Interval Finite Element Analysis Research Articles

A sequential simulation strategy for response bounds analysis of structures with interval uncertainties

Prediction of response bounds of structures with interval uncertainties is a major concern in interval finite element analysis. In many cases, the structural response is a variable regarding to physical parameters such as location, node, time, or other degrees of freedom. Different kinds of interval methods have been proposed and developed for response bounds analysis, which mainly include the interval arithmetic-based methods, optimization methods, perturbation methods, etc. This paper proposes a sequential simulation strategy for response bounds analysis of structures with interval uncertainties, through which we aim to find the upper and lower bounds by implementing the simulation procedure sequentially. The proposed sequential simulation strategy suggests an initial sampling and simulation, from which those contributive samples that result in the current upper or lower response bound are retained. In the subsequent simulation sequence, local samples within neighborhoods of the present contributive samples as well as a set of global samples are generated for the input interval uncertainties. With such a simulation procedure, the response bounds are expected to expand outwards sequentially until convergence. By illustration and comparison, the proposed sequential simulation strategy is proved to be more efficient than the direct simulation method for structural response bounds analysis.

Interval field model and interval finite element analysis

Spatially uncertain parameters are traditionally represented by random field models. However, the large amount of information required for construction of precise probability distribution is often difficult to obtain for many practical engineering problems. In this paper, an interval field model is proposed to represent spatial uncertainties with insufficient information, in which the variation of the parameter at any location is quantified by an interval with upper and lower bounds. The spatial dependency is measured by a covariance function or a correlation coefficient function, defined for the interval variables at different locations. An interval Karhunen–Loève expansion is formulated for the proposed interval field model, in which the continuous spatial uncertainty is expressed through a series of deterministic functions with uncorrelated interval coefficients. Furthermore, by incorporating the interval field model into the finite element method, interval finite element analysis with spatially uncertain parameters is carried out. Perturbation-based interval finite element methods are developed to evaluate the upper and lower bounds of structural responses such as displacement and stress. A Monte Carlo simulation method is also presented to provide a reference solution for the structural analysis with interval fields. Finally, two numerical examples are investigated to demonstrate the effectiveness of the interval field model and the interval finite element methods.

Interval Field Model and Interval Finite Element Analysis

Abstract Spatially uncertain parameters are traditionally represented by random field models . However, the large amount of information required for construction of precise probability distribution is often difficult to obtain for many practical engineering problems. In this paper, an interval field model is proposed to represent spatial uncertainties with insufficient information, in which the variation of the parameter at any location is quantified by an interval with upper and lower bounds. The spatial dependency is measured by a covariance function or a correlation coefficient function, defined for the interval variables at different locations. An interval Karhunen–Loeve expansion is formulated for the proposed interval field model, in which the continuous spatial uncertainty is expressed through a series of deterministic functions with uncorrelated interval coefficients. Furthermore, by incorporating the interval field model into the finite element method , interval finite element analysis with spatially uncertain parameters is carried out. Perturbation-based interval finite element methods are developed to evaluate the upper and lower bounds of structural responses such as displacement and stress. A Monte Carlo simulation method is also presented to provide a reference solution for the structural analysis with interval fields. Finally, two numerical examples are investigated to demonstrate the effectiveness of the interval field model and the interval finite element methods.

Non-stochastic interval factor method-based FEA for structural stress responses with uncertainty

The goal of this study is to evaluate behavior uncertainties of structures by using interval finite element analysis based on interval factor method as a specific non-stochastic tool. The interval finite element method, i.e., interval FEM, is a finite element method that uses interval parameters in situations where it is not possible to get reliable probabilistic characteristics of the structure. The present method solves the uncertainty problems of a 2D solid structure, in which structural characteristics are assumed to be represented as interval parameters. An interval analysis method using interval factors is applied to obtain the solution. Numerical applications verify the intuitive effectiveness of the present method to investigate structural uncertainties such as displacement and stress without the application of probability theory.

