=1. It is nature to ask whether the converse is true. Hortfieland Meyer [2] gave a positive answer. They introduced the notion of uncoupling measureof Stochastic matrices. For an n×n stochastic matrix P the uncoupling measure of P is de-fined as σ（p）=min((sum from i∈M1,j∈M1(Pij))+(sum from i∈M1,j∈M1(Pij)), where the minimum is taken over

Dynamic Analysis of Stochastic Finite Element Based on Sensitivity Computation

In this paper, material properties, geometry parameters and applied loads are assumed to be stochastic, sensitivity computation of structural vibration is presented. The vibration equation of a system is transformed to a static problem by using the Newmark method, and the Taylor expansion stochastic finite element method （TSFEM） is extended for the structural vibration analysis. An example is given, and the calculation results show the validity of the proposed method.

Nonlinear dynamics in Divisia monetary aggregates:an application of recurrence quantification analysis

We construct recurrence plots(RPs)and conduct recurrence quantification analysis(RQA)to investigate the dynamic properties of the new Center for Financial Stability(CFS)Divisia monetary aggregates for the United States.In this study,we use the lat-est vintage of Divisia aggregates,maintained within CFS.We use monthly data,from January 1967 to December 2020,which is a sample period that includes the extreme economic events of the 2007–2009 global financial crisis.We then make comparisons between narrow and broad Divisia money measures and find evidence of a nonlinear but reserved possible chaotic explanation of their origin.The application of RPs to broad Divisia monetary aggregates encompasses an additional drift structure around the global financial crisis in 2008.Applying the moving window RQA to the growth rates of narrow and broad Divisia monetary aggregates,we identify periods of changes in data-generating processes and associate such changes to monetary policy regimes and financial innovations that occurred during those times.

Equivalent Stochastic Linearization for Nonlinear Uncertain Structure Under Stationary Gaussian Stochastic Excitation

Equivalent stochastic linearization （ESL） for nonlinear uncertain structure under stationary stochastic excitation is presented. There are two parts of difference between the original system and equivalent system： one is caused by the difference between the means of original and equivalent stochastic structure; and another is caused by the difference between the original and equivalent stochastic structure which has the relation with stochastic variables. Statistical characteristics of equivalent stochastic structure can be obtained in accordance with mean square criterion, so nonlinear stochastic structure is transformed into linear stochastic structure. In order to attain that objective, the compound response spectrum of linear stochastic structure under stationary random excitation which is used in the solution is derived in the case of the mutual independence between stochastic excitation and stochastic structure. Finally, the example shows the accuracy and validity of the proposed method.

Sliding surface searching method for slopes containing a potential weak structural surface

Weak structural surface is one of the key factors controlling the stability of slopes. The stability of rock slopes is in general concerned with set of discontinuities. However, in soft rocks, failure can occur along surfaces approaching to a circular failure surface. To better understand the position of potential sliding surface, a new method called simplex-finite stochastic tracking method is proposed. This method basically divides sliding surface into two parts： one is described by smooth curve obtained by random searching, the other one is po｜yline formed by the weak structural surface. Single or multiple sliding surfaces can be considered, and consequently several types of combined sliding surfaces can be simu- lated. The paper will adopt the arc-polyline to simulate potential sliding surface and analyze the searching process of sliding surface. Accordingly, software for slope stability analysis using this method was developed and applied in real cases. The results show that, using simplex-finite stochastic tracking method, it is possible to locate the position of a potential sliding surface in the slope.

Advances in structural vibration control application of magneto-rheological visco-elastomer

Magneto-rheological visco-elastomer （MRVE） as a new smart material developed in recent years has several significant advantages over magneto-rheological liquid. The adjustability of structural dynamics to random environmental excitations is required in vibration control. MRVE can supply considerably adjustable damping and stiffness for structures, and the adjustment of dynamic properties is achieved only by applied magnetic fields with changeless structure design. Increasing researches on MRVE dy- namic properties, modeling, and vibration control application are presented. Recent advances in MRVE dynamic properties and structural vibration control application including composite structural vibration mitigation under uniform magnetic fields, vibration response characteristics improvement through harmonic parameter distribution, and optimal bounded parametric control design based on the dynamical programming principle are reviewed. Relevant main methods and results introduced are beneficial to understanding and researches on MRVE application and development.