• Proceedings of the Computational Structural Engineering Institute Conference
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• 1993.10a
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• pp.207-215
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• 1993

With the aid of finite element method, this paper deals with the problem of structural response variability of transmission tower subjected to the spatial variability of material properties, Young's modulus herein. The spatial variability of material property are modeled as two-dimensional stochastic field which has an isotropic auto-correlation function. Response variability has been computed based on two numerical techniques, such as the Neumann expansion method in conjunction with the Monte Carlo simulation method. The results by these numerical methods are compared with those by the deterministic approach.

• Transactions of Materials Processing
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• v.13 no.3
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• pp.248-252
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• 2004

The mechanical properties of polycrystalline thin-films, critical for Micro-Electro-Mechanical Systems (MEMS) components, are known to have the size effect and the scatter in the length scale of microns by the numbers of intensive investigation by experiments and simulations. So, the consideration of the microstructure is essential to cover these length scale effects. The lattice based stochastic model for the microstructure evolution is used to simulate the actual microstructure, and the fast and reliable algorithm is described in this paper. The kinetics parameters, which are the key parameters for the microstructure evolution based on the nucleation and growth mechanism, are extracted from the given micrograph of a polycrystalline material by an inverse method. And the method is verified by the comparison of the quantitative measures, the number of grains and the grain size distribution, for the actual and simulated microstructures. Finite element mesh is then generated on this lattice based microstructure by the developed code. And the statistical finite element analysis is accomplished for selected microstructure.

• Journal of Korean Society of Steel Construction
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• v.16 no.6 s.73
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• pp.819-832
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• 2004

This study describes an efficient and facile method for configuration optimum design of structures. One of the ways to achieve numerical shape representation and the selection of design variables is using the design element concept. Using this technique, the number of design variables could be drastically reduced. Isoparametric mapping was utilized to automatically generate the finite element mesh during the optimization process, and this made it possible to easily calculate the derivatives of the coordinates of generated finite element nodes w.r.t. the design variables. For the structural analysis, finite element analysis was adopted in the optimization procedure, and two different techniques(the deterministic method, a modified method of feasible direction; and the stochastic method, a genetic algorithms) were applied to obtain the minimum volumes and section areas for an efficient configuration optimization procedure. Futhermore, spline interpolation was introduced to present a realistic optimum configuration that meet the manufacturing requirements. According to the results of several numerical examples(steel structures), the two techniques suggested in this study simplified the process of configuration optimum design of structures, and yielded improved objective function values with a robust convergence rate. This study's applicability and capability have therefore been demonstrated.

• Economic and Environmental Geology
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• v.28 no.5
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• pp.503-512
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• 1995

Groundwater flow in fracture networks is simulated using a discrete fracture (DF) model which assume that groundwater flows only through the fracture network. This assumption is available if the permeability of rock matrix is very low. It is almost impossible to describe fracture networks perfectly, so a stochastic approach is used. The stochastic approach assumes that the characteristic parameters in fracture network have special distribution patterns. The stochastic model generates fracture networks with some characteristic parameters. The finite element method is used to compute fracture flows. One-dimensional line element is the element type of the finite elements. The simulation results are shown by dominant flow paths in the fracture network. The dominant flow path can be found from the simulated groundwater flow field. The model developed in this study provides the tool to estimate the influences of characteristic parameters on groundwater flow in fracture networks. The influences of some characteristic parameters on the frcture flow are estimated by the Monte Carlo simulation based on 30 realizations.

• Coupled systems mechanics
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• v.11 no.2
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• pp.167-198
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• 2022

In this paper we deal with classical instability problems of heterogeneous Euler beam under conservative loading. It is chosen as the model problem to systematically present several possible solution methods from simplest deterministic to more complex stochastic approach, both of which that can handle more complex engineering problems. We first present classical analytic solution along with rigorous definition of the classical Euler buckling problem starting from homogeneous beam with either simplified linearized theory or the most general geometrically exact beam theory. We then present the numerical solution to this problem by using reduced model constructed by discrete approximation based upon the weak form of the instability problem featuring von Karman (virtual) strain combined with the finite element method. We explain how such numerical approach can easily be adapted to solving instability problems much more complex than classical Euler's beam and in particular for heterogeneous beam, where analytic solution is not readily available. We finally present the stochastic approach making use of the Duffing oscillator, as the corresponding reduced model for heterogeneous Euler's beam within the dynamics framework. We show that such an approach allows computing probability density function quantifying all possible solutions to this instability problem. We conclude that increased computational cost of the stochastic framework is more than compensated by its ability to take into account beam material heterogeneities described in terms of fast oscillating stochastic process, which is typical of time evolution of internal variables describing plasticity and damage.

• Structural Engineering and Mechanics
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• v.20 no.3
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• pp.293-312
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• 2005

In this paper, free vibration of rotating beam with random properties is studied. The cross-sectional area, elasticity modulus, moment of inertia, shear modulus and density are modeled as random fields and the rotational speed as a random variable. To study uncertainty, stochastic finite element method based on second order perturbation method is applied. To discretize random fields, the three methods of midpoint, interpolation and local average are applied and compared. The effects of rotational speed, setting angle, random property variances, discretization scheme, number of elements, correlation of random fields, correlation function form and correlation length on "Coefficient of Variation" (C.O.V.) of first mode eigenvalue are investigated completely. To determine the significant random properties on the variation of first mode eigenvalue the sensitivity analysis is performed. The results are studied for both Timoshenko and Bernoulli-Euler rotating beam. It is shown that the C.O.V. of first mode eigenvalue of Timoshenko and Bernoulli-Euler rotating beams are approximately identical. Also, compared to uncorrelated random fields, the correlated case has larger C.O.V. value. Another important result is, where correlation length is small, the convergence rate is lower and more number of elements are necessary for convergence of final response.

