• Structural Engineering and Mechanics
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• v.28 no.2
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• pp.129-152
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• 2008

This paper considers the solution of the stochastic differential equations (SDEs) with random operator and/or random excitation using the spectral SFEM. The random system parameters (involved in the operator) and the random excitations are modeled as second order stochastic processes defined only by their means and covariance functions. All random fields dealt with in this paper are continuous and do not have known explicit forms dependent on the spatial dimension. This fact makes the usage of the finite element (FE) analysis be difficult. Relying on the spectral properties of the covariance function, the Karhunen-Loeve expansion is used to represent these processes to overcome this difficulty. Then, a spectral approximation for the stochastic response (solution) of the SDE is obtained based on the implementation of the concept of generalized inverse defined by the Neumann expansion. This leads to an explicit expression for the solution process as a multivariate polynomial functional of a set of uncorrelated random variables that enables us to compute the statistical moments of the solution vector. To check the validity of this method, two applications are introduced which are, randomly loaded simply supported reinforced concrete beam and reinforced concrete cantilever beam with random bending rigidity. Finally, a more general application, randomly loaded simply supported reinforced concrete beam with random bending rigidity, is presented to illustrate the method.

• Interaction and multiscale mechanics
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• v.4 no.1
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• pp.49-64
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• 2011

A methodology for jointed rock mass characterization starts with a research based on geological data and tests in order to define the geotechnical models used to support the decision about location, orientation and shape of cavities. Afterwards a more detailed characterization of the rock mass is performed allowing the update of the geomechanical parameters defined in the previous stage. The observed results can be also used to re-evaluate the geotechnical model using inverse methodologies. Cases of large underground structures modeling are presented. The first case concerns the modeling of cavities in volcanic formations. Then, an application to a large station from the Metro do Porto project developed in heterogeneous granite formations is also presented. Finally, the last case concerns the modeling of large cavities for a hydroelectric powerhouse complex. The finite element method and finite difference method software used is acquired from Rocscience and ITASCA, respectively.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.1 s.173
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• pp.190-195
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• 2000

It has been established that a crack has an important effect on the dynamic behavior of a structure. This effect depends mainly on the location and depth of the crack. To identify the location and depth of a crack in a structure. Nikolakopoulos et. al. used the intersection point of the superposed contours that correspond to the eigenfrequency caused by the crack presence. However the intersecting point of the superposed contours is not only difficult to find but also incorrect to calculate. A method is presented in this paper which uses optimization technique for the location and depth of the crack. The basic idea is to find parameters which use the structural eigenfrequencies on crack depth and location and optimization algorithm. With finite element model of the structure to calculate eigenfrequencies, it is possible to formulate the inverse problem in optimization format. Method of optimization is augmented lagrange multiplier method and search direction method is BFGS variable metric method and one dimensional search method is polynomial interpolation.

• Geomechanics and Engineering
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• v.13 no.5
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• pp.775-791
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• 2017

Surface wave techniques are widely used as non-invasive method for geotechnical site characterization. Field surface wave data are collected and analyzed using different processing techniques to generate the dispersion curves, which are further used to extract the shear wave velocity profile by inverse problem solution. Characteristics of a dispersion curve depend on the subsurface layering information of a vertically heterogeneous medium. Sometimes soft layer can be found between two stiff layers in the vertically heterogeneous media, and it can affect the wave propagation dramatically. Now most of the surface wave techniques use the fundamental mode Rayleigh wave propagation during the inversion, but this may not be the actual scenario when a soft layer is present in a vertically layered medium. This paper presents a detailed and comprehensive study using finite element method to examine the effect of soft layers which sometimes get trapped between two high velocity layers. Determination of the presence of a soft layer is quite important for proper mechanical characterization of a soil deposit. Present analysis shows that the thickness and position of the trapped soft layer highly influence the dispersion of Rayleigh waves while the higher modes also contribute in the resulting wave propagation.

• Honam Mathematical Journal
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• v.37 no.3
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• pp.299-315
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• 2015

In this paper, we study the first-order system least-squares (FOSLS) spectral method for parabolic partial differential equations. There were lots of least-squares approaches to solve elliptic partial differential equations using finite element approximation. Also, some approaches using spectral methods have been studied in recent. In order to solve the parabolic partial differential equations in parallel, we consider a parallel numerical method based on a hybrid method of the frequency-domain method and first-order system least-squares method. First, we transform the parabolic problem in the space-time domain to the elliptic problems in the space-frequency domain. Second, we solve each elliptic problem in parallel for some frequencies using the first-order system least-squares method. And then we take the discrete inverse Fourier transforms in order to obtain the approximate solution in the space-time domain. We will introduce such a hybrid method and then present a numerical experiment.

