• Composites Research
• /
• v.30 no.6
• /
• pp.343-349
• /
• 2017

A multifield variational formulation is developed for the finite element (FE) cross-sectional analysis of composite beams. The cross-sectional warping displacements and sectional stresses are considered to be the primary variables through the application of Reissner's partially mixed principle. The warping displacements are modeled using generic FE shape functions with nonlinear distribution over the beam section. A generalized Timoshenko level stiffness matrix is derived which incorporates the effects of elastic couplings, transverse shear, and Poisson's deformations. The accuracy of the present analysis is validated for the stiffness constants and elastostatic responses of composite box beams which correlate well with the experimental data and other state-of-the-art approaches.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.12 no.1
• /
• pp.13-23
• /
• 2008

In [7, 8], they proposed a new singular function(NSF) method to compute singular solutions of Poisson equations on a polygonal domain with re-entrant angles. Singularities are eliminated and only the regular part of the solution that is in $H^2$ is computed. The stress intensity factor and the solution can be computed as a post processing step. This method was extended to the interface problem and Poisson equations with the mixed boundary condition. In this paper, we give NSF method for the Helmholtz equations ${\Delta}u+Ku=f$ with homogeneous Dirichlet boundary condition. Examples with a singular point are given with numerical results.

• Smart Structures and Systems
• /
• v.16 no.3
• /
• pp.401-414
• /
• 2015

A developed hybrid method for crack identification of beams is presented. Based on the Euler-Bernouli beam theory and concepts of fracture mechanics, governing equation of the cracked beams is reformulated. Finite element (FE) method as a powerful numerical tool is used to discritize the equation in space domain. After transferring the equations from time domain to frequency domain, frequencies and mode shapes of the beam are obtained. Efficiency of the governed equation for free vibration analysis of the beams is shown by comparing the results with those available in literature and via ANSYS software. The used equation yields to move the influence of cracks from the stiffness matrix to the mass matrix. For crack identification measured data are produced by applying random error to the calculated frequencies and mode shapes. An objective function is prepared as root mean square error between measured and calculated data. To minimize the function, hybrid genetic algorithms (GAs) and particle swarm optimization (PSO) technique is introduced. Efficiency, Robustness, applicability and usefulness of the mixed optimization numerical tool in conjunction with the finite element method for identification of cracks locations and depths are shown via solving different examples.

• Structural Engineering and Mechanics
• /
• v.4 no.6
• /
• pp.645-653
• /
• 1996

In order to avoid pathological mesh dependency in finite element modelling of strain localization, an isotropic elasto-plastic model with a yield function depending on the Laplacian of the equivalent plastic strain is implemented in a 4-node quadrilateral finite element with one integration point based on a mixed formulation derived from Hu-Washizu principle. The evaluation of the Laplacian is based on a least square polynomial approximation of the equivalent plastic strain around each integration point. This non local approach allows to satisfy exactly the consistency condition at each integration point. Some examples are treated to illustrate the effectiveness of the method.

• Structural Engineering and Mechanics
• /
• v.55 no.1
• /
• pp.93-109
• /
• 2015

Finite element analysis (FEA) combined with the concepts of linear elastic fracture mechanics (LEFM) provides a practical and convenient means to study the fracture and crack growth of materials. In this paper, a numerical modeling of crack propagation in the cement mantle of the reconstructed acetabulum is presented. This work is based on the implementation of the displacement extrapolation method (DEM) and the strain energy density (SED) theory in a finite element code. At each crack increment length, the kinking angle is evaluated as a function of stress intensity factors (SIFs). In this paper, we analyzed the mechanical behavior of cracks initiated in the cement mantle by evaluating the SIFs. The effect of the defect on the crack propagation path was highlighted.

• Steel and Composite Structures
• /
• v.45 no.1
• /
• pp.147-157
• /
• 2022

This study assessed the compressive and tensile strengths and modulus of elasticity of waste polyethylene terephthalate (PET) using the ASTM standard tests. In addition, short carbon and glass fibers were mixed with waste PET to examine the improvements in ductility and strength during compression. The bonding was examined via field-emission scanning electron microscopy. The strength degradation of the waste PET tested under UV was 40-50%. However, it had a compressive strength of 32.37 MPa (equivalent to that of concrete), tensile strength of 31.83 MPa (approximately ten times that of concrete), and a unit weight of 12-13 kN/m3 (approximately half that of concrete). A finite element analysis showed that, compared with concrete, a waste PET pile foundation can support approximately 1.3 times greater loads. Mixing reinforcing fibers with waste PET further mitigated this, thereby extending ductility. Waste PET holds excellent potential for use in foundation piles, especially while mitigating brittleness using short reinforcing fibers and avoiding UV degradation.

• Journal of Mechanical Science and Technology
• /
• v.16 no.4
• /
• pp.476-484
• /
• 2002

The aim of this study is to investigate the ductile fracture behavior under mixed mode (I/II) loading using SA533B pressure vessel steel. Anti-symmetric 4-point (AS4P) bending tests were performed to obtain the J-R curves under two different mixed mode (I/II) loadings. In addition, finite element analysis using Rousselier Ductile Damage Theory was carried out to predict the J-R curves under mixed mode (I/II) loadings. In conclusions, the J-R curves under. Mixed Mode (I/II) loading were located between those of Mode I and Mode II loading. When the mixity of mixed mode (I/II) loading was high, the J-R curve of mixed mode (I/II) loading approached that of pure mode I loading after some amount of crack propagation. In contrast with the above fact, if the mixity was low, the J-R curve took after that of pure mode II loading. Finally, it was found that the predicted J-R curves made a good agreement with the test data through the tuning procedures of $\beta$ values at the different mixed mode (I/II) loading.

• 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.

• Journal of the Korean Mathematical Society
• /
• v.59 no.3
• /
• pp.519-548
• /
• 2022

In this paper, a stabilized-penalized collocated finite volume (SPCFV) scheme is developed and studied for the stationary generalized Navier-Stokes equations with mixed Dirichlet-traction boundary conditions modelling an incompressible biological fluid flow. This method is based on the lowest order approximation (piecewise constants) for both velocity and pressure unknowns. The stabilization-penalization is performed by adding discrete pressure terms to the approximate formulation. These simultaneously involve discrete jump pressures through the interior volume-boundaries and discrete pressures of volumes on the domain boundary. Stability, existence and uniqueness of discrete solutions are established. Moreover, a convergence analysis of the nonlinear solver is also provided. Numerical results from model tests are performed to demonstrate the stability, optimal convergence in the usual L² and discrete H¹ norms as well as robustness of the proposed scheme with respect to the choice of the given traction vector.

• Journal of applied mathematics & informatics
• /
• v.29 no.3_4
• /
• pp.621-639
• /
• 2011

The purpose of this paper is to introduce a general iterative process by viscosity approximation method with parallel method to ap-proximate a common element of the set of solutions of a mixed equilibrium problem and of the set of common fixed points of a finite family of $k_i$-strict pseudo-contractions in a Hilbert space. We obtain a strong convergence theorem of the proposed iterative method for a finite family of $k_i$-strict pseudo-contractions to the unique solution of variational inequality which is the optimality condition for a minimization problem under some mild conditions imposed on parameters. The results obtained in this paper improve and extend the corresponding results announced by Liu (2009), Plubtieng-Panpaeng (2007), Takahashi-Takahashi (2007), Peng et al. (2009) and some well-known results in the literature.