• Smart Structures and Systems
• /
• v.13 no.4
• /
• pp.587-614
• /
• 2014

In recent years the interest in online monitoring of lightweight structures with ultrasonic guided waves is steadily growing. Especially the aircraft industry is a driving force in the development of structural health monitoring (SHM) systems. In order to optimally design SHM systems powerful and efficient numerical simulation tools to predict the behaviour of ultrasonic elastic waves in thin-walled structures are required. It has been shown that in real industrial applications, such as airplane wings or fuselages, conventional linear and quadratic pure displacement finite elements commonly used to model ultrasonic elastic waves quickly reach their limits. The required mesh density, to obtain good quality solutions, results in enormous computational costs when solving the wave propagation problem in the time domain. To resolve this problem different possibilities are available. Analytical methods and higher order finite element method approaches (HO-FEM), like p-FEM, spectral elements, spectral analysis and isogeometric analysis, are among them. Although analytical approaches offer fast and accurate results, they are limited to rather simple geometries. On the other hand, the application of higher order finite element schemes is a computationally demanding task. The drawbacks of both methods can be circumvented if regions of complex geometry are modelled using a HO-FEM approach while the response of the remaining structure is computed utilizing an analytical approach. The objective of the paper is to present an efficient method to couple different HO-FEM schemes with an analytical description of an undisturbed region. Using this hybrid formulation the numerical effort can be drastically reduced. The functionality of the proposed scheme is demonstrated by studying the propagation of ultrasonic guided waves in plates, excited by a piezoelectric patch actuator. The actuator is modelled utilizing higher order coupled field finite elements, whereas the homogenous, isotropic plate is described analytically. The results of this "semi-analytical" approach highlight the opportunities to reduce the numerical effort if closed-form solutions are partially available.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.21 no.12
• /
• pp.2121-2133
• /
• 1997

A finite element code is developed for 3-D self-contact problems, using continuum elements with a SRI(Selective Reduced Integration) scheme to prevent locking phenomenon by the incompressibility of rubber. Contact treatment is carried out in two ways : using the displacement constraints in case of rigid contact ; and imposing the same contact forces on two contact boundaries in case of self-contact. The finite element code developed is applied to the deformation analysis of C.V.joint boots which maintain lubrication conditions and protect the C.V.joint assembly from impact and dust. The boot accompanies large rotation depending on the rotation of the wheel axis and leading to the self-contact phenomena of the boot bellows. Since this contact phenomenon causes wear of the product and has great influence on the endurance life of the product, it is indispensable to carry out stress analysis of the rubber boots. In case of self-contact, various methods for determining contact forces have been suggested with an appropriate contact formulation. Especially, the types of penetration in self-contact are modularized to accelerate conputation with a contact algorithm.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.17 no.1
• /
• pp.90-100
• /
• 1993

A finite element formulation of vibration control of a laminated plate with piezoelectric sensor/ actuators is presented. Classical lamination theory with the induced strain actuation and Hamilton's principle are used to formulate the equations of motion of the system. The total charge developed on the sensor layer is calculated from the direct piezoelectric equation. The equations of motion and the total charge are discretized with 4 node, 12 degrees of freedom quadrilateral plate bending elements with one electrical degree of freedom. The mass and stiffness of the piezoelectric layer are introduced by treating them as another layer in laminated plate. Piezoelectric sensor/actuators are distributed, but discrete due to the geometry of electrodes. By defining an i.d. number of electrode for each element, modelling of electrodes with variable geometry can be achieved. The static response of a piezoelectric bimorph beam to electrical loading and sensor voltage to given displacement are calculated. For a laminated plate under the negative velocity feedback control, the direct time response by the Newmark-.betha. method and damped frequencies and modal damping ratios by modal state space analysis are derived.

• Tunnel and Underground Space
• /
• v.9 no.1
• /
• pp.1-11
• /
• 1999

A finite element code was developed to analyze coupled thermo-hydro-mechanical phenomena. This code is based on the finite element formulation provided by Noorishad et al. (1984) and Joint behavior was simulated Goodman's joint constitutive model. The developed code was applied for T-H-M coupling analysis for two kinds of shaft models, with a joint or without a joint respectively. For a model without a joint, temperature increased from the shaft wall to outward evidently. The radial displacement showed opposite directions of outward and inward at some distance from shaft wall. For a model with a joint, closure of joint was found due to thermal expansion. The temperature distribution along a joint showed relatively lower than that of rock matrix because of low thermal conductivity and high specific heat of water. And it could be concluded that effects of thermal flow to joint were more than that of hydraulic flow in a rock mass.

• Structural Engineering and Mechanics
• /
• v.53 no.6
• /
• pp.1215-1240
• /
• 2015

In this work, a novel simple first-order shear deformation plate theory based on neutral surface position is developed for bending and free vibration analysis of functionally graded plates and supported by either Winkler or Pasternak elastic foundations. By dividing the transverse displacement into bending and shear parts, the number of unknowns and governing equations of the present theory is reduced, and hence, makes it simple to use. The governing equations are derived by employing the Hamilton's principle and the physical neutral surface concept. There is no stretching-bending coupling effect in the neutral surface-based formulation, and consequently, the governing equations and boundary conditions of functionally graded plates based on neutral surface have the simple forms as those of isotropic plates. Numerical results of present theory are compared with results of the traditional first-order and the other higher-order theories reported in the literature. It can be concluded that the proposed theory is accurate and simple in solving the static bending and free vibration behaviors of functionally graded plates.

