• Structural Engineering and Mechanics
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• v.62 no.6
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• pp.703-708
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• 2017

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.

• Structural Engineering and Mechanics
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• v.29 no.5
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• pp.469-488
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• 2008

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.

• Structural Engineering and Mechanics
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• v.12 no.6
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• pp.669-684
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• 2001

A new method for solving the uncertain eigenvalue problems of the structures with interval parameters, interval finite element method based on the element, is presented in this paper. The calculations are done on the element basis, hence, the efforts are greatly reduced. In order to illustrate the accuracy of the method, a continuous beam system is given, the results obtained by it are compared with those obtained by Chen and Qiu (1994); in order to demonstrate that the proposed method provides safe bounds for the eigenfrequencies, an undamping spring-mass system, in which the exact interval bounds are known, is given, the results obtained by it are compared with those obtained by Qiu et al. (1999), where the exact interval bounds are given. The numerical results show that the proposed method is effective for estimating the eigenvalue bounds of structures with interval parameters.

• Coupled systems mechanics
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• v.1 no.4
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• pp.345-360
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• 2012

In this article we have presented a unique representation for interval arithmetic. The traditional interval arithmetic is transformed into crisp by symbolic parameterization. Then the proposed interval arithmetic is extended for fuzzy numbers and this fuzzy arithmetic is used as a tool for uncertain finite element method. In general, the fuzzy finite element converts the governing differential equations into fuzzy algebraic equations. Fuzzy algebraic equations either give a fuzzy eigenvalue problem or a fuzzy system of linear equations. The proposed methods have been used to solve a test problem namely heat conduction problem along with fuzzy finite element method to see the efficacy and powerfulness of the methodology. As such a coupled set of fuzzy linear equations are obtained. These coupled fuzzy linear equations have been solved by two techniques such as by fuzzy iteration method and fuzzy eigenvalue method. Obtained results are compared and it has seen that the proposed methods are reliable and may be applicable to other heat conduction problems too.

• Structural Engineering and Mechanics
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• v.44 no.1
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• pp.73-84
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• 2012

This paper strongly addresses to the problem of the mechanical systems in which parameters are uncertain and bounded. Interval calculation is used to find sharp bounds of the structural parameters for infilled frame system modeled with finite element method. Infill walls are generally treated as non-structural elements considerably to improve the lateral stiffness, strength and ductility of the structure together with the frame elements. Because of their complex nature, they are often neglected in the analytical model of building structures. However, in seismic design, ignoring the effect of infill wall in a numerical model does not accurately simulate the physical behavior. In this context, there are still some uncertainties in mechanical and also geometrical properties in the analysis and design procedure of infill walls. Structural uncertainties can be studied with a finite element formulation to determine sharp bounds of the structural parameters such as wall thickness and Young's modulus. In order to accomplish this sharp solution as much as possible, interval finite element approach can be considered, too. The structural parameters can be considered as interval variables by using the interval number, thus the structural stiffness matrix may be divided into the product of two parts which correspond to the interval values and the deterministic value.

• Smart Structures and Systems
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• v.26 no.3
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• pp.311-318
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• 2020

The goal of this study is to analytically and non-stochastically generate structural uncertainty behaviors of isotropic beams and laminated composite plates under plane stress conditions by using an interval finite element method. Uncertainty parameters of structural properties considering resistance and load effect are formulated by interval arithmetic and then linked to the finite element method. Under plane stress state, the isotropic cantilever beam is modeled and the laminated composite plate is cross-ply lay-up [0/90]. Triangular shape with a clamped-free boundary condition is given as geometry. Through uncertainties of both Young's modulus for resistance and applied forces for load effect, the change of structural maximum deflection and maximum von-Mises stress are analyzed. Numerical applications verify the effective generation of structural behavior uncertainties through the non-stochastic approach using interval arithmetic and immediately the feasibility of the present method.

• Structural Engineering and Mechanics
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• v.25 no.5
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• pp.613-629
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• 2007

A finite element method (FEM) of B-spline wavelet on the interval (BSWI) is used in this paper to solve the static and vibration problems of thin plate. Instead of traditional polynomial interpolation, the scaling functions of two-dimensional tensor product BSWI are employed to construct the transverse displacements field. The method combines the accuracy of B-spline functions approximation and various basis functions for structural analysis. Some numerical examples are studied to demonstrate the proposed method and the numerical results presented are in good agreement with the solutions of other methods.

• Structural Engineering and Mechanics
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• v.26 no.2
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• pp.163-178
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• 2007

In practical engineering, the uncertain concept plays an important role in the control problems of the vibration structures. In this paper, based on matrix perturbation theory and interval finite element method, the closed-loop vibration control system with uncertain parameters is discussed. A new method is presented to develop an algorithm to estimate the upper and lower bounds of the real parts and imaginary parts of the complex eigenvalues of vibration control systems. The results are derived in terms of physical parameters. The present method is implemented for a vibration control system of the frame structure. To show the validity and effectiveness, we compare the numerical results obtained by the present method with those obtained by the classical random perturbation.

• Structural Engineering and Mechanics
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• v.27 no.3
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• pp.263-276
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• 2007

This paper presents a fuzzy finite element model for the analysis of structures in the presence of multiple uncertainties. A new methodology to evaluate the cumulative effect of multiple uncertainties on structural response is developed in the present work. This is done by modifying Muhanna's approach for handling single uncertainty. Uncertainty in load and material properties is defined by triangular membership functions with equal spread about the crisp value. Structural response is obtained in terms of fuzzy interval displacements and rotations. The results are further post-processed to obtain interval values of bending moment, shear force and axial forces. Membership functions are constructed to depict the uncertainty in structural response. Sensitivity analysis is performed to evaluate the relative sensitivity of displacements and forces to uncertainty in structural parameters. The present work demonstrates the effectiveness of fuzzy finite element model in establishing sharp bounds to the uncertain structural response in the presence of multiple uncertainties.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 1999.08a
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• pp.98-106
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• 1999

In this study cold rolling process for the irregular cross-sectional shape has been investigated. The product analyzed in present study is the steel cutter, which is frequently used to cut the desired shape on leather. Because steel cutter always has a irregular cross-section, after rolling process the workpiece is severely bended to every direction. The bending of the workpiece affects the processed performed after rolling such as heat treatment and grinding, then that of the workpiece becomes more severe. In this study, therefore, to prevent the bending of the workpiece to the left and right sides. rigid-plastic finite element method has been utilized and in order to find optimal roll geometry rapidly, one dimensional equal interval search technique has been also introduced. By using both rigid plastic finite element method and optimum technique, cold rolling process for the irregular cross-sectional shape has been successfully investigated.