• Journal of the Korean Mathematical Society
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• v.48 no.3
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• pp.529-550
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• 2011

In this work, a numerical solution of the incompressible Navier-Stokes equations is proposed. The method suggested is based on an algorithm of discretization by mixed finite elements with a posteriori error estimation of the computed solutions. In order to evaluate the performance of the method, the numerical results are compared with some previously published works or with others coming from commercial code like Adina system.

• Structural Engineering and Mechanics
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• v.15 no.5
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• pp.563-578
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• 2003

Delaunay triangulation is combined with an adaptive finite element method for analysis of two-dimensional crack propagation problems. The content includes detailed descriptions of the proposed procedure which consists of the Delaunay triangulation algorithm and an adaptive remeshing technique. The adaptive remeshing technique generates small elements around the crack tips and large elements in the other regions. Three examples for predicting the stress intensity factors of a center cracked plate, a compact tension specimen, a single edge cracked plate under mixed-mode loading, and an example for simulating crack growth behavior in a single edge cracked plate with holes, are used to evaluate the effectiveness of the procedure. These examples demonstrate that the proposed procedure can improve solution accuracy as well as reduce total number of unknowns and computational time.

• Structural Engineering and Mechanics
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• v.42 no.5
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• pp.701-713
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• 2012

Results pertaining to 3D investigations on the effect of the thickness on the stress fields at the crack front are presented. A 3D finite element analysis is performed using a modified single edge-notched tension specimen configuration, with an inclined crack to include mixed mode I-II. A technique to mesh the crack front (3D) with singular finite elements in ANSYS without using third party software is introduced and used in this study. The effect of the specimen thickness is explicitly investigated for six thicknesses ranging from 1 to 32 mm. In addition, three crack inclination angles, including pure Mode-I, are used to study the effect of mixed-mode I-II fracture. An attempt is made to correlate the extent of a particular stress state along the crack front to thickness. In addition, ${\sigma}_{zz}/{\nu}({\sigma}_{xx}+{\sigma}_{yy})$ contours at the crack front are presented as a useful means to analyze the stress state.

• Structural Engineering and Mechanics
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• v.35 no.3
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• pp.283-299
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• 2010

This paper addresses the numerical simulation of fatigue crack growth in arbitrary 2D geometries under constant amplitude loading by the using a new finite element software. The purpose of this software is on the determination of 2D crack paths and surfaces as well as on the evaluation of components Lifetimes as a part of the damage tolerant assessment. Throughout the simulation of fatigue crack propagation an automatic adaptive mesh is carried out in the vicinity of the crack front nodes and in the elements which represent the higher stresses distribution. The fatigue crack direction and the corresponding stress-intensity factors are estimated at each small crack increment by employing the displacement extrapolation technique under facilitation of singular crack tip elements. The propagation is modeled by successive linear extensions, which are determined by the stress intensity factors under linear elastic fracture mechanics (LEFM) assumption. The stress intensity factors range history must be recorded along the small crack increments. Upon completion of the stress intensity factors range history recording, fatigue crack propagation life of the examined specimen is predicted. A consistent transfer algorithm and a crack relaxation method are proposed and implemented for this purpose. Verification of the predicted fatigue life is validated with relevant experimental data and numerical results obtained by other researchers. The comparisons show that the program is capable of demonstrating the fatigue life prediction results as well as the fatigue crack path satisfactorily.

• Structural Engineering and Mechanics
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• v.85 no.2
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• pp.147-161
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• 2023

