• Journal of the Korean Society for Precision Engineering
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• v.20 no.7
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• pp.208-216
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• 2003

In this paper, a two-dimensional electroelastic analysis is performed on a piezoelectric material with an open crack. The approach of Lekhnitskii's complex potential functions is used in the derivation and Bueckner's weight function theory is extended to piezoelectric materials. The stress intensity factors and the electric displacement intensity factor are calculated by the weight function theory.

• Earthquakes and Structures
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• v.22 no.6
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• pp.571-584
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• 2022

The residual displacement ratio (RDRs) response spectra have been generally used as an important means to evaluate the post-earthquake repairability, and the ratios of residual to maximum inelastic displacement are considered to be more appropriate for development of the spectra. This methodology, however, assumes that the expected residual displacement can be computed as the product of the RDRs and maximum inelastic displacement, without considering the correlation between these two variables, which inevitably introduces potential systematic error. For providing an adequately accurate estimate of residual displacement, while accounting for the collapse resistance performance prior to the repairability evaluation, a probability-based procedure to estimate the residual displacement demands using the nonlinear static analysis (NSA) is developed for single-degree-of-freedom (SDOF) systems. To this end, the energy-based equivalent damping ratio used for NSA is revised to obtain the maximum displacement coincident with the nonlinear time history analysis (NTHA) results in the mean sense. Then, the possible systematic error resulted from RDRs spectra methodology is examined based on the NTHA results of SDOF systems. Finally, the statistical relation between the residual displacement and the NSA-based maximum displacement is established. The results indicate that the energy-based equivalent damping ratio will underestimate the damping for short period ranges, and overestimate the damping for longer period ranges. The RDRs spectra methodology generally leads to the results being non-conservative, depending on post-yield stiffness. The proposed approach emphasizes that the repairability evaluation should be based on the premise of no collapse, which matches with the current performance-based seismic assessment procedure.

• Smart Structures and Systems
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• v.8 no.2
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• pp.173-190
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• 2011

As a practical and effective seismic resisting technology, the base isolation system has seen extensive applications in buildings and bridges. However, a few problems associated with conventional lead-rubber bearings have been identified after historical strong earthquakes, e.g., excessive permanent deformations of bearings and potential unseating of bridge decks. Recently the applications of shape memory alloys (SMA) have received growing interest in the area of seismic response mitigation. As a result, a variety of SMA-based base isolators have been developed. These novel isolators often lead to minimal permanent deformations due to the self-centering feature of SMA materials. However, a rational design approach is still missing because of the fact that conventional design method cannot be directly applied to these novel devices. In light of this limitation, a displacement-based design approach for highway bridges with SMA isolators is proposed in this paper. Nonlinear response spectra, derived from typical hysteretic models for SMA, are employed in the design procedure. SMA isolators and bridge piers are designed according to the prescribed performance objectives. A prototype reinforced concrete (RC) highway bridge is designed using the proposed design approach. Nonlinear dynamic analyses for different seismic intensity levels are carried out using a computer program called "OpenSees". The efficacy of the displacement-based design approach is validated by numerical simulations. Results indicate that a properly designed RC highway bridge with novel SMA isolators may achieve minor damage and minimal residual deformations under frequent and rare earthquakes. Nonlinear static analysis is also carried out to investigate the failure mechanism and the self-centering ability of the designed highway bridge.

• Structural Engineering and Mechanics
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• v.62 no.6
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• pp.749-758
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• 2017

In structural mechanics, traditional analyses methods usually employ matrix operations for obtaining displacement and internal forces of the structure under the external effects, such as distributed loads, earthquake or wind excitations, and temperature changing inter alia. These matrices are derived from the well-known principle of mechanics called minimum potential energy. According to this principle, a system can be in the equilibrium state only in case when the total potential energy of system is minimum. A close examination of the expression of the well-known equilibrium condition for linear problems, $P=K{\Delta}$, where P is the load vector, K is the stiffness matrix and ${\Delta}$ is the displacement vector, it is seen that, basically this principle searches the displacement set (or deformed shape) for a system that minimizes the total potential energy of it. Instead of using mathematical operations used in the conventional methods, with a different formulation, meta-heuristic algorithms can also be used for solving this minimization problem by defining total potential energy as objective function and displacements as design variables. Based on this idea the technique called Total Potential Optimization using Meta-heuristic Algorithms (TPO/MA) is proposed. The method has been successfully applied for linear and non-linear analyses of trusses and truss-like structures, and the results have shown that the approach is much more successful than conventional methods, especially for analyses of non-linear systems. In this study, the application of TPO/MA, with Harmony Search as the selected meta-heuristic algorithm, to cables net system is presented. The results have shown that the method is robust, powerful and accurate.

• Structural Engineering and Mechanics
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• v.57 no.3
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• pp.529-541
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• 2016

Under the interaction between dam body, dam foundation and external environment, the dam structural behavior presents the time-varying nonlinear characteristics. According to the prototypical observations, the correct identification on above nonlinear characteristics is very important for dam safety control. It is difficult to implement the description, analysis and diagnosis for dam structural behavior by use of any linear method. Based on the rescaled range analysis approach, the algorithm is proposed to identify and extract the fractal feature on observed dam structural behavior. The displacement behavior of one actual dam is taken as an example. The fractal long-range correlation for observed displacement behavior is analyzed and revealed. The feasibility and validity of the proposed method is verified. It is indicated that the mechanism evidence can be provided for the prediction and diagnosis of dam structural behavior by using the fractal identification method. The proposed approach has a high potential for other similar applications.