• Journal of the Computational Structural Engineering Institute of Korea
• /
• v.17 no.2
• /
• pp.183-192
• /
• 2004

New dynamic analysis procedures lot the vertically drilled sea water pile are suggested and demonstrated by the typical design Problem. Pile structure submerged in the sea water as well as forces by the ocean waves and tidal currents are modeled and formulated by finite element method. To obtain wave forces for the finite element equation, Airy's wave theory is tested and selected among others. Lateral lifting forces induced by the vortex shedding of current flow is simply based on the harmonic function with the Strouhal frequency and lifting coefficient. Natural frequencies and frequency responses for the pile are calculated by NASTRAN using the results of the formulation. Dynamic displacement and stress results obtained by these procedures are shown to be applicable to predict the dynamic behaviors of the ocean pile by the wave and lifting forces as a preliminary design analysis.

• Journal of the Computational Structural Engineering Institute of Korea
• /
• v.33 no.5
• /
• pp.279-286
• /
• 2020

In this study, we investigate the accuracy of higher order derivatives in the moving least square (MLS) difference method. An interpolation function is constructed by employing a Taylor series expansion via MLS approximation. The function is then applied to the mixed variational theorem in which the displacement and stress resultants are treated as independent variables. The higher order derivatives are evaluated by solving simply supported beams and cantilevers. The results are compared with the analytical solutions in terms of the order of polynomials, support size of the weighting function, and number of nodes. The accuracy of the higher order derivatives improves with the employment of the mean value theorem, especially for very high-order derivatives (e.g., above fourth-order derivatives), which are important in a classical asymptotic analysis.

• Bulletin of the Society of Naval Architects of Korea
• /
• v.27 no.1
• /
• pp.45-56
• /
• 1990

This study deals with the nonlinear strength analysis of laminated composite cylindrical shells to find the optimum structure of pressure vessel. By applying the F.E.M. using the 8-node degenerated Isoparametric shell element and Total Lagrangian formulation and being adopted Newton-Raphson method with incremental load as a solution scheme. the optimum structure is found from the viewpoint of minimum displacement. As a results of linear analysis on the 9 cases of laminated structure, $[50^{\circ}/-50^{\circ}]$ composition of the shell laminate give the minimum deflection. In case of the nonlinear analysis by applying Quadratic Failure Criteria on laminated combination $[{\theta}^{\circ}/-{\theta}^{\circ}]$, shell laminate structure of ${\theta}=50^{\circ}$ under external uniform pressure was founded as a optimum structure and ${\theta}=50^{\circ}$ for the case of external and axial loading combined.

• Journal of the Korean Geotechnical Society
• /
• v.15 no.3
• /
• pp.113-129
• /
• 1999

In this study, a total of 12 types of sequential model tests were conducted at the laboratory for small scale anchored walls. The sequential behavior for flexible wall embedded in sand was investigated by varying degrees of relative density of Joomoonjin sand and flexibility number of model wall. The model tests were carried out in a 1000mm width, 1500mm length, and 1000mm high steel box. Load cells, pressure cells, displacement transducer and dial gauges were used to measure the anchor forces, lateral wall deflections, lateral earth pressures and vertical displacements of ground surface, respectively. Limited model tests were performed to examine the parameters for soil-wall interaction model and the formulation of analytical method was revised in order to predict the behavior of anchored wall in sand. Based on the model tests and proposed analytical method, model simulations were performed and the predictions by the present approach were compared with measurements by the model tests and predictions by other commercial programs. It is shown that the prediction by the present approach simulates qualitatively well the general trend observed for model test.

• Smart Structures and Systems
• /
• v.25 no.6
• /
• pp.719-732
• /
• 2020

Real-time hybrid simulation (RTHS) which combines physical experiment with numerical simulation is an advanced method to investigate dynamic responses of structures subjected to earthquake excitation. The desired displacement computed from the numerical substructure is applied to the experimental substructure by a servo-hydraulic actuator in real time. However, the magnitude decay and phase delay resulted from the dynamics of the servo-hydraulic system affect the accuracy and stability of a RTHS. In this study, a robust stability analysis procedure for a general single-degree-of-freedom structure is proposed which considers the uncertainty of servo-hydraulic system dynamics. For discussion purposes, the experimental substructure is a portion of the entire structure in terms of a ratio of stiffness, mass, and damping, respectively. The dynamics of the servo-hydraulic system is represented by a multiplicative uncertainty model which is based on a nominal system and a weight function. The nominal system can be obtained by conducting system identification prior to the RTHS. A first-order weight function formulation is proposed which needs to cover the worst possible uncertainty envelope over the frequency range of interest. Then, the Nyquist plot of the perturbed system is adopted to determine the robust stability margin of the RTHS. In addition, three common delay compensation methods are applied to the RTHS loop to investigate the effect of delay compensation on the robust stability. Numerical simulation and experimental validation results indicate that the proposed procedure is able to obtain a robust stability margin in terms of mass, damping, and stiffness ratio which provides a simple and conservative approach to assess the stability of a RTHS before it is conducted.