Interval finite element analysis and reliability-based optimization of coupled structural-acoustic system with uncertain parameters

A modified interval parameter perturbation finite element method (MIPPM) and a reliability-based optimization model are proposed for the coupled structural-acoustic field prediction and structural design with uncertainties in both the physical parameters and boundary conditions. Interval variables are used to quantitatively describe all the uncertain parameters with limited information. The interval matrix and vector are expanded by the modified Taylor series. Compared with the traditional perturbation method, the proposed MIPPM can yield more accurate ranges of the uncertain structural-acoustic field, in which the higher order terms of Neumann series are employed to approximate the interval matrix inverse. The reliability idea is introduced to establish an interval optimization model relying on the satisfaction degree of interval. The uncertain constraints can be transformed into deterministic ones if given the confidence level. The proposed MIPPM is used to predict the intervals of the constraints, and whereby eliminate the optimization nesting. Numerical results about a 3D car are given to demonstrate the feasibility and efficiency of the proposed model and algorithm.

Interval finite element analysis of masonry-infilled walls

Interval finite element analysis of masonry-infilled walls

Interval Finite Element Analysis and Sensitivity Study of Engineering Structure

Abstract: The material parameters and the load are considered interval uncertainty and regarded as interval variables in this paper. The interval finite element analysis model is established for engineering structures. The interval parameter perturbation method and endpoint combination method based on monotonic are used to calculate deformation range. Sensitivity on the material parameters and load is studied.as an example for truss structure, the conclusion is more reasonable and applicable.

Fuzzy finite element analysis of heat conduction problems with uncertain parameters

In this article we have used four different global optimisation algorithms for interval finite element analysis of (non)linear heat conduction problems: (i) sequential quadratic programming (SQP), (ii) a scatter search method (SSm), (iii) the vertex algorithm, and (iv) the response surface method (RSM). Their performance was compared based on a thermal sterilisation problem and a food freezing problem. The vertex method proved to be by far the fastest method but is only effective if the solution is a monotonic function of the uncertain parameters. The RSM was also fast albeit much less than the vertex method. Both SQP and SSm were considerably slower than the former methods; SQP did not converge to the real solution in the food freezing test problem. The interval finite element method was used as a building block for a fuzzy finite element analysis based on the α-cuts method. The RSM fuzzy finite element method was identified as the fastest algorithm among all the tested methods. It was shown that uncertain parameters may cause large uncertainties in the process variables. The algorithms can be used to obtain more realistic modelling of food processes that often have significant uncertainty in the model parameters.

Non-stochastic interval arithmetic-based finite element analysis for structural uncertainty response estimate

Finite element methods have often been used for structural analyses of various mechanical problems. When finite element analyses are utilized to resolve mechanical systems, numerical uncertainties in the initial data such as structural parameters and loading conditions may result in uncertainties in the structural responses. Therefore the initial data have to be as accurate as possible in order to obtain reliable structural analysis results. The typical finite element method may not properly represent discrete systems when using uncertain data, since all input data of material properties and applied loads are defined by nominal values. An interval finite element analysis, which uses the interval arithmetic as introduced by Moore (1966) is proposed as a non-stochastic method in this study and serves a new numerical tool for evaluating the uncertainties of the initial data in structural analyses. According to this method, the element stiffness matrix includes interval terms of the lower and upper bounds of the structural parameters, and interval change functions are devised. Numerical uncertainties in the initial data are described as a tolerance error and tree graphs of uncertain data are constructed by numerical uncertainty combinations of each parameter. The structural responses calculated by all uncertainty cases can be easily estimated so that structural safety can be included in the design. Numerical applications of truss and frame structures demonstrate the efficiency of the present method with respect to numerical analyses of structural uncertainties.

Interval Finite Element Analysis of Structural Systems with Uncertainties. Static Analyses of Truss Structures with Geometrical Uncertainties.

In the Interval Finite Element Analysis of structure the uncertainties given by the interval are studied within the finite element formulation to determine the sharp bounds of the displacement response. Two approaches namely, the Direct Interval Finite Element Analysis (DIFEA) and the Iterative Interval Finite Element Analysis (IIFEA) are proposed to obtain the sharp solution as much as possible. In DIFEA, each step of the standard FEA, using ordinary real arithmetic, is simply replaced with the corresponding interval arithmetic step. In IIFEA, the interval structural analysis is formulated as a nonlinear optimization problem, while components of the displacement vector as well as parameters of the structural system with uncertainties are dealt as decision variables. A specific component of the displacement vector is considered as the objective function, which is minimized and maximized to obtain the lower and upper bounds. Validation of these methods is tested to the analysis of truss structural systems with uncertainties in nodal coordinates.