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The uncertainty of the interval variable is represented by interval factor, and the interval variable is described as its mean value multiplied by its interval factor. Based on interval arithmetic rules, an analytical method of interval finite element for uncertain structures but not probabilistic structure or fuzzy structure is presented by combining the interval analysis with finite element method. The static analysis of truss with interval parameters under interval load is studied and the expressions of structural interval displacement response and stress response are deduced. The influences of uncertainty of one of structural parameters or load on the displacement and stress of the structure are examined through examples and some significant conclusions are obtained.

The purpose of this paper is to introduce an interval finite element method (IFEM) to simulate the temperature field of mass concrete under multiple influence uncertainties e.g. environmental temperature, material properties, pouring construction and pipe cooling.

Uncertainties of the significant factors such as the ambient temperature, the adiabatic temperature rise, the placing temperature and the pipe cooling are comprehensively studied and represented as the interval numbers. Then, an IFEM equation is derived and a method for obtaining interval results based on monotonicity is also presented. To verify the proposed method, a non-adiabatic temperature rise test was carried out and subsequently simulated with the method. An excellent agreement is achieved between the simulation results and the monitoring data.

An IFEM method is proposed and a non-adiabatic temperature rise test is simulated to verify the method. The interval results are discussed and compared with monitoring data. The proposed method is found to be feasible and effective.

Compared with the traditional finite element methods, the proposed method taking the uncertainty of various factors into account and it will be helpful for engineers to gain a better understanding of the real condition.

The purpose of this paper is to discuss about evaluating the integrals involving B-spline wavelet on the interval (BSWI), in wavelet finite element formulations, using Gauss Quadrature.

In the proposed scheme, background cells are placed over each BSWI element and Gauss quadrature rule is defined for each of these cells. The nodal discretization used for BSWI WFEM element is independent to the selection of number of background cells used for the integration process. During the analysis, background cells of various lengths are used for evaluating the integrals for various combination of order and resolution of BSWI scaling functions. Numerical examples based on one-dimensional (1D) and two-dimensional (2D) plane elasto-statics are solved. Problems on beams based on Euler Bernoulli and Timoshenko beam theory under different boundary conditions are also examined. The condition number and sparseness of the formulated stiffness matrices are analyzed.

It is found that to form a well-conditioned stiffness matrix, the support domain of every wavelet scaling function should possess sufficient number of integration points. The results are analyzed and validated against the existing analytical solutions. Numerical examples demonstrate that the accuracy of displacements and stresses is dependent on the size of the background cell and number of Gauss points considered per background cell during the analysis.

The current paper gives the details on implementation of Gauss Quadrature scheme, using a background cell-based approach, for evaluating the integrals involved in BSWI-based wavelet finite element method, which is missing in the existing literature.

This paper aims to develop an efficient numerical method for mid-frequency analysis of built-up structures with large convex uncertainties.

Based on the Chebyshev polynomial approximation technique, a Chebyshev convex method (CCM) combined with the hybrid finite element/statistical energy analysis (FE-SEA) framework is proposed to fulfil the purpose. In CCM, the Chebyshev polynomials for approximating the response functions of built-up structures are constructed over the uncertain domain by using the marginal intervals of convex parameters; the bounds of the response functions are calculated by applying the convex Monte–Carlo simulation to the approximate functions. A relative improvement method is introduced to evaluate the truncated order of CCM.

CCM has an advantage in accuracy over CPM when the considered order is the same. Furthermore, it is readily to consider the CCM with the higher order terms of the Chebyshev polynomials for handling the larger convex parametric uncertainty, and the truncated order can be effectively evaluated by the relative improvement method.

The proposed CCM combined with FE-SEA is the first endeavor to efficiently handling large convex uncertainty in mid-frequency vibro-acoustic analysis of built-up structures. It also has the potential to serve as a powerful tool for other kinds of system analysis when large convex uncertainty is involved.

Advanced computational methods help to solve complex engineering problems via finite-element simulation. However, uncertainties during the process occurred due to the nature of geometry, material properties, loading, and boundary conditions. These inaccuracies affect the accuracy of results obtained from the analysis. This paper aims to analyse the uncertainty parameters of a finite element model in Excel-Visual Basic Application (VBA) by applying a random simulation method.

This study focuses on a finite element model with a different mesh. Young's Modulus, E, Poisson's ratio, and load, L are the uncertainty input parameters considered random variables.

Results obtained proved that the finite element model with the most nodes and elements has better solution convergence.

Random simulation method is a tool to perform uncertainty analysis of a finite element model.

The purpose of this paper is to propose a unified optimization design method and apply it to handle the brake squeal instability involving various uncertainties in a unified framework.

Fuzzy random variables are taken as equivalent variables of conventional uncertain variables, and a unified response analysis method is first derived based on level-cut technique, Taylor expansion and central difference scheme. Next, a unified reliability analysis method is developed by integrating the unified response analysis and fuzzy possibility theory. Finally, based on the unified reliability analysis method, a unified reliability-based optimization model is established, which is capable of optimizing uncertain responses in a unified way for different uncertainty cases.

The proposed method is extended to perform squeal instability analysis and optimization involving various uncertainties. Numerical examples under eight uncertainty cases are provided and the results demonstrate the effectiveness of the proposed method.

Most of the existing methods of uncertainty analysis and optimization are merely effective in tackling one uncertainty case. The proposed method is able to handle the uncertain problems involving various types of uncertainties in a unified way.

Gives introductory remarks about chapter 1 of this group of 31 papers, from ISEF 1999 Proceedings, in the methodologies for field analysis, in the electromagnetic community. Observes that computer package implementation theory contributes to clarification. Discusses the areas covered by some of the papers ‐ such as artificial intelligence using fuzzy logic. Includes applications such as permanent magnets and looks at eddy current problems. States the finite element method is currently the most popular method used for field computation. Closes by pointing out the amalgam of topics.

This paper discusses the issues involved in the development of combined finite/discrete element methods; both from a fundamental theoretical viewpoint and some related algorithmic considerations essential for the efficient numerical solution of large scale industrial problems. The finite element representation of the solid region is combined with progressive fracturing, which leads to the formation of discrete elements, which may be composed of one or more deformable finite elements. The applicability of the approach is demonstrated by the solution of a range of examples relevant to various industrial sections.

Methods that use spatial gradients of enthalpy to evaluate effective specific heats and capture latent heat effects in phase change problems have been used successfully in finite element formulations based on linear interpolation. In view of the greater geometrical flexibility and efficiency of biquadratic isoparametric elements, it is of interest to assess the use of the methods with these elements. In comparisons with an accurate semi‐analytic solution for a test problem, it is shown that the enthalpy gradient methods with quadratic interpolation are prone to error. A new procedure is proposed that uses bilinear sub‐elements for enthalpy, formed by subdivision of the biquadratic temperature elements. This is shown to be accurate and robust, for phase change intervals as small as 0.02°C.

We describe a visual method—stress band plots—for displaying the stress solution within a two‐dimensional finite element mesh. The stress band plots differ from conventional stress contour plots because stress band plots display unaveraged stresses (the stresses are computed directly from the solution variables) and stress discontinuities in the finite element solution are directly displayed. Stress band plots are useful in judging the accuracy of a finite element solution, in the comparison of different finite element solutions and during mesh refinement. These uses are demonstrated in an axisymmetric pressure vessel analysis.