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Publication Metadata only A comparison of stochastic and interval finite elements applied to shear frames with uncertain stiffness properties(Elsevier, 1998) Elishakoff, I; Department of Mathematics; Köylüoğlu, Hasan Uğur; Teaching Faculty; Department of Mathematics; College of Sciences; N/AStructural uncertainties are modelled using stochastic and interval methods to quantify the uncertainties in the response quantities. Through a suitable discretization, stochastic and interval finite element methods are constructed. A comparison of these methods is illustrated using a shear frame with uncertain stiffness properties.Publication Metadata only A differential integrability condition for two-dimensional Hamiltonian systems(Czech Technical Univ Prague, 2014) N/A; Department of Mathematics; Mostafazadeh, Ali; Faculty Member; Department of Mathematics; College of Sciences; 4231We review, restate, and prove a result due to Kaushal and Korsch [Phys. Lett. A 276, 47 (2000)] on the complete integrability of two-dimensional Hamiltonian systems whose Hamiltonian satisfies a set of four linear second order partial differential equations. In particular, we show that a two- dimensional Hamiltonian system is completely integrable, if the Hamiltonian has the form H = T + V where V and T are respectively harmonic functions of the generalized coordinates and the associated momenta.Publication Metadata only A faster simulation method for the stochastic response of hysteretic structures subject to earthquakes(Elsevier, 1996) Çakmak, Ahmet Ş.; Nielsen, Søren R.K.; Department of Mathematics; Köylüoğlu, Hasan Uğur; Teaching Faculty; Department of Mathematics; College of Sciences; N/AA semi-analytical forward-difference Monte Carlo simulation procedure is proposed for the determination of the lower order statistical moments and the joint probability density function of the stochastic response of hysteretic non-linear multi-degree-of-freedom structural systems subject to nonstationary gaussian white noise excitation, as an alternative to conventional direct simulation methods. The method generalizes the so-called Ermak-Allen algorithm developed for simulation applications in molecular dynamics to structural hysteretic systems. The proposed simulation procedure rely on an assumption of local gaussianity during each time step. This assumption is tantamount to various linearizations of the equations of motion. The procedure then applies an analytical convolution of the excitation process, hereby reducing the generation of stochastic processes and numerical integration to the generation of random vectors only. Such a treatment offers higher rates of convergence, faster speed and higher accuracy. The procedure has been compared to the direct Monte Carlo simulation procedure, which uses a fourth-order Runge-Kutta scheme with the white noise process approximated by a broad band Ruiz-Penzien broken line process. The considered system was a multi-dimenensional hysteretic shear frame, where the constitutive equation of the hysteretic shear forces are described by a bilinear hysteretic model. The comparisons show that significant savings in computer time and accuracy can be achieved.Publication Metadata 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/AA 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.Publication Metadata 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/AThis 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.Publication Open Access Estimates of the coverage of parameter space by Latin hypercube and orthogonal array-based sampling(Elsevier, 2018) Donovan, D.; Burrage, K.; Burrage, P.; McCourt, T. A.; Thompson, B.; Department of Mathematics; Yazıcı, Emine Şule; Faculty Member; Department of Mathematics; College of Sciences; 27432In this paper we use counting arguments to prove that the expected percentage coverage of a d dimensional parameter space of size n when performing k trials with either Latin Hypercube sampling or Orthogonal Array-based Latin Hypercube sampling is the same. We then extend these results to an experimental design setting by projecting onto a t < d dimensional subspace. These results are confirmed by simulations. The theory presented has both theoretical and practical significance in modelling and simulation science when sampling over high dimensional spaces.Publication Metadata only Exploratory and inferential methods for spatio-temporal analysis of residential fire clustering in urban areas(Elsevier, 2013) Ertugay, Kıvanç; Düzgün, Şebnem; Department of Mathematics; Ceyhan, Elvan; Faculty Member; Department of Mathematics; College of Sciences; N/AThe spatio-temporal analysis of residential fires could allow decision makers to plan effective resource allocations in fire management according to fire clustering levels in space and time. In this study, we provide guidelines for the use of various methods in detecting the differences in clustering patterns of fire and non-fire (i.e., background