• Structural Engineering and Mechanics
• /
• v.11 no.1
• /
• pp.105-122
• /
• 2001

A new three-dimensional 13-node hexahedral element with rotational degrees of freedom, which is designated as MR-H13 element, is presented. The proposed element is established by adding five nodes to one of the six faces of basic 8-node hexahedral element. The new element can be effectively used in the connection between the refined mesh and the coarser mesh. The derivation of the current element in this paper is based on the variational principles in which the rotation and skew-symmetric stress are introduced as independent variables. Numerical examples show that the performance of the new element is satisfactory.

• Journal of Mechanical Science and Technology
• /
• v.17 no.3
• /
• pp.457-466
• /
• 2003

In this paper, the numerical finite element formulations were derived for the linearized Navier-Stokes' equations with assumptions of two-dimensional incompressible, homogeneous viscous fluid field, and small oscillation and the FAMD (Fluid Added Mass and Damping) code was developed for practical applications calculating the fluid added mass and damping. In formulations, a fluid domain is discretized with C$\^$0/-type quadratic quadrilateral elements containing eight nodes using a mixed interpolation method, i.e., the interpolation function for the velocity variable is approximated by a quadratic function based on all eight nodal points and the interpolation function for the pressure variable is approximated by a linear function based on the four nodal points at vertices. Using the developed code, the various characteristics of the fluid added mass and damping are investigated for the concentric cylindrical shell and the actual hexagon arrays of the liquid metal reactor cores.

• Interaction and multiscale mechanics
• /
• v.2 no.3
• /
• pp.277-293
• /
• 2009

The Enriched Free Mesh Method (EFMM) is a patch-wise procedure in which both a displacement field on an element and a stress/strain field on a cluster of elements connected to a node can be defined. On the other hand, the Superconvergent Patch Recovery (SPR) is known to be an efficient post-processing procedure of the finite element method to estimate the error norm at a node. In this paper, we discuss the relationship between solutions of the EFMM and those of the SPR through several convergence studies. In addition, in order to solve the demerit of the smoothing effect on the fracture mechanics fields, we implement a singular stress field to a local patch in the EFMM, and its effectiveness is investigated.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.13 no.3
• /
• pp.461-471
• /
• 1989

For the mixed-mode crack problems the direction of crack growth, the crack path and the rational representation of fatigue crack growth rates should be studied to predict fatigue life and safety of structures. In this study, a round specimen which produce nearly identical effects in all loading directions is proposed to make an easy measurement of initial direction of crack growth. The mode I and mode II stress intensity factors of the specimen were calculated using finite element method, in which the square root singular stresses at the crack tip are modeled by means of four rectangular quarter-point eight-noded elements surrounding the crack tip. Experimental results for high strength aluminum alloy showed that the direction of mixed-mode crack growth agree well with maximum principal stress criterion as well as minimum strain energy density criterion, but not with maximum shear stress criterion. From data of fatigue crack growth rates using crack geometry projected on the line perpendicular to the loading direction it is easily established that mixed-mode fatigue crack growth in 5083-H115 aluminum alloy goes predominantly with mode I crack growth behaviors.

• Transactions of the Korean Society of Mechanical Engineers B
• /
• v.28 no.11
• /
• pp.1348-1358
• /
• 2004

The filling pattern and an adaptive grid refinement based on the finite element method and Eulerian mesh advancement approach have been developed to analyze incompressible transient viscous flow with free surfaces. The governing equation fur flow analysis is Navier-Stokes equation including inertia and gravity effects. The mixed FE formulation and predictor-corrector method are used effectively for unsteady numerical simulation. The flow front surface and the volume inflow rate are calculated using the filling pattern technique to select an adequate pattern among seven filling patterns at each tetrahedral control volume. By adaptive grid refinement, the new flow field that renders better prediction in flow surface shape is generated and the velocity field at the flow front part is calculated more exactly. In this domain the elements in the surface region are made finer than those in the remaining regions for more efficient computation. The collapse of a water dam and the filling of a fluidity spiral have been analyzed. The numerical results have been in good agreement with the experimental results and the efficiency of the adaptive grid refinement and filling pattern techniques have been verified.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.35 no.9
• /
• pp.1041-1050
• /
• 2011

