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Hybrid probabilistic and convex modeling of excitation and response of periodic structures
Title
Hybrid probabilistic and convex modeling of excitation and response of periodic structures.
Creator
Zhu, L. P., Elishakoff, Isaac
Abstract/Description
In this paper, a periodic finite-span beam subjected to the stochastic acoustic pressure with bounded parameters is investigated. Uncertainty parameters exist in this acoustic excitation due to the deviation or imperfection. First, a finite-span beams subjected to the random acoustic pressure field are studied, the exact analytic forms of the cross-spectral density of both the transverse displacement and the bending moment responses of the structure are formulated. The combined probabilistic...
Show moreIn this paper, a periodic finite-span beam subjected to the stochastic acoustic pressure with bounded parameters is investigated. Uncertainty parameters exist in this acoustic excitation due to the deviation or imperfection. First, a finite-span beams subjected to the random acoustic pressure field are studied, the exact analytic forms of the cross-spectral density of both the transverse displacement and the bending moment responses of the structure are formulated. The combined probabilistic and convex modeling of acoustic excitation appears to be most suitable, since there is an insufficient information available on the acoustic excitation parameters, to justify the totally probabilitic analysis. Specifically, we postulate that the uncertainty parameters in the acoustic loading belong to a bounded, convex set. In the special case when this convex set is an ellipsoid, closed form solutions are obtained for the most and least favorable mean square responses of both the transverse displacement and bending moment of the structure. Several finite-span beams are exemplified to gain insight into proposal methodology.
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Date Issued
1996
PURL
http://purl.flvc.org/fau/fd/FAUIR000090
Format
Citation
Dynamic response and stability of viscoelastic structures by interval mathematics
Title
Dynamic response and stability of viscoelastic structures by interval mathematics.
Creator
Duan, Dehe., Florida Atlantic University, Elishakoff, Isaac
Abstract/Description
It is demonstrated in this thesis that the interval mathematics is a powerful tool to deal with uncertain phenomena especially when the uncertainty in bounded. In this thesis, we apply interval mathematics to several engineering problems, apparently for the first time in the world literature. The following topics are included: (1) The application of interval mathematics in several applied mechanics problems. A brief review of basis concepts is given, and some problems are presented to...
Show moreIt is demonstrated in this thesis that the interval mathematics is a powerful tool to deal with uncertain phenomena especially when the uncertainty in bounded. In this thesis, we apply interval mathematics to several engineering problems, apparently for the first time in the world literature. The following topics are included: (1) The application of interval mathematics in several applied mechanics problems. A brief review of basis concepts is given, and some problems are presented to illustrate the application of interval mathematics. (2) The stability and dynamic response of viscoelastic plate are studied. The effect of viscoelastic parameters on critical velocity is elucidated. (3) The application of Qiu-Chen-Elishakoff theorem in uncertain string and beam problems is investigated.
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Date Issued
1994
PURL
http://purl.flvc.org/fcla/dt/15090
Subject Headings
Interval analysis (Mathematics), Viscoelasticity, Fractional calculus
Format
Document (PDF)
Antioptimization of earthquake exitation and response
Title
Antioptimization of earthquake exitation and response.
Creator
Zuccaro, G., Elishakoff, Isaac, Baratta, A.
Abstract/Description
The paper presents a novel approach to predict the response of earthquake-excited structures. The earthquake excitation is expanded in terms of series of deterministic functions. The coefficients of the series are represented as a point in N-dimensional space. Each available accelerogram at a certain site is then represented as a point in the above space, modeling the available fragmentary historical data. The minimum volume ellipsoid, containing all points, is constructed. The ellipsoidal...
Show moreThe paper presents a novel approach to predict the response of earthquake-excited structures. The earthquake excitation is expanded in terms of series of deterministic functions. The coefficients of the series are represented as a point in N-dimensional space. Each available accelerogram at a certain site is then represented as a point in the above space, modeling the available fragmentary historical data. The minimum volume ellipsoid, containing all points, is constructed. The ellipsoidal models of uncertainty, pertinent to earthquake excitation, are developed. The maximum response of a structure, subjected to the earthquake excitation, within ellipsoidal modeling of the latter, is determined. This procedure of determining least favorable response was termed in the literature (Elishakoff, 1991) as an antioptimization. It appears that under inherent uncertainty of earthquake excitation, antioptimization analysis is a viable alternative to stochastic approach.
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Date Issued
1998
PURL
http://purl.flvc.org/fau/fd/FAUIR000014
Format
Citation
Buckling of composite cylindrical shells with geometric, thickness and material imperfections
Title
Buckling of composite cylindrical shells with geometric, thickness and material imperfections.