Based on the ideas of variational differential quadrature (VDQ) and finite element method (FEM), a numerical approach named as VDQFEM is applied herein to study the large deformations of plate-type structures under static loading with arbitrary shape hole made of functionally graded graphene platelet-reinforced composite (FG-GPLRC) in the context of higher-order shear deformation theory (HSDT). The material properties of composite are approximated based upon the modified Halpin-Tsai model and rule of mixture. Furthermore, various FG distribution patterns are considered along the thickness direction of plate for GPLs. Using novel vector/matrix relations, the governing equations are derived through a variational approach. The matricized formulation can be efficiently employed in the coding process of numerical methods. In VDQFEM, the space domain of structure is first transformed into a number of finite elements. Then, the VDQ discretization technique is implemented within each element. As the last step, the assemblage procedure is performed to derive the set of governing equations which is solved via the pseudo arc-length continuation algorithm. Also, since HSDT is used herein, the mixed formulation approach is proposed to accommodate the continuity of first-order derivatives on the common boundaries of elements. Rectangular and circular plates under various boundary conditions with circular/rectangular/elliptical cutout are selected to generate the numerical results. In the numerical examples, the effects of geometrical properties and reinforcement with GPL on the nonlinear maximum deflection-transverse load amplitude curve are studied.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.14 no.3
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• pp.189-200
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• 2010

A numerical method is proposed and analyzed to approximate a mathematical model of age-dependent population dynamics with spatial diffusion. The model takes a form of nonlinear and nonlocal system of integro-differential equations. A finite difference method along the characteristic age-time direction is considered and primal mixed finite elements are used in the spatial variable. A priori error estimates are derived for the relevant variables.

• Structural Engineering and Mechanics
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• v.4 no.6
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• pp.655-678
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• 1996

The paper reports on alternative hybrid/mixed formulations being developed by the Structural Analysis Research Group of Institute Superior T$\acute{e}$cnico. These formulations open the scope and increase the power of the finite element method by allowing different fields to be independently approximated, within certain consistency criteria, and by enhancing the use of a wide range of approximation functions. They have been applied to the analysis of 2-D problems, laminar structures and solids, using different constitutive relations, both in quasi-static and dynamic regimes. The fundamental properties of the formulations are identified and assessed and their performance is illustrated using simple, linear applications.

• Structural Engineering and Mechanics
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• v.19 no.6
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• pp.619-637
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• 2005

The objective of this research was to determine the Vlasov soil parameters for quadratically varying elasticity modulus $E_s$(z) of the compressible soil continuum and discuss the interaction affect between two close plates. Interaction problem carried on for uniformly distributed load carrying plates. Plate region was simulated by Kirchhoff plate theory based (mixed or displacement type) 2D elements and the foundation continuum was simulated by displacement type 2D elements. At the contact region, plate and foundation elements were geometrically coupled with each other. In this study the necessary formulas for the Vlasov parameters were derived when Young's modulus of the soil continuum was varying as a quadratic function of z-coordinate through the depth of the foundation. In the examples, first the elements and the iterative FE algorithm was verified and later the results of quadratic variation of $E_s$(z) were compared with the previous examples in order to discuss the general behavior. As a final example two plates close to each other resting on elastic foundation were handled to see their interaction influences on the Vlasov foundation parameters. Original examples were solved using both mixed and displacement type plate elements in order to confirm the results.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.12 no.3
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• pp.363-370
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• 1999

This study presented an modeling method for the connections in mixed structure with reinforced concrete columns and steel beam using finite element method. The contacting surfaces between concrete and steel are modeled using master-slave contact algorithm and the incompatible mode elements were used in the steel tube subjected to bending. The characteristics of mixed structure was that diaphragm was used for transferring force from beam to column. The three dimensional nonlinear analysis was performed and the analytical results compared with experimental results in order to prove modeling method.

• Structural Engineering and Mechanics
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• v.11 no.6
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• pp.591-604
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• 2001

In this paper, a finite element with embedded displacement discontinuity which eliminates the need for remeshing of elements in the discrete crack approach is applied for the progressive fracture analysis of concrete structures. A finite element formulation is implemented with the extension of the principle of virtual work to a continuum which contains internal displacement discontinuity. By introducing a discontinuous displacement shape function into the finite element formulation, the displacement discontinuity is obtained within an element. By applying either a nonlinear or an idealized linear softening curve representing the fracture process zone (FPZ) of concrete as a constitutive equation to the displacement discontinuity, progressive fracture analysis of concrete structures is performed. In this analysis, localized progressive fracture simultaneous with crack closure in concrete structures under mixed mode loading is simulated by adopting the unloading path in the softening curve. Several examples demonstrate the capability of the analytical technique for the progressive fracture analysis of concrete structures.