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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)
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