Creator
Li, Yiwei., Florida Atlantic University, Elishakoff, Isaac, College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering
Abstract/Description
This dissertation deals with the determination of buckling loads of composite cylindrical shell structures which involve uncertainty either in geometry, namely thickness variation, or in material properties. Systematic research has been carried out, which evolves from the simple isotropic cases to anisotropic cases. Since the initial geometric imperfection has a dominant role in the reduction of those imperfection-sensitive structures such as cylindrical shells, the combined effect of...
Show moreThis dissertation deals with the determination of buckling loads of composite cylindrical shell structures which involve uncertainty either in geometry, namely thickness variation, or in material properties. Systematic research has been carried out, which evolves from the simple isotropic cases to anisotropic cases. Since the initial geometric imperfection has a dominant role in the reduction of those imperfection-sensitive structures such as cylindrical shells, the combined effect of thickness variation and initial imperfection is also investigated in depth. Both analytic and numerical methods are used to derive the solutions to the problems and asymptotic formulas relating the buckling load to the geometric (thickness variation and/or initial imperfection) parameter are established. It is shown that the axisymmetric thickness variation has the most detrimental effect on the buckling load when the modal number of thickness variation is twice as much as that of the classical buckling mode. For the composite shells with uncertainty in material properties, the convex modelling is employed to evaluate the variability of buckling load. Based on the experimental data for the elastic moduli of the composite laminates, the upper and lower bounds of the buckling load are derived, which are numerically substantiated by the results from nonlinear programming. These bounds will be useful in practice and can provide engineers with a better view of the real load-carrying capacity of the composite structure. Finally, the elastic modulus is modeled as a function of coordinates to complete the study on variability of material property so that the result can be obtained to account for the situation where the elastic modulus is different from one place to another in the structure.
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Date Issued
1996
PURL
http://purl.flvc.org/fcla/dt/12444
Subject Headings
Composite materials, Buckling (Mechanics), Shells (Engineering), Structural dynamics
Format
Document (PDF)
Convex identification and nonlinear random vibration analysis of elastic and viscoelastic structures
Title
Convex identification and nonlinear random vibration analysis of elastic and viscoelastic structures.
Creator
Fang, Jianjie, Florida Atlantic University, Elishakoff, Isaac, College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering
Abstract/Description
This dissertation deals with the identification of boundary conditions of elastic structures, and nonlinear random vibration analysis of elastic and viscoelastic structures through a new energy-based equivalent linearization technique. In the part of convex identification, convex models are utilized to represent the degree of uncertainty in the boundary condition modification. This means that the identification is actually the identification of the convex model to which the actual boundary...
Show moreThis dissertation deals with the identification of boundary conditions of elastic structures, and nonlinear random vibration analysis of elastic and viscoelastic structures through a new energy-based equivalent linearization technique. In the part of convex identification, convex models are utilized to represent the degree of uncertainty in the boundary condition modification. This means that the identification is actually the identification of the convex model to which the actual boundary stiffness profile belongs. Two examples are presented to illustrate the application of the method. For the beam example the finite element analysis is performed to evaluate the frequencies of a beam with any specific boundary conditions. For the plate example, the Bolotin's dynamic edge effect method, generalized by Elishakoff, is employed to determine the approximate natural frequencies and normal modes of elastically supported isotropic, uniform rectangular plates. In the part of nonlinear random analysis, first a systematic finite element analysis procedure, based on the element's energy formulation, through conventional stochastic linearization technique, is proposed. The procedure is applicable to a wide range of nonlinear random vibration problem as long as element's energy formulations are presented. Secondly, the new energy-based stochastic linearization method in finite element analysis setting is developed to improve the conventional stochastic linearization technique. The entire formulation is produced in detail for the first time. The theory is applied to beam problem subjected to space-wise and time-wise white noise excitations. Finally, the new energy-based stochastic linearization technique is applied to treat nonlinear vibration problems of viscoelastic beams.
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Date Issued
1996
PURL
http://purl.flvc.org/fcla/dt/12467
Subject Headings
Elasticity, Viscoelasticity, Structural dynamics--Mathematical models, Vibration--Mathematical models
Format
Document (PDF)
Finite element methods for stochastic structures and conditional simulation
Title
Finite element methods for stochastic structures and conditional simulation.
Creator
Ren, Yongjian., Florida Atlantic University, Elishakoff, Isaac, College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering
Abstract/Description
This dissertation deals with the non-perturbative finite element methods for stochastic structures and conditional simulation techniques for random fields. Three different non-perturbative finite element schemes have been proposed to compute the first and second moments of displacement responses of stochastic structures. These three methods are based, respectively, on (i) the exact inverse of the global stiffness matrix for simple stochastic structures; (ii) the variational principles for...
