Interval static displacement analysis for structures with interval parameters

Chen, Suhuan; Lian, Huadong; Yang, Xueli

doi:10.1002/nme.281

Cited by 104 publications

(42 citation statements)

References 10 publications

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“…Contact angle b is another interval parameter, and it is expressed as b 2 b I = ½1 À u b , 1 + u b b c , where b c = 758; and u b is the uncertain factor; its value is 2%. The result of second-order Taylor series expansion and first-order Taylor series expansion 13 is compared with that of MCS method, which is listed in Tables 1 and 2. MCS method is the numerical method for estimating the upper and lower bounds in a box region…”

Section: Validationmentioning

confidence: 99%

Uncertainty analysis of torque-induced bending deformations in ball screw systems

Gao

Wang

et al. 2015

Advances in Mechanical Engineering

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In order to study the torque-induced bending deformation in ball screw systems with uncertain-but-bounded parameters, uncertainty analysis of torque-induced bending deformations in ball screw systems based on an numerical method combined second-order Taylor series expansion with difference of convex functions algorithm is conducted in this research. The maximum torque-induced bending deformation in ball screw systems with certain parameters is solved by modeling the ball screw as a simple Euler-Bernoulli beam. On the basis of the model, the general expression of maximum deformation of ball screw systems in terms of uncertain parameters is derived based on the second-order Taylor series expansion. Then the problem of determining bounds of the maximum deformation of uncertain systems is transformed into a series of box constrained quadratic programming problems. Box constrained quadratic programming problems are solved by difference of convex functions algorithm. The effectiveness of the analysis is validated by Monte Carlo simulation method. Through demonstration, the conclusion can be drawn that the torque-induced bending deformation in ball screw systems with uncertain-but-bounded parameters can be analyzed explicitly by the numerical method combined second-order Taylor series expansion with difference of convex functions algorithm, which offers a new approach for estimating the torque-induced bending deformation in ball screw systems.

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Section: Validationmentioning

confidence: 99%

Uncertainty analysis of torque-induced bending deformations in ball screw systems

Gao

Wang

et al. 2015

Advances in Mechanical Engineering

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“…Recently, Chen et al [10] have used interval set models to study the eigenvalues of structures with bounded uncertain parameters. In References [11,12], Chen et al investigated the static and dynamic responses of uncertain structures using the interval finite element (IFE) method. In these studies, several important results have been obtained, using interval analysis and matrix perturbation techniques.…”

Section: Introductionmentioning

confidence: 99%

Interval finite element method for dynamic response of closed‐loop system with uncertain parameters

Zhang

Ding

Chen

2006

Numerical Meth Engineering

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SUMMARYIn practical engineering, it is difficult to obtain all possible solutions of dynamic responses with sharp bounds even if an optimum scheme is adopted where there are many uncertain parameters. In this paper, using the interval finite element (IFE) method and precise time integration (PTI) method, we discuss the dynamic response of vibration control problem of structures with interval parameters. With matrix perturbation theory and interval arithmetic, the algorithm for estimating upper and lower bounds of dynamic response of the closed-loop system is developed directly from the interval parameters. Two numerical examples are given to illustrate the application of the present method. The example 1 is used to show the applicability of the present method. The example 2 is used to show the validity of the present method by comparing the results with those obtained by the classical random perturbation method.

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“…Mcwilliam [14] discussed how to calculate the static displacement bounds of structures with uncertain parameters. On the basis of perturbation and the interval extension, Chen et al [15] proposed an approach to find the upper and lower bounds of the static displacements. Recently, with the use of quadratic embedding of uncertainty and the semi-definite relaxation techniques, Kanno and Takewaki [16,17] proposed an elegant approach to compute the robustness function and confidence ellipsoids for static response of truss structures with load and structural uncertainties.…”

Section: Introductionmentioning

confidence: 99%

Extreme structural response analysis of truss structures under material uncertainty via linear mixed 0–1 programming

Gao

Bai

Zhang

2008

Numerical Meth Engineering

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SUMMARYThis paper concerns the extreme structural response analysis of truss structures taking the possible uncertainties of Young's moduli of the bars into consideration. The uncertainty of Young's modulus is described by a non-probability but bounded interval model. With the use of this uncertain model, it is shown that the structural responses such as nodal displacement and bar stress will attain their extreme values when Young's moduli of the bars take either their upper or lower bound value. Based on this conclusion and simultaneous analysis and design formulation, a linear mixed 0-1 programming problem can be constructed to find the extreme values of the structural response by the well-established branchand-bound approach with global optimality. The proposed approach is applied to several test problems for the demonstration of its validity.

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Interval static displacement analysis for structures with interval parameters

Cited by 104 publications

References 10 publications

Uncertainty analysis of torque-induced bending deformations in ball screw systems

Uncertainty analysis of torque-induced bending deformations in ball screw systems

Interval finite element method for dynamic response of closed‐loop system with uncertain parameters

Extreme structural response analysis of truss structures under material uncertainty via linear mixed 0–1 programming

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