residential) locations and how these patterns change over time. As a preliminary analysis step, various exploratory data analysis methods, such as, intensity plots (i.e., kernel density estimates) are used. Moreover, the use of Diggle's-function (a second order analysis technique) is proposed for detecting the clustering of residential fire locations (if any) and whether there is additional clustering (or regularity) in the locations of the fires compared to background residential pattern. A test for trend over time (in years, months, and weeks) of the fire location patterns are provided with a space-time interaction analysis by the spatio-temporal-function. Residential fire data from Cankaya Municipality of Ankara, Turkey is used as an illustrative example. The presented methodology is also applicable to residential fire data from similar urban settings. (C) 2013 Elsevier Ltd. All rights reserved.Publication Metadata only Fast cell-to-cell mapping (path integration) for nonlinear white noise and Poisson driven systems(Elsevier Science Bv, 1995) Nielsen, SRK; Cakmak, AS; Department of Mathematics; Köylüoğlu, Hasan Uğur; Teaching Faculty; Department of Mathematics; College of Sciences; N/AThe stochastic response of nonlinear nonhysteretic single-degree-of-freedom oscillators subject to random excitations with independent increments is studied, where the state vector made up of the displacement and the velocity components becomes a Markov process. Random stationary white noise excitations and homogeneous Poisson driven impulses are considered as common examples of random excitations with independent increments. The applied method for the solution of the joint probability density function (jpdf) of the response is based on the cell-to-cell mapping (path integration) method, in which a mesh of discrete states of the Markov vector process is initially defined by a suitable distribution throughout the phase plane and the transition probability matrix related to the Markov chain originating from this discretization is approximately calculated. For white noise driven systems, transitions are assumed to be locally Gaussian and the necessary conditional mean values and covariances for only the first time step are obtained from the numerical integration of the differential equations for these quantities in combination with a Gaussian closure scheme, For Poisson driven systems, the transition time interval is taken sufficiently small so that at most one impulse is likely to arrive during the interval. The conditional transitional jpdf for exactly one impulse occurrence in the transition time interval is obtained by a new technique in which a convection expansion in terms of pulse intensities is employed. Next, the time dependent jpdf of the response is obtained by passing the system through a sequence of transient states. The formulation allows for a very fast and very accurate calculation of the stationary jpdf of the displacement and velocity by solving an eigenvector problem of the transition probability matrix with eigenvalue equal to 1. The method has been applied to the Duffing oscillator and the results for the stationary jpdf and extreme values have been compared to analytically available results for white noise driven systems acid to those obtained from extensive Monte Carlo simulations for Poisson driven systems.Publication Metadata only Faster simulation methods for the non-stationary random vibrations of non-linear mdof systems(A A Balkema, 1995) Department of Mathematics; Department of Mathematics; N/A; N/A; Aşkar, Attila; Köylüoğlu, Hasan Uğur; Çakmak, Ayşe Selin; Nielsen, Susanne Ramtung; Faculty Member; Teaching Faculty; Other; Other; Department of Mathematics; College of Sciences; College of Sciences; N/A; N/A; 178822 N/A; N/A; N/AN/APublication Metadata only Hysteretic mdof model to quantify damage for rc shear frames subject to earthquakes(Amer Soc Civil Engineers, 1996) Nielsen, Sasha Revelius Gaj; Çakmak, Ayşe Selin; Department of Mathematics; Köylüoğlu, Hasan Uğur; Teaching Faculty; Department of Mathematics; College of Sciences; N/AA hysteretic mechanical formulation is derived to quantify local, modal and overall damage in reinforced concrete (RC) shear frames subject to seismic excitation. Each interstorey is represented by a Clough and Johnston (1966) hysteretic constitutive relation with degrading elastic fraction of the restoring force. The local maximum softening damage indicators are based on the variation of the local stiffness and strength deterioration. The modal damage indicators are calculated from the variation of the eigenfrequencies of the structure. A statistical analysis is performed where a sample 5 storey shear frame is subject to simulated earthquake excitations, which are modelled as a stationary Gaussian stochastic process with Kanai-Tajimi spectrum, multiplied by an envelope function. The relationship between local, modal and overall damage indices are investigated statistically.
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