• Earthquakes and Structures
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• v.15 no.3
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• pp.335-350
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• 2018

This paper presents numerical modelling, modal testing, finite element model updating, linear and nonlinear earthquake behavior of a reinforced concrete building model. A 1/2 geometrically scale, two-storey, reinforced concrete frame model with raft base were constructed, tested and analyzed. Modal testing on the model using ambient vibrations is performed to illustrate the dynamic characteristics experimentally. Finite element model of the structure is developed by ANSYS software and dynamic characteristics such as natural frequencies, mode shapes and damping ratios are calculated numerically. The enhanced frequency domain decomposition method and the stochastic subspace identification method are used for identifying dynamic characteristics experimentally and such values are used to update the finite element models. Different parameters of the model are calibrated using manual tuning process to minimize the differences between the numerically calculated and experimentally measured dynamic characteristics. The maximum difference between the measured and numerically calculated frequencies is reduced from 28.47% to 4.75% with the model updating. To determine the effects of the finite element model updating on the earthquake behavior, linear and nonlinear earthquake analyses are performed using 1992 Erzincan earthquake record, before and after model updating. After model updating, the maximum differences in the displacements and stresses were obtained as 29% and 25% for the linear earthquake analysis and 28% and 47% for the nonlinear earthquake analysis compared with that obtained from initial earthquake results before model updating. These differences state that finite element model updating provides a significant influence on linear and especially nonlinear earthquake behavior of buildings.

• Tunnel and Underground Space
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• v.13 no.5
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• pp.397-402
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• 2003

Generally it is likely that rock mass properties are expressed not by a mean value but by values with variation due to its characteristic uncertainty. This characteristic is one of the most important parts for the design of undergound structures, but yet to be fully examined. Stochastic finite element method (SFEM) is contrary to deterministic finite element method in its concept as the former has been developed in order to take the randomness of structural systems into account. Using SFEM, the response variability of structural system can be obtained and it leads probabilistic stability of structure to be analyzed. In this study, displacement response variability of circular opening with hydrostatic stress field are analyzed in terms of rock mass properties having a certain mean and a standard deviation using the SFEM. The analyzed response variability shows that the necessity of probabilistic stability analysis of underground structures using reliable mean value and standard deviation of deformation modulus.

• Journal of the Korean Society of Fisheries and Ocean Technology
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• v.34 no.3
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• pp.328-338
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• 1998

It is main objective of this approach to present a method to analyse stochastic design sensitivity for problems of structural dynamics with randomness in design parameters. A combination of the adjoint variable approach and the second oder perturbation method is used in the finite element approach. An alternative form of the constant functional that holds for all times is introduced to consider the time response of dynamic sensitivity. The terminal problem of the adjoint system is solved using equivalent homogeneous equations excited by initial velocities. The numerical procedures are shown to be much more efficient when based on the fold superposition method : the generalized co-ordinates are normalized and the correlated random variables are transformed to uncorrelated variables, where as the secularities are eliminated by the fast Fourier transform of complex valued sequences. Numerical algorithms have been worked out and proved to be accurate and efficient : they codes whose element derivative matrices can be explicitly generated. The numerical results of two cases - 2-dimensional portal frame and 3/4-cylindrical shell structure - for the deterministic and stochastic sensitivity analysis illustrates in this paper.

• Smart Structures and Systems
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• v.10 no.2
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• pp.131-154
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• 2012

In this paper, it is aimed to determine the seismic behaviour of highway bridges by nondestructive testing using ambient vibration measurements. Eynel Highway Bridge which has arch type structural system with a total length of 216 m and located in the Ayvaclk county of Samsun, Turkey is selected as an application. The bridge connects the villages which are separated with Suat U$\breve{g}$urlu Dam Lake. A three dimensional finite element model is first established for a highway bridge using project drawings and an analytical modal analysis is then performed to generate natural frequencies and mode shapes in the three orthogonal directions. The ambient vibration measurements are carried out on the bridge deck under natural excitation such as traffic, human walking and wind loads using Operational Modal Analysis. Sensitive seismic accelerometers are used to collect signals obtained from the experimental tests. To obtain experimental dynamic characteristics, two output-only system identification techniques are employed namely, Enhanced Frequency Domain Decomposition technique in the frequency domain and Stochastic Subspace Identification technique in time domain. Analytical and experimental dynamic characteristic are compared with each other and finite element model of the bridge is updated by changing of boundary conditions to reduce the differences between the results. It is demonstrated that the ambient vibration measurements are enough to identify the most significant modes of highway bridges. After finite element model updating, maximum differences between the natural frequencies are reduced averagely from 23% to 3%. The updated finite element model reflects the dynamic characteristics of the bridge better, and it can be used to predict the dynamic response under complex external forces. It is also helpful for further damage identification and health condition monitoring. Analytical model of the bridge before and after model updating is analyzed using 1992 Erzincan earthquake record to determine the seismic behaviour. It can be seen from the analysis results that displacements increase by the height of bridge columns and along to middle point of the deck and main arches. Bending moments have an increasing trend along to first and last 50 m and have a decreasing trend long to the middle of the main arches.