An elasto-plastic finite element method using the theory of strain gradient plasticity is proposed to evaluate the size dependency of structural plasticity that occurs when the configuration size decreases to micron scale. For this method, we suggest a low-order plane and three-dimensional displacement-based elements, eliminating the need for a high order, many degrees of freedom, a mixed element, or super elements, which have been considered necessary in previous researches. The proposed method can be performed in the framework of nonlinear incremental analysis in which plastic strains are calculated and averaged at nodes. These strains are then interpolated and differentiated for gradient calculation. We adopted a strain-gradient-hardening constitutive equation from the Taylor dislocation model, which requires the plastic strain gradient. The developed finite elements are tested numerically on the basis of typical size-effect problems such as micro-bending, micro-torsion, and micro-voids. With respect to the strain gradient plasticity, i.e., the size effects, the results obtained by using the proposed method, which are simple in their calculation, are in good agreement with the experimental results cited in previously published papers.

• Journal of the Computational Structural Engineering Institute of Korea
• /
• v.16 no.2
• /
• pp.165-172
• /
• 2003

In this study, a new and efficient harmonic axisymmetric shell element for static and dynamic analysis Is proposed. The present element considering shear strain is based on a modified mixed variational principle in which the independent unknowns are only the Quantities prescribable at the shell edges. Unlike existing hybrid-mixed axisymmetric shell elements, the present element introduces additional nodeless degrees for displacement field Interpolation In order to enhance the numerical performance. The stress parameters are eliminated by the stationary condition and the nodeless degrees are condensed out by the Guyan reduction. Through several numerical examples, the hybrid-miked shell element with the additional nodeless degrees and the consistent stress parameters is shown to be efficient and yield very accurate results for static and vibration analysis.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.23 no.4
• /
• pp.367-380
• /
• 2019

A 1kW-class horizontal axis wind turbine (HAWT) rotor blade is taken into account to investigate elastic characteristics in 2-D. The elastic blade field is composed of symmetric cross-ply laminated composite material. Blade element momentum theory is applied to obtain the boundary conditions pressuring the blade, and the plane stress elasticity problem is formulated in terms of two displacement parameters with mixed boundary conditions. For the elastic characteristics a fair of differential equations are derived based on the elastic theory. The domain is divided by triangular and rectangular elements due to the complexity of the blade configuration, and a finite element method is developed for the governing equations to search approximate solutions. The results describe that the elastic behavior is deeply influenced by the layered angle of the middle laminate and the stability of the blade can be improved by controlling the layered angle of laminates, which can be evaluated by the mathematical approach.

• Steel and Composite Structures
• /
• v.27 no.1
• /
• pp.27-33
• /
• 2018

In this study, a mixed-interpolated tensorial component 4 nodes method (MITC4) is treated as a numerical analysis model for topology optimization using multiple materials assigned within Reissner-Mindlin plates. Multi-material optimal topology and shape are produced as alternative plate retrofit designs to provide reasonable material assignments based on stress distributions. Element density distribution contours of mixing multiple material densities are linked to Solid Isotropic Material with Penalization (SIMP) as a design model. Mathematical formulation of multi-material topology optimization problem solving minimum compliance is an alternating active-phase algorithm with the Gauss-Seidel version as an optimization model of optimality criteria. Numerical examples illustrate the reliability and accuracy of the present design method for multi-material topology optimization with Reissner-Mindlin plates using MITC4 elements and steel materials.

• KSCE Journal of Civil and Environmental Engineering Research
• /
• v.30 no.2B
• /
• pp.199-209
• /
• 2010

A finite element model for analyzing surface water flow was developed. Shallow water equation was discretized and solved by Galerkin and Newton-Raphson method. Triangular or rectangular elements can be mixed together to construct meshes. The algebraic equation was solved by frontal method which is very efficient in finite element problem. The developed model was applied to rectangular meandering channel with two bends and transverse velocities and water depth distributions were examined. High velocity was located near the inner bank at the apexes of the bends and velocity distribution was symmetrical about the centerline at the midsection of two bend and super elevation also occurred. Simulation results showed very good agreement with measured data. Another numerical simulation was carried out in mild, steep, adverse and abrupt bottom change slope and channels with weir. 12 water surface profiles of gradually varied flow were correct in terms of hydraulic interpretation.