• Smart Structures and Systems
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• v.30 no.6
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• pp.673-686
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• 2022

Deep learning algorithms for Structural Health Monitoring (SHM) have been extracting the interest of researchers and engineers. These algorithms commonly used loss functions and evaluation indices like the mean square error (MSE) which were not originally designed for SHM problems. An updated loss function which was specifically constructed for deep-learning-based structural damage detection problems has been proposed in this study. By tuning the coefficients of the loss function, the weights for damage localization and quantification can be adapted to the real situation and the deep learning network can avoid unnecessary iterations on damage localization and focus on the damage severity identification. To prove efficiency of the proposed method, structural damage detection using convolutional neural networks (CNNs) was conducted on a truss bridge model. Results showed that the validation curve with the updated loss function converged faster than the traditional MSE. Data augmentation was conducted to improve the anti-noise ability of the proposed method. For reducing the training time, the normalized modal strain energy change (NMSEC) was extracted, and the principal component analysis (PCA) was adopted for dimension reduction. The results showed that the training time was reduced by 90% and the damage identification accuracy could also have a slight increase. Furthermore, the effect of different modes and elements on the training dataset was also analyzed. The proposed method could greatly improve the performance for structural damage detection on both the training time and detection accuracy.

• Journal of Theoretical and Applied Mechanics
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• v.1 no.1
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• pp.69-88
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• 1995

The paper attempts to estimate the incubation time of a cavity in the interface between a power law creep particle and an elastic matrix subjected to a uniaxial stress. Since the power law creep particle is time dependent, the stresses in the interface relax. Through previous stress analysis related to the present physical model, the relaxation time is defined by ${\alpha}$2 which satisfies the equation $\Gamma$0 ｜1+${\alpha}$2k｜m=1-${\alpha}$2 [19]. $\Gamma$0=2(1/√3)1+m($\sigma$$\infty$/2${\mu}$)m($\sigma$0/$\sigma$$\infty$tm) where $\sigma$$\infty$ is an applied stress, ${\mu}$ is a shear modulus of a matrix, $\sigma$$\infty$ is a material constant of a power law particle, $\sigma$=$\sigma$0 $\varepsilon$ and t elapsed time. the volume free energy associated with Helmholtz free energy includes strain energies associated with Helmholtz free energy includes strain energies caused by applied stress anddislocations piled up in interface (DPI). The energy due to DPI is found by modifying the results of Dundurs and Mura[20]. The volume free energies caused by both applied stress and DPI are a function of the cavity size(${\gamma}$) and elapsed time(t) and arise from stress relaxation in the interface. Critical radius ${\gamma}$ and incubation time t to maximize Helmholtz free energy is found in present analysis. Also, kinetics of cavity fourmation are investigated using the results obtained by Riede[16]. The incubation time is defied in the analysis as the time required to satisfy both the thermodynamic and kinetic conditions. Through the analysis it is found that [1] strain energy caused by the applied stress does not contribute significantly to the thermodynamic and kinetic conditions of a cavity formation, 2) in order to satisfy both thermodynamic and kinetic conditions, critical radius ${\gamma}$ decreases or holds constant with increase of time until the kinetic condition(eq.40) is satisfied. Therefore the cavity may not grow right after it is formed, as postulated by Harris[11], and Ishida and Mclean[12], 3) the effects of strain rate exponent (m), material constant $\sigma$0, volume fraction of the particle to matrix(f) and particle size on the incubation time are estimated using material constants of the copper as matrix.

• Transactions of the Korean Society of Mechanical Engineers
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• v.9 no.1
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• pp.31-39
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• 1985

Using the tensor elastic Green functions an exact integral equation is formulated for two anisotropic precipitates embedded in an infinite anisotropic matrix; the matrix is subjected to an applied strain field or the precipitates undergo a stress-free transformation strain. This equation is reduced to an infinite system of algebraic equations by expanding the strains in Taylor series about the two points within each precipitate, and an approximation of the strain distributions within the two spherical precipitates is obtained by truncating the higher order terms. Since the present method requires no symmetry conditio between the two shperical precipitates, it is possible to obtain the strain distribution within the precipitates when the elastic constants and/or the sizes of the precipitates are different each other. The strains are expanded about arbitrary points, giving more accurate distributions of the strains than those presented elsewhere. The present method can be directly estended to the case of more than two spherical precipitates.

