Reduced Expanding Load Method for Simulation-Based Structural System Reliability Analysis

The current situation and difficulties of the structural system reliability analysis are mentioned. Then on the basis of Monte Carlo method and computer simulation, a new analysis method reduced expanding load method (RELM) is presented, which can be used to solve structural reliability problems effectively and conveniently. In this method, the uncertainties of loads, structural material properties and dimensions can be fully considered. If the statistic parameters of stochastic variables are known, by using this method, the probability of failure can be estimated rather accurately. In contrast with traditional approaches,RELM method gives a much better understanding of structural failure frequency and its reliability index β is more meaningful.To illustrate this new idea, a specific example is given.

An H^1-Galerkin Expanded Mixed Element Method for Semi-linear Hyperbolic Wave Equation

An H1-Galerkin expanded mixed finite element method is discussed for a class of second order semi-linear hyperbolic wave equations. By using the mixed formulation, we can get the optimal approximation for three variables: the scalar unknown, its gradient and its flux(coefficient times the gradient), simultaneously. We also prove the existence and uniqueness of semi-discrete solution. Finally, we obtain some numerical results to illustrate the efficiency of the method.

EXPANDABLE PARALLEL FINITE ELEMENT METHODS FOR LINEAR ELLIPTIC PROBLEMS

In this article,two kinds of expandable parallel finite element methods,based on two-grid discretizations,are given to solve the linear elliptic problems.Compared with the classical local and parallel finite element methods,there are two attractive features of the methods shown in this article:1)a partition of unity is used to generate a series of local and independent subproblems to guarantee the final approximation globally continuous;2)the computational domain of each local subproblem is contained in a ball with radius of O(H)(H is the coarse mesh parameter),which means methods in this article are more suitable for parallel computing in a large parallel computer system.Some a priori error estimation are obtained and optimal error bounds in both H^1-normal and L^2-normal are derived.Finally,numerical results are reported to test and verify the feasibility and validity of our methods.

Homotopy analysis solutions for the asymmetric laminar flow in a porous channel with expanding or contracting walls

In this paper, the asymmetric laminar flow in a porous channel with expanding or contracting walls is investigated. The governing equations are reduced to ordinary ones by using suitable similar transformations. Homotopy analysis method （HAM） is employed to obtain the expres- sions for velocity fields. Graphs are sketched for values of parameters and associated dynamic characteristics, especially the expansion ratio, are analyzed in detail.

New Explicit Rational Solitary Wave Solutions for Discretized mKdV Lattice Equation

In this letter, we study discretized mKdV lattice equation by using a new generalized ansatz. As a result,many explicit rational exact solutions, including some new solitary wave solutions, are obtained by symbolic computation code Maple.

New exact periodic solutions to (2+1)-dimensional dispersive long wave equations

In this paper, we make use of the auxiliary equation and the expanded mapping methods to find the new exact periodic solutions for （2＋1）-dimensional dispersive long wave equations in mathematical physics, which are expressed by Jacobi elliptic functions, and obtain some new solitary wave solutions （m → 1）. This method can also be used to explore new periodic wave solutions for other nonlinear evolution equations.

Application of the expanded distinct element method for the study of crack growth in rock-like materials under uniaxial compression

The expanded distinct element method(EDEM)was used to investigate the crack growth in rock-like materials under uniaxial compression.The tensile-shear failure criterion and the Griffith failure criterion were implanted into the EDEM to determine the initiation and propagation of pre-existing cracks,respectively.Uniaxial compression experiments were also performed with the artificial rock-like samples to verify the validity of the EDEM.Simulation results indicated that the EDEM model with the tensile-shear failure criterion has strong capabilities for modeling the growth of pre-existing cracks,and model results have strong agreement with the failure and mechanical properties of experimental samples.The EDEM model with the Griffith failure criterion can only simulate the splitting failure of samples due to tensile stresses and is incapable of providing a comprehensive interpretation for the overall failure of rock masses.Research results demonstrated that sample failure primarily resulted from the growth of single cracks(in the form of tensile wing cracks and shear secondary cracks)and the coalescence of two cracks due to the growth of wing cracks in the rock bridge zone.Additionally,the inclination angle of the pre-existing crack clearly influences the final failure pattern of the samples.

Fuzzy norm method for evaluating random vibration of airborne platform from limited PSD data

For random vibration of airborne platform, the accurate evaluation is a key indicator to ensure normal operation of airborne equipment in flight. However, only limited power spectral density（PSD） data can be obtained at the stage of flight test. Thus, those conventional evaluation methods cannot be employed when the distribution characteristics and priori information are unknown. In this paper, the fuzzy norm method（FNM） is proposed which combines the advantages of fuzzy theory and norm theory. The proposed method can deeply dig system information from limited data, which probability distribution is not taken into account. Firstly, the FNM is employed to evaluate variable interval and expanded uncertainty from limited PSD data, and the performance of FNM is demonstrated by confidence level, reliability and computing accuracy of expanded uncertainty. In addition, the optimal fuzzy parameters are discussed to meet the requirements of aviation standards and metrological practice. Finally, computer simulation is used to prove the adaptability of FNM. Compared with statistical methods, FNM has superiority for evaluating expanded uncertainty from limited data. The results show that the reliability of calculation and evaluation is superior to 95%.

Analysis of Two-Grid Methods for Nonlinear Parabolic Equations by Expanded Mixed Finite Element Methods

In this paper,we present an efficient method of two-grid scheme for the approximation of two-dimensional nonlinear parabolic equations using an expanded mixed finite element method.We use two Newton iterations on the fine grid in our methods.Firstly,we solve an original nonlinear problem on the coarse nonlinear grid,then we use Newton iterations on the fine grid twice.The two-grid idea is from Xu's work[SIAM J.Numer.Anal.,33(1996),pp.1759–1777]on standard finite method.We also obtain the error estimates for the algorithms of the two-grid method.It is shown that the algorithm achieve asymptotically optimal approximation rate with the two-grid methods as long as the mesh sizes satisfy h=O(H^((4k+1)/(k+1))).