• Transactions of the Korean Society of Mechanical Engineers A
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• v.39 no.6
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• pp.583-588
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• 2015

Asymptotic method has been often used to theoretically analyze the complete contact problem. The error of the asymptotic results increases as the distance from the contact edge increases. The singularity cannot be properly obtained from a finite element (FE) analysis owing to the finiteness of the element size. In the present work, the complete contact problem in bonded condition is analyzed using a combined experimental-numerical approach to assist and/or compare with the asymptotic results. Al and Cu alloys are used for the material combination of the punch and substrate. 120 and 135 degrees are used for the punch angle. The FE models are validated by comparison of displacement distributions obtained by the FE analysis and $moir{\acute{e}}$ experiment. Generalized stress intensity factors are evaluated using the validated FE models. Stress field in the vicinity of the sharp contact edges obtained from the FE and asymptotic analyses are compared. The discrepancies are also discussed.

• Structural Engineering and Mechanics
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• v.66 no.1
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• pp.85-96
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• 2018

This study investigates the response of functionally graded (FG) gas pipe under unsteady internal pressure and temperature. The pipe is proposed to be manufactured from FGMs rather than custom carbon steel, to reduce the erosion, corrosion, pressure surge and temperature variation effects caused by conveying of gases. The distribution of material graduations are obeying power and sigmoidal functions varying with the pipe thickness. The sigmoidal distribution is proposed for the 1st time in analysis of FG pipe structure. A Two-dimensional (2D) plane strain problem is proposed to model the pipe cross-section. The Fourier law is applied to describe the heat flux and temperature variation through the pipe thickness. The time variation of internal pressure is described by using exponential-harmonic function. The proposed problem is solved numerically by a two-dimensional (2D) plane strain finite element ABAQUS software. Nine-node isoparametric element is selected. The proposed model is verified with published results. The effects of material graduation, material function, temperature and internal pressures on the response of FG gas pipe are investigated. The coupled temperature and displacement FEM solution is used to find a solution for the stress displacement and temperature fields simultaneously because the thermal and mechanical solutions affected greatly by each other. The obtained results present the applicability of alternative FGM materials rather than classical A106Gr.B steel. According to proposed model and numerical results, the FGM pipe is more effective in natural gas application, especially in eliminating the corrosion, erosion and reduction of stresses.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.31 no.2 s.257
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• pp.277-284
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• 2007

The steam generator in a nuclear power plant is a large heat exchanger that uses heat from a reactor to generate steam to drive the turbine generator. Rupture of a steam generator tube can result in release of fission products to environment outside. Therefore, an accurate integrity assessment of the steam generator tubes with cracks is of great importance for maintaining the safety of a nuclear power plant. The steam generator tubes are supported at regular intervals by support plates and rotations of the tubes are restrained. Although it has been reported that the limit load for a circumferential crack is significantly affected by boundary condition of the tube, existing limit load solutions do not consider the restraining effect of support plate correctly. In addition, there are no limit load solutions for circumferential cracks in U-bend region with the effect of the support plate. This paper provides detailed limit load solutions for circumferential cracks in top of tube sheet and the U-bend regions of the steam generator tube with the actual boundary conditions to simulate the restraining effect of the support plate. Such solutions are developed based on three dimensional finite element analyses. The resulting limit load solutions are given in a polynomial form, and thus can be simply used in practical integrity assessment of the steam generator tubes.

• Structural Engineering and Mechanics
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• v.87 no.3
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• pp.283-296
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• 2023

Free-vibration and buckling analyses of plate problems are investigated with the aid of the strain gradient notation finite element method (SGN-FEM). As SGN-FEM employs physically interpretable polynomials in developing finite elements, parasitic shear sources, which are the cause of shear locking, can be precisely identified and subsequently eliminated. This allows two mutually complementary objectives to be defined in this work, namely, evaluate the efficiency of free-vibration and buckling results provided by corrected models, and study the severity of parasitic shear effects on plate models performance. Parasitic shear are flexural terms erroneously present in shear strain polynomials. It is reviewed here that six parasitic shear terms arise during the formulation of the four-node Mindlin plate element. Two parasitic shear terms have been identified in the in-plane shear strain polynomial while other two have been identified in each of the transverse shear strain polynomials. The element is corrected a-priori, i.e., during development, by simply removing the spurious terms from the shear strain polynomials. The computational implementation of the element in its two versions, namely, containing the parasitic shear terms (PS) and corrected for parasitic shear (SG), allows for assessments of the accuracy of results and of the deleterious effects of parasitic shear in free vibration and buckling analyses. This assessment of the parasitic shear effects is a novelty of this work. Validation of the SG model is done comparing its results with analytical results and results provided by other numerical procedures. Analyses are performed for square plates with different thickness-to-length ratios and boundary conditions. Results for thin plates provided by the PS model do not converge to the correct solutions, which indicates that parasitic shear must be eliminated. That is, analysts should not rely on refinement alone. For thick plates, PS model results can be considered acceptable as deleterious effects are really critical in thin plates. On the other hand, results provided by the SG model converge well for both thin and thick plates. The effectiveness of the SG model is established via high-accuracy results obtained in several examples. It is concluded that corrected SGN-FEM models are efficient alternatives for free-vibration and buckling analysis of Mindlin plate problems, and that precise elimination of parasitic shear is a requirement for sound analyses.