• Smart Structures and Systems
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• v.8 no.5
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• pp.433-447
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• 2011

The present paper addresses the nonlinear response of a FG square plate with two smart layers as a sensor and actuator under pressure. Geometric nonlinearity was considered in the strain-displacement relation based on the Von-Karman assumption. All the mechanical and electrical properties except Poisson's ratio can vary continuously along the thickness of the plate based on a power function. Electric potential was assumed as a quadratic function along the thickness direction and trigonometric function along the planar coordinate. By evaluating the mechanical and electrical energy, the total energy equation can be minimized with respect to amplitude of displacements and electrical potential. The effect of non homogenous index was investigated on the responses of the system. Obtained results indicate that with increasing the non homogenous index, the displacements and electric potential tend to an asymptotic value. Displacements and electric potential can be presented in terms of planar coordinate system. A linear analysis was employed and then the achieved results are compared with those results that are obtained using the nonlinear analysis. The effect of the geometric nonlinearity is investigated by using the comparison between the linear and nonlinear results. Displacement-load and potential-load curves verified the necessity of a nonlinear analysis rather than a linear analysis. Improvement of the previous results (by the linear analysis) through employing a nonlinear analysis can be presented as novelty of this study.

• Journal of the Korea Concrete Institute
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• v.15 no.6
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• pp.802-810
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• 2003

In this paper, the modified singular fracture process zone (S-FPZ) model is proposed to consider variation of a fracture criterion for continuous crack propagation in concrete. The fracture properties of the proposed fracture model are strain energy release rate at a micro-crack tip and crack closure stress (CCS) versus crack opening displacement (COD) relationship in the FPZ. The proposed model can simulate the estimated fracture energy of experimental results. The analysis results of the experimental data shows that specimen geometry and loading condition did not affect the CCS-COD relation. But the strain energy release rate is a function of not only specimen geometry but also crack extension. Until 25 mm crack extension, the strain energy release rate is a constant minimum value, and then it increased linearly to the maximum value. The maximum fracture criterion occurred at the peak load for an large size specimen. The fracture criterion remains the maximum value after the peak load. The variation of the fracture criterion is caused by micro-cracking and micro-crack localizing. The fracture criterion of strain energy release rate can simply be the size effect of concrete fracture, and it can be used to quantify the micro-tracking and micro-crack localizing behaviors of concrete.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.21 no.11
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• pp.1844-1851
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• 1997

Displacement fields and interface stresses are obtained by modifying the potential energy functional with a penalty function which enforces the continuity of stresses at the interface of two-materials. Based on the displacement field and the interface stresses, a new methodology to generate a continuous stress field over the entire domain including the interface of the dissimilar materials has been proposed by combining the L$^{2}$ projection method of stress-smoothing and the Loubignac's iterative method of improving the displacement field. Stress analysis was carried out on two examples which are made of highly dissimilar materials. As a result of the analysis, it is found that the proposed method provides improved continuity of the stress field over the entire domain as well as predicting accurate nodal stresses at the interface. In contrast, the conventional displacement-based finite element method provides significant stress discontinuties at the interfaces. In addition, it was found that the total strain energy evaluated from the improved continuous stress field converge to the exact value as increasing the number of iterations in the proposed method.

• Journal of Korean Society of Steel Construction
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• v.16 no.3 s.70
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• pp.295-303
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• 2004

In this paper, an improved four-node Reissner-Mindlin plate-bending element with enhanced assumed strain field is presented for the analysis of isotropic and laminated composite plates. To avoid the shear locking and spurious zero energy modes, the transverse shear behavior is improved by the addition of a new enhanced shear strain based on the incompatible displacement mode approach and bubble function. The "standard" enhanced strain fields (Andelfinger and Ramm, 1993) are also employed to improve the in-plane behaviors of the plate elements. The four-node quadrilateral element derived using the first-order shear deformation theory is designated as "14EASP". Several applications are investigated to assess the features and the performances of the proposed element. The results are compared with other finite element solutions and analytical solutions. Numerical examples show that the element is stable, invariant, passes the patch test, and yields good results especially in highly distorted regimes.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2003.04a
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• pp.227-234
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• 2003

In this study, an equivalent continuum model for single wall carbon nanotube is proposed. The model links interatomic potentials and atom structure of a materials to a constitutive model on the continuum level. The Young's modulus and shear modulus were predicted by the model. The predictions were in good agreement with the prior experimental results available in the literatures. Also, the strain energy of the carbon nanotube was predicted as a function of the radius of the carbon nanotube.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2001.10a
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• pp.311-318
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• 2001

The R-adaptivity method to the shell surface which is presented by the NURBS is proposed. The r-adaptiivty method , given by Liao and Anderson〔2〕, aggregate the grid in the region where is relatively high weight function without any grid-tanggling. In numerical examples, the strain energy error estimate of shell in the whole domain can be reduced effectively by using applied r- adaptivity method mesh.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2001.04a
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• pp.42-49
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• 2001

In this paper the efficient finite element for stress analysis of plane stress/strain problems is proposed. This element is achieved by adding the bubble-mode function to 8-node element. The stiffness matrix of the element is calculated by using modified numerical integration order to avoid spurious zero energy mode. In order to demonstrate the performance of this element numerical tests for various verification problems are carried out. The results of numerical tests show accuracy and reliability of the element presented in this paper.