• Transactions of the Korean Society of Automotive Engineers
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• v.12 no.1
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• pp.106-113
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• 2004

Most of mechanical structures are composed of many substructures connected to one another by various types of mechanical joints. In automotive engineering, it is important to study these connected structures under various dynamic forces for the evaluations of fatigue life and stress concentration exactly. In this study, the dynamic response of vehicle structure to external forces is classified an inverse problem involving strains from the experiment and the analysis. The practical dynamic forces are determined by the combination of the analytical and experimental method with analyzed strain by quasi-static finite element analysis under unit force and with measured strain by a strain gage under driving load, respectively. In a stressed body, inter-molecular chemical bonds are failed beyond the certain magnitude. The failure of molecular structure in material is considered as a time process of which rate is determined by mechanical stress. That is, the failure of inter-molecular chemical bonds is the fatigue lift of material. This kinetic concept is expressed as lethargy coefficient. And S-N curve is obtained with the lethargy coefficient from quasi-static tensile test. Equivalent practical dynamic force is obtained from the identification of practical dynamic force for one loading point. Using the practical dynamic force and S-N curve, fatigue life of a window pillar is analyzed with FEM under the identified force by the procedure of above mentioned.

• Structural Engineering and Mechanics
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• v.32 no.5
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• pp.667-683
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• 2009

FE model-based dynamic analysis has been widely used to predict the dynamic characteristics of civil structures. In a physical point of view, an FE model is unavoidably different from the actual structure as being formulated based on extremely idealized engineering drawings and design data. The conventional model updating methods such as direct method and sensitivity-based parameter estimation are not flexible for model updating of complex and large structures. Thus, it is needed to develop a model updating method applicable to complex structures without restriction. The main objective of this paper is to present the model updating method based on the hybrid genetic algorithm (HGA) by combining the genetic algorithm as global optimization method and modified Nelder-Mead's Simplex method as local optimization method. This FE model updating method using HGA does not need the derivation of derivative function related to parameters and without application of complicated inverse analysis methods. In order to allow its application on diversified and complex structures, a commercial FEA tool is adopted to exploit previously developed element library and analysis algorithms. Moreover, an output-level objective function making use of measurement and analytical results is also presented to update simultaneously the stiffness and mass of the analysis model. The numerical examples demonstrated that the proposed method based on HGA is effective for the updating of the FE model of bridge structures.

• Composites Research
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• v.28 no.5
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• pp.277-284
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• 2015

This paper presents a method to detect the fiber property variation of laminated GFRP plates from natural frequency response data. The combined finite element analysis using ABAQUS and the inverse algorithm described in this paper may allow us not only to detect the deteriorated elements from the mirco-mechanical point of view but also to find their numbers, locations, and the extent of damage. To solve the inverse problem using the combined method, this study uses several natural frequencies instead of mode shapes in a structure as the measured data. Several numerical results show that the proposed system is computationally efficient in identifying fiber stiffness degradation for complex structures such as composites with various layup sequences.

• Transactions of the Korean Society of Automotive Engineers
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• v.2 no.1
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• pp.116-127
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• 1994

A method using the linear matrix algebra is developed in order to determine unknown external forces in linear structural analyses. The method defines a matrix which represents the linearity of the vibrational analysis for a structural system. The unknown external forces are determined by the operations of the matrix. The method is applied to find an engine motion in an automobile system. For a simulation process, an exhaust system is modeled and analyzed by the finite element method. The validity of the simulation is verified by comparing with the experimental results the free vibration. Also, an experiment on the forced vibration is performed to determine the damping ratio of the exhaust sysetm. Estimated model parameters(natural frequency, mode shape) are in accord with the experimental results. Because the method merely repeats the transpose and inverse operations of a matrix, the solution is extremely easy and simple. Moreover, it is more accurate than the existing methods in that there is no artificial assumptions in the calculation processes. Therefore, the method is found to be reliable for the analysis of the exhaust system considering the characteristics of vibrations. Although the suggested method is tested by only the exhaust system here, it can be applied to general structures.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2008.10a
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• pp.259-262
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• 2008

This paper introduces a simplified method to consider forming effects in a car crash analysis. Representative value was used to consider forming effects simply. Four representative values, which are the mean value of thicknesses and effective plastic strains at nodes, the median of thicknesses and effective plastic strains at nodes, were evaluated. A crash analysis of a front side member shows that analysis results from the suggested methods are similar to those from the conventional method to consider forming effects. Use of the mean effective plastic strain shows the best results. A car crash analysis for a ULSAB/AVC model under the condition of US SINCAP were carried out to demonstrate the validity of the suggested method. Analysis results show that the error of suggested method is less than 1.5%.