• Structural Engineering and Mechanics
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• v.59 no.1
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• pp.101-122
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• 2016

Elasticity solutions for bi-directional functionally graded beams subjected to arbitrary lateral loads are conducted, with emphasis on the end effects. The material is considered macroscopically isotropic, with Young's modulus varying exponentially in both axial and thickness directions, while Poisson's ratio remaining constant. In order to obtain an exact analysis of stress and displacement fields, the symplectic analysis based on Hamiltonian state space approach is employed. The capability of the symplectic framework for exact analysis of bi-directional functionally graded beams has been validated by comparing numerical results with corresponding ones in open literature. Numerical results are provided to demonstrate the influences of the material gradations on localized stress distributions. Thus, the material properties of the bi-directional functionally graded beam can be tailored for the potential practical purpose by choosing suitable graded indices.

• Structural Engineering and Mechanics
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• v.75 no.6
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• pp.747-769
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• 2020

This paper provides a semi-analytical approach to investigate the variations of 3D displacement components, electric potential, stresses, electric displacements and transverse vibration frequencies in laminated piezoelectric composite plates based on the scaled boundary finite element method (SBFEM) and the precise integration algorithm (PIA). The proposed approach can analyze the static and dynamic responses of multilayered piezoelectric plates with any number of laminae, various geometrical shapes, boundary conditions, thickness-to-length ratios and stacking sequences. Only a longitudinal surface of the plate is discretized into 2D elements, which helps to improve the computational efficiency. Comparing with plate theories and other numerical methods, only three displacement components and the electric potential are set as the basic unknown variables and can be represented analytically through the transverse direction. The whole derivation is built upon the three dimensional key equations of elasticity for the piezoelectric materials and no assumptions on the plate kinematics have been taken. By virtue of the equilibrium equations, the constitutive relations and the introduced set of scaled boundary coordinates, three-dimensional governing partial differential equations are converted into the second order ordinary differential matrix equation. Furthermore, aided by the introduced internal nodal force, a first order ordinary differential equation is obtained with its general solution in the form of a matrix exponent. To further improve the accuracy of the matrix exponent in the SBFEM, the PIA is employed to make sure any desired accuracy of the mechanical and electric variables. By virtue of the kinetic energy technique, the global mass matrix of the composite plates constituted by piezoelectric laminae is constructed for the first time based on the SBFEM. Finally, comparisons with the exact solutions and available results are made to confirm the accuracy and effectiveness of the developed methodology. What's more, the effect of boundary conditions, thickness-to-length ratios and stacking sequences of laminae on the distributions of natural frequencies, mechanical and electric fields in laminated piezoelectric composite plates is evaluated.

• Advances in biomechanics and applications
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• v.1 no.1
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• pp.1-14
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• 2014

In this paper, a simple and accurate finite element model coupled to quasi-brittle damage law able to describe the multiple cracks initiation and their progressive propagation is developed in order to predict the complete force-displacement curve and the fracture pattern of human proximal femur under quasi-static load. The motivation of this work was to propose a simple and practical FE model with a good compromise between complexity and accuracy of the simulation considering a limited number of model parameters that can predict proximal femur fracture more accurately and physically than the fracture criteria based models. Different damage laws for cortical and trabecular bone are proposed based on experimental results to describe the inelastic damage accumulation under the excessive load. When the damage parameter reaches its critical value inside an element of the mesh, its stiffness matrix is set to zero leading to the redistribution of the stress state in the vicinity of the fractured zone (crack initiation). Once a crack is initiated, the propagation direction is simulated by the propagation of the broken elements of the mesh. To illustrate the potential of the proposed approach, the left femur of a male (age 61) previously investigated by Keyak and Falkinstein, 2003 (Model B: male, age 61) was simulated till complete fracture under one-legged stance quasi-static load. The proposed finite element model leads to more realistic and precise results concerning the shape of the force-displacement curve (yielding and fracturing) and the profile of the fractured edge.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.4
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• pp.981-989
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• 1995

A new weight function approach to determine SIF(stress intensity factor) using single-layer potential has been presented. The crack surface displacement field was represented by one boundary integral term whose kernel was modified from Kelvin's fundamental solution. The proposed method enables the calculation of SIF using only one SIF solution without any modification for the crack geometries symmetric in two-dimensional plane such as a center crack in a plate with or without an internal hole, double edge cracks, circumferential crack or radial cracks in a pipe. The application procedure to those crack problems is very simple and straightforward with only one SIF solution. The necessary information in the analysis is two reference SIFs. The analysis results using present closed-form solution were in good agreement with those of the literature.

• Smart Structures and Systems
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• v.1 no.3
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• pp.309-324
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• 2005

This paper presents an efficient and accurate coupled beam model for piezoelectric bimorphs based on improved first-order shear deformation theory (FSDT). The model combines the equivalent single layer approach for the mechanical displacements and a layerwise modeling for the electric potential. General electric field function is proposed to reasonably approximate the through-the-thickness distribution of the applied and induced electric potentials. Layerwise defined shear correction factor (k) accounting for nonlinear shear strain distribution is introduced into both the shear stress resultant and the electric displacement integration. Analytical solutions for free vibrations and forced response under electromechanical loads are obtained for the simply supported piezoelectric bimorphs with series or parallel arrangement, and the numerical results for various length-to-thickness ratios are compared with the exact two-dimensional piezoelasticity solution. Excellent predictions with low error estimates of local and global responses as well as the modal frequencies are observed.