Show moreThis dissertation deals with the non-perturbative finite element methods for stochastic structures and conditional simulation techniques for random fields. Three different non-perturbative finite element schemes have been proposed to compute the first and second moments of displacement responses of stochastic structures. These three methods are based, respectively, on (i) the exact inverse of the global stiffness matrix for simple stochastic structures; (ii) the variational principles for statically-determinate beams; and (iii) the element-level flexibility for general stochastic statically indeterminate structures. The non-perturbative finite element method for stochastic structures possesses several advantages over the conventional perturbation-based finite element method for stochastic structures, including (i) applicability to large values of the coefficient of variation of random parameters; (ii) convergence to exact solutions when the finite element mesh is refined; (iii) requirement of less statistical information than that demanded by the high-order perturbation methods. Conditional simulation of random fields has been an extremely important research field in most recent years due to its application in urban earthquake monitoring systems. This study generalizes the available simulation technique for one-variate Gaussian random fields, conditioned by realizations of the fields, to multi-variate vector random field, conditioned by the realizations of the fields themselves as well as the realizations of the fields derivatives. Furthermore, a conditional simulation for non-Gaussian random fields is also proposed in this study by combining the unconditional simulation technique of non-Gaussian fields and the conditional simulation technique of Gaussian fields. Finally, the dissertation incorporates the simulation technique of random field into the non-perturbation finite element method for stochastic structures, to handle the cases where only one-dimensional probability density function and the correlation function of the random parameters are available, the demanded two-dimensional probability density function is unavailable. Simulation technique is applied to generate the samples of random fields which are used to estimate the correlation between flexibilities over elements. The estimated correlation of flexibility is then used in finite element analysis for stochastic structures. For each proposed approach, numerous examples and numerical results have been implemented.
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Date Issued
1998
PURL
http://purl.flvc.org/fcla/dt/12580
Subject Headings
Finite element method, Stochastic processes, Random fields--Mathematical models
Format
Document (PDF)
Some topics related to the vibrations of deterministic and non-deterministic metamaterial structures
Title
Some topics related to the vibrations of deterministic and non-deterministic metamaterial structures.
Creator
Li, Yuchen, Elishakoff, Isaac, Challamel, Noël, Florida Atlantic University, Department of Ocean and Mechanical Engineering, College of Engineering and Computer Science
Abstract/Description
In this thesis, we will explore different kinds of metamaterial or architectural structural problems, including structures composed of heterogeneous media with bi periodic sub-structures, discrete structures with sub-elements or continuous structures with discrete attached sub-elements. The thesis is composed of seven parts. After having introduced the specificities of metamaterial mechanics, the second chapter is devoted to the vibration of discrete beam problems called Hencky bar-chain...
Show moreIn this thesis, we will explore different kinds of metamaterial or architectural structural problems, including structures composed of heterogeneous media with bi periodic sub-structures, discrete structures with sub-elements or continuous structures with discrete attached sub-elements. The thesis is composed of seven parts. After having introduced the specificities of metamaterial mechanics, the second chapter is devoted to the vibration of discrete beam problems called Hencky bar-chain model in a stochastic framework. It is shown that the lattice beam behaves as a nonlocal continuous beam problem, both in the deterministic and the non-deterministic analyses. The third chapter considers the vibration of continuous beams with the introduction of shear effects and attached periodically oscillators. A discussion on beam modelling, for example Timoshenko beam models or truncated Timoshenko beam models is included. It is shown that the bandgap phenomenon observed for metamaterial beams can be accurately captured by a truncated Timoshenko beam model which means the last term in the Timoshenko equation is not that important.
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Date Issued
2023
PURL
http://purl.flvc.org/fau/fd/FA00014289
Subject Headings
Metamaterials, Hencky bar-chain model, Lattice theory, Engineering
Format
Document (PDF)
Combination of anti-optimization and fuzzy-set-based analysis for structural optimization under uncertainty
Title
Combination of anti-optimization and fuzzy-set-based analysis for structural optimization under uncertainty.
Creator
Fang, Jianjie, Smith, Samuel M., Elishakoff, Isaac
Abstract/Description
An approach to the optimum design of structures, in which uncertainties with a fuzzy nature in the magnitude of the loads are considered, is proposed in this study. The optimization process under fuzzy loads is transformed into a fuzzy optimization problem based on the notion of Wemers' maximizing set by defining membership functions of the objective function and constraints. In this paper, Werner's maximizing set is defined using the results obtained by first conducting an optimization...
Show moreAn approach to the optimum design of structures, in which uncertainties with a fuzzy nature in the magnitude of the loads are considered, is proposed in this study. The optimization process under fuzzy loads is transformed into a fuzzy optimization problem based on the notion of Wemers' maximizing set by defining membership functions of the objective function and constraints. In this paper, Werner's maximizing set is defined using the results obtained by first conducting an optimization through anti-optimization modeling of the uncertain loads. An example of a ten-bar truss is used to illustrate the present optimization process. The results are compared with those yielded by other optimization methods.
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Date Issued
1998
PURL
http://purl.flvc.org/fau/fd/FAUIR000069
Format
Citation