Research Outputs

Permanent URI for this communityhttps://hdl.handle.net/20.500.14288/2

Browse

Filters

1995 - 19985

Advanced Search

Filter by

Settings

Department: search.filters.department.Department of MathematicsSubject: search.filters.subject.Mechanical engineering

Search Results

Now showing 1 - 5 of 5
  • Placeholder
    PublicationMetadata only
    A solution method for linear and geometrically nonlinear MDOF systems with random properties subject to random excitation
    (Elsevier, 1998) Micaletti, RC; Çakmak, Ahmet Ş.; Nielsen, Søren R.K.; Department of Mathematics; Köylüoğlu, Hasan Uğur; Teaching Faculty; Department of Mathematics; College of Sciences; N/A
    A method for computing the lower-order moments of response of randomly excited multi-degree-of-freedom (MDOF) systems with random structural properties is proposed. The method is grounded in the techniques of stochastic calculus, utilizing a Markov diffusion process to model the structural system with random structural properties. The resulting state-space formulation is a system of ordinary stochastic differential equations with random coefficients and deterministic initial conditions which are subsequently transformed into ordinary stochastic differential equations with deterministic coefficients and random initial conditions, This transformation facilitates the derivation of differential equations which govern the evolution of the unconditional statistical moments of response. Primary consideration is given to linear systems and systems with odd polynomial nonlinearities, for in these cases there is a significant reduction in the number of equations to be solved. The method is illustrated for a five-story shear-frame structure with nonlinear interstory restoring forces and random damping and stiffness properties. The results of the proposed method are compared to those estimated by extensive Monte-Carlo simulation.
  • Placeholder
    PublicationMetadata only
    Error analysis of statistical linearization with gaussian closure for large-degree-of-freedom systems
    (Elsevier Sci Ltd, 1998) Micaletti, RC; Cakmak, AS; Nielsen, SRK; Department of Mathematics; Köylüoğlu, Hasan Uğur; Teaching Faculty; Department of Mathematics; College of Sciences; N/A
    This paper contains an analysis of the error induced by applying the method of equivalent statistical linearization (ESL) to randomly excited multi-degree-of-freedom (m.d.f.) geometrically nonlinear shear-frame structures as the number of degrees of freedom increases. The quantity that is analyzed is the variance of the top-story displacement. The m.d.f. systems under consideration obtain their nonlinearity through cubic polynomial interstory restoring forces and the external excitation is modeled as the stationary output of a Kanai-Tajimi filter. Parameters of the filter and the m.d.f. structures, as well as the intensity of the gaussian white noise, are calibrated such that quantitative comparisons of the error between the exact solutions, estimated from Monte Carlo simulations, and the ESL solutions are possible among systems of different dimensions.
  • Placeholder
    PublicationMetadata only
    Interval algebra to deal with pattern loading and structural uncertainties
    (Asce-Amer Soc Civil Eng, 1995) Çakmak, Ahmet Ş.; Nielsen, Søren R.K.; Department of Mathematics; Köylüoğlu, Hasan Uğur; Teaching Faculty; Department of Mathematics; College of Sciences; N/A
    Structural and loading uncertainties, bounded from above and below, are considered within a finite-element formulation to determine conservative bounds for the displacement and force response quantities. Discretization of a continuum with material uncertainties is illustrated using a linear elastic beam. This yields the elements of the stiffness matrix with uncertainties and the components of the force vector with uncertainties, to be defined in bounded intervals. Then, the response quantities become uncertain, yet bounded, in-a multidimensional rectangular prism. The discretized linear static interval equation is solved using the triangle inequality and linear programming to determine the conservative bounds for the response quantities. For the case when only loading uncertainties are considered, the problem reduces to the pattern loading problem of structural design. The proposed formulation is applied to the structural analysis of frames with material uncertainty under static loads with uncertainties.
  • Placeholder
    PublicationMetadata only
    Interval algebra to deal with pattern loading and structural uncertainties - Closure
    (Asce-Amer Soc Civil Engineers, 1997) Çakmak, Ahmet Ş.; Nielsen, Søren R.K.; Department of Mathematics; Köylüoğlu, Hasan Uğur; Teaching Faculty; Department of Mathematics; College of Sciences; N/A
    N/A
  • Placeholder
    PublicationMetadata only
    Local and modal damage indicators for rc frames subject to earthquakes
    (Asce-Amer Soc Civil Engineers, 1998) Nielsen, SRK; Abbott, J; Cahmak, AS; Department of Mathematics; Köylüoğlu, Hasan Uğur; Teaching Faculty; Department of Mathematics; College of Sciences; N/A
    Local, modal, and overall damage indicators for reinforced concrete shear frames subject to seismic excitation are defined and studied. Each story of the shear frame is represented by a Clough and Johnston hysteretic oscillator with a degrading elastic fraction of the restoring force. The local maximum softening damage indicators are defined in a closed form based on the variation of the eigenfrequency of the local oscillators due to the local stiffness and strength deterioration. The modal maximum softening damage indicators are calculated from the variation of the eigenfrequencies of the structure during excitation. The linear and nonlinear parameters of the local oscillators are assumed to be known. Next, a statistical analysis is performed where a sample five-story shear frame is subject to sinusoidal and simulated earthquake excitations. The shear frame is subject to 30 independent simulations of the earthquake excitation, which is modeled as a stationary Gaussian stochastic process with the Kanai-Tajimi spectrum, multiplied by an envelope function. Equations of motion of the storys are solved by a Runge-Kutta fourth-order scheme, where the local softening value is recorded. The modal maximum softening indicators are calculated from the known instantaneous stiffness matrix, which is a function of the structural properties and local damage. Alternatively, a Fourier analysis is performed for consecutive time windows to measure the same evolution using the top story displacement. Finally, the relationship between local and modal damage indices are investigated statistically.