Isaac Elishakoff

Bio: Isaac Elishakoff is an academic researcher from Florida Atlantic University. The author has contributed to research in topics: Buckling & Beam (structure). The author has an hindex of 47, co-authored 460 publications receiving 9144 citations. Previous affiliations of Isaac Elishakoff include Clark Atlanta University & University of Notre Dame.

Convex models of uncertainty in applied mechanics

Abstract: 1. Probabilistic Modelling: Pros and Cons. Preliminary considerations. Probabilistic modelling in mechanics. Reliability of structures. Sensitivity of failure probability. Some quotations on the limitations of probabilistic methods. 2. Mathematics of Convexity. Convexity and Uncertainty. What is convexity? Geometric convexity in the Euclidean plane. Algebraic convexity in Euclidean space. Convexity in function spaces. Set-convexity and function-convexity. The structure of convex sets. Extreme points and convex hulls. Extrema of linear functions on convex sets. Hyperplane separation of convex sets. Convex models. 3. Uncertain Excitations. Introductory examples. The massless damped spring. Excitation sets. Maximum responses. Measurement optimization. Vehicle vibration. Introduction. The vehicle model. Uniformly bounded substrate profiles. Extremal responses on uniformly bounded substrates. Duration of acceleration excursions on uniformly bounded substrates. Substrate profiles with bounded slopes. Isochronous obstacles. Solution of the Euler-Lagrange equations. Seismic excitation. Vibration measurements. Introduction. Damped vibrations: full measurement. Example: 2-dimensional measurement. Damped vibrations: partial measurement. Transient vibrational acceleration. 4. Geometric Imperfections. Dynamics of thin bars. Introduction. Analytical formulation. Maximum deflection. Duration above a threshold. Maximum integral displacements. Impact loading of thin shells. Introduction. Basic equations. Extremal displacement. Numerical example. Buckling of thin shells. Introduction. Bounded Fourier coefficients: first-order analysis. Bounded Fourier coefficients: second-order analysis. Uniform bounds on imperfections. Envelope bounds on imperfections. Estimates of the knockdown factor. First and second-order analyses. 5. Concluding Remarks. Bibliography. Index.

Antioptimization of structures with large uncertain-but-non-random parameters via interval analysis

Abstract: Non-probabilistic, interval modeling of uncertain-but-non-random parameters for structures is developed in this paper for antioptimization analysis, consisting in determining the least favorable responses. The uncertain-but-non-random parameter is considered to be a deterministic variable belonging to a set modeled as an interval. The least favorable static displacement bound estimation for structures with uncertain-but-non-random parameters is transformed into solving interval linear equations. For small interval parameters (the width of interval being small), the uncertainties of interval parameters are treated as the perturbed quantities around the midpoint of interval parameters, by means of the interval matrix central notation and the natural interval extension. Interval perturbation method for estimating the static displacement bound of structures with interval parameters was presented in the recent study by Qiu et al. [1]. For large interval parameters, a subinterval perturbation method for estimating the static displacement bound of structures with interval parameters is put forward in the study. The numerical results show that a subinterval perturbation method yields tighter bounds than those yielded by the interval perturbation method.

Probabilistic Methods in the Theory of Structures

Abstract: Keywords: probabilites ; structures ; vibration ; methodes de : calcul Reference Record created on 2005-11-18, modified on 2016-08-08

Structural design under bounded uncertainty-optimization with anti-optimization

Abstract: In many cases precise probabilistic data are not available on uncertainty in loads, but the magnitude of the uncertainty can be bound. This paper proposes a design approach for structural optimization with uncertain but bounded loads. The problem of identifying critical loads is formulated mathematically as an optimization problem in itself (called anti-optimization), so that the design problem is formulated as a two-level optimization. For linear structural analysis it is shown that the antioptimization part is limited to consideration of the vertices of the load-uncertainty domain. An example of a ten-bar truss is used to demonstrate that we cannot replace the anti-optimization process by considering the largest possible loads.

Table Of Integrals Series And Products

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Structural (n,m) determination of isolated single wall carbon nanotubes by resonant Raman scattering

Abstract: We show that the Raman scattering technique can give complete structural information for one-dimensional systems, such as carbon nanotubes. Resonant confocal micro-Raman spectroscopy of an (n,m) individual single-wall nanotube makes it possible to assign its chirality uniquely by measuring one radial breathing mode frequency omega(RBM) and using the theory of resonant transitions. A unique chirality assignment can be made for both metallic and semiconducting nanotubes of diameter d(t), using the parameters gamma(0) = 2.9 eV and omega(RBM) = 248/d(t). For example, the strong RBM intensity observed at 156 cm(-1) for 785 nm laser excitation is assigned to the (13,10) metallic chiral nanotube on a Si/SiO2 surface.

Modeling and Analysis of Functionally Graded Materials and Structures

Abstract: This paper presents a review of the principal developments in functionally graded materials (FGMs) with an emphasis on the recent work published since 2000. Diverse areas relevant to various aspects of theory and applications of FGM are reflected in this paper. They include homogenization of particulate FGM, heat transfer issues, stress, stability and dynamic analyses, testing, manufacturing and design, applications, and fracture. The critical areas where further research is needed for a successful implementation of FGM in design are outlined in the conclusions. DOI: 10.1115/1.2777164