• Journal of the Korean Society of Hazard Mitigation
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• v.7 no.5
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• pp.61-71
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• 2007

Navier's and Finite element solutions based on the first-order shear deformation theory are presented for the analysis of through-thickness functionally graded plates and shells. The functionally graded materials are considered: a sigmoid function is utilized for the mechanical properties through the thickness of the isotropic structure which varies smoothly through the plate and shell thickness. The formulation of a nonlinear 9-node Element-based Lagrangian shell element is presented for the geometrically nonlinear analysis. Natural-coordinate-based strains are used in present shell element. Numerical results of the linear and nonlinear analysis are presented to show the effect of the different top/bottom elastic modulus, loading conditions, aspect ratios and side-to-thickness ratios on the mechanical behaviors. Besides, the result according to the variation of the power-law index of isotropic functionally graded structures is investigated.

• Structural Engineering and Mechanics
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• v.73 no.2
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• pp.109-121
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• 2020

This study aims to estimate crack location and crack length in damaged beam structures using transfer matrix formulations, which are based on analytical solutions of governing equations of motion. A single variable shear deformation theory (SVSDT) that considers parabolic shear stress distribution along beam cross-section is used, as well as, Timoshenko beam theory (TBT). The cracks are modelled using massless rotational springs that divide beams into segments. In the forward problem, natural frequencies of intact and cracked beam models are calculated for different crack length and location combinations. In the inverse approach, which is the main concern of this paper, the natural frequency values obtained from experimental studies, finite element simulations and analytical solutions are used for crack identification via plots of rotational spring flexibilities against crack location. The estimated crack length and crack location values are tabulated with actual data. Three different beam models that have free-free, fixed-free and simple-simple boundary conditions are considered in the numerical analyses.

• Structural Engineering and Mechanics
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• v.64 no.1
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• pp.81-92
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• 2017

Many materials in engineering exhibit different modulus in tension and compression, which are known as bi-modulus materials. Based on the bi-modulus elastic theory, a modified semi-analytical model, by introducing a stress function, is established in this paper to study the mechanical response of a bi-modulus cylinder placed in an axisymmetric temperature field. Meanwhile, a numerical procedure to calculate the temperature stresses in bi-modulus structures is developed. It is proved that the bi-modulus solution can be degenerated to the classical same modulus solution, and is in great accordance with the solutions calculated by the semi-analytical model proposed by Kamiya (1977) and the numerical solutions calculated both by the procedure complied in this paper and by the finite element software ABAQUS, which demonstrates that the semi-analytical model and the numerical procedure are accurate and reliable. The result shows that the modified semi-analytical model simplifies the calculation process and improves the speed of computation. And the numerical procedure simplifies the modeling process and can be extended to study the stress field of bi-modulus structures with complex geometry and boundary conditions. Besides, the necessity to introduce the bi-modulus theory is discussed and some suggestions for the qualitative analysis and the quantitative calculation of such structure are proposed.

• Journal of Magnetics
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• v.17 no.1
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• pp.19-26
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• 2012

This paper deals with the performance analysis and estimation of the electrical parameters of a permanent magnet synchronous generator (PMSG) for hydrokinetic energy conversion applications using vortex induced vibration (VIV). The analytical solutions for the magnetic fields produced by permanent magnets (PMs) and stator winding currents are obtained using a 2D polar coordinate system and a magnetic vector potential. An analytical expression for the 2D permeance is also derived, which takes into account stator skew effects. Based on these magnetic field solutions and the 2D permeance function, electrical circuit parameters such as the backemf constant and the air-gap inductance are obtained analytically. The performances of the PMSG are investigated using the estimated electrical circuit parameters and an equivalent circuit (EC). All analytical results are validated extensively using 2D finite element (FE) analyses. Experimental measurements for parameters such as the back-emf and inductance are also presented to confirm the analyses.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.19 no.3
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• pp.183-193
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• 2007

Analytic solutions are derived for wave scattering by a semi-infinite breakwater or a breakwater gap with partially reflective front and fully reflective back. The water depth is constant and a regular wave train is normally incident to the breakwater. Wave scattering is studied based on the linear potential wave theory. The governing equation is transformed into ordinary differential equation by using the method of variation of parameters and coordinate transformation. Comparison with finite element numerical solution shows that the analytic solution obtained in this paper gives quite good results. Using the analytic solution, the tranquility of harbor entrance is investigated by changing the reflection coefficient at the breakwater.

• Computers and Concrete
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• v.2 no.6
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• pp.499-516
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• 2005

A composite model is used to represent the heterogeneity of plain concrete consisting of coarse aggregates, mortar matrix and the mortar-aggregate interface. The composite elements of plain concrete are modeled using triangular finite element units which have six interface nodes along the sides. Fracture is captured through a constitutive single branch softening-fracture law at the interface nodes, which bounds the elastic domain inside each triangular unit. The inelastic displacement at an interface node represents the crack opening or sliding displacement and is conjugate to the internodal force. The path-dependent softening behaviour is developed within a quasi-prescribed displacement control formulation. The crack profile is restricted to the interface boundaries of the defined mesh. No re-meshing is carried out. Solutions to the rate formulation are obtained using a mathematical programming procedure in the form of a linear complementary problem. An event by event solution strategy is adopted to eliminate solutions with simultaneous formation of softening zones in symmetric problems. The composite plain concrete model is compared to experimental results for the tensile crack growth in a Brazilian test and three-point bending tests on different sized specimens. The model is also used to simulate wedge-type shear-compression failure directly under the loading platen of a Brazilian test.