• Computers and Concrete
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• v.27 no.2
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• pp.85-97
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• 2021

In this study, the effect of steel fiber utilization, boundary conditions, different beam cross-section, and length parameter are investigated on the free vibration behavior of fiber reinforced self-compacting concrete beam on elastic foundation. In the analysis of the beam model recommended by Euler-Bernoulli, a method utilizing Stokes transformations and Fourier Sine series were used. For this purpose, in addition to the control beam containing no fiber, three SCC beam elements were prepared by utilization of steel fiber as 0.6% by volume. The time-dependent fresh properties and some mechanical properties of self-compacting concrete mixtures were investigated. In the modelled beam, four different beam specimens produced with 0.6% by volume of steel fiber reinforced and pure (containing no fiber) SCC were analyzed depending on different boundary conditions, different beam cross-sections, and lengths. For this aim, the effect of elasticity of the foundation, cross-sectional dimensions, beam length, boundary conditions, and steel fiber on natural frequency and frequency parameters were investigated. As a result, it was observed that there is a noticeable effect of fiber reinforcement on the dynamic behavior of the modelled beam.

• Steel and Composite Structures
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• v.49 no.5
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• pp.587-602
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• 2023

This article presents the numerical modelling of transient heat transfer in highly heterogeneous composite materials where the thermal conductivity, specific heat and density are assumed to be directional-dependent. This article uses a coupled finite element-finite difference scheme to perform the transient heat transfer analysis of unidirectional (1D) and multidirectional (2D/3D) functionally graded composite panels. Here, 1D/2D/3D functionally graded structures are subjected to nonuniform heat source and inhomogeneous boundary conditions. Here, the multidirectional functionally graded materials are modelled by varying material properties in individual or in-combination of spatial directions. Here, fully spatial-dependent material properties are evaluated using Voigt's micromechanics scheme via multivariable power-law functions. The weak form is obtained through the Galerkin method and solved further via the element-space and time-step discretisation through the 2D-isoparametric finite element and the implicit backward finite difference schemes, respectively. The present model is verified by comparing it with the previously reported results and the commercially available finite element tool. The numerous illustrations confirm the significance of boundary conditions and material heterogeneity on the transient temperature responses of 1D/2D/3D functionally graded panels.

• Journal of Welding and Joining
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• v.17 no.2
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• pp.84-90
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• 1999

The shape of weld nuggest in arc spot welding of 304 stainless steel was found by searching thermal history of a weld joint through a three-dimensional finite element model. The problem consists of one in which the finite element mesh is growing continuously in time in order to accomodate metal transfer in arc spot welding using element rebirth technique. The analysis was performed on the basis of experimental results. The finite element program MARC, along with a few user subroutines, was employed to obtain the numerical results. Temperature-dependent thermal properties, stir effect in weld pool, effect of phase transformation, and the convective and radiative boundary conditions are included in the model. Numerically predicted shape of weld nuggest is compared with the experimentally observed shape.

• Steel and Composite Structures
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• v.48 no.3
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• pp.293-303
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• 2023

In this paper, geometrically nonlinear free vibration analysis of Mindlin viscoelastic plates with various geometrical and material properties is studied based on the Von-Karman assumptions. A novel solution is proposed in which the nonlinear frequencies of time-dependent plates are predicted according to the nonlinear frequencies of plates not dependent on time. This method greatly reduces the cost of calculations. The viscoelastic properties obey the Boltzmann integral law with constant bulk modulus. The SHPC meshfree method is employed for spatial discretization. The Laplace transformation is used to convert equations from the time domain to the Laplace domain and vice versa. Solving the nonlinear complex eigenvalue problem in the Laplace-Carson domain numerically, the nonlinear frequencies, the nonlinear viscous damping frequencies, and the nonlinear damping ratios are verified and calculated for rectangular, skew, trapezoidal and circular plates with different boundary conditions and different material properties.

• Geomechanics and Engineering
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• v.28 no.2
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• pp.107-116
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• 2022

The steady state of unsaturated soil takes a long time to achieve. The soil seepage behaviours and hydraulic properties depend highly on the wetting/drying rate. It is observed that the soil-water characteristic curve (SWCC) is dependent on the wetting/drying rate, which is known as the dynamic effect. The dynamic effect apparently influences the scanning curves and will substantially affect the seepage behavior. However, the previous models commonly ignore the dynamic effect and cannot quantitatively describe the hysteresis scanning loops under dynamic conditions. In this study, a dynamic hysteresis model for SWCC is proposed considering the dynamic change of contact angle and the moving of the contact line. The drying contact angle under dynamic condition is smaller than that under static condition, while the wetting contact angle under dynamic condition is larger than that under static condition. The dynamic contact angle is expressed as a function of the saturation rate according to the Laplace equation. The model is given by a differential equation, in which the slope of the scanning curve is related to the slope of the boundary curve by means of contact angle. Empirical models can simulate the boundary curves. Given the two boundary curves, the scanning curve can be well predicted. In this model, only two parameters are introduced to describe the dynamic effect. They can be easily obtained from the experiment, which facilitates the calibration of the model. The proposed model is verified by the experimental data recorded in the literature and is proved to be more convenient and effective.

• Advances in aircraft and spacecraft science
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• v.8 no.4
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• pp.345-372
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• 2021

The analysis of nonlinear vibrations, buckling, post-buckling, flutter boundary determination and post-flutter behavior of a homogeneous curved plate assuming cylindrical bending is conducted in this article. Other assumptions include simply-supported boundary conditions, supersonic aerodynamic flow at the top of the plate, constant pressure conditions below the plate, non-viscous flow model (using first- and third-order piston theory), nonlinear structural model with large deformations, and application of mechanical and thermal loads on the curved plate. The analysis is performed with constant environmental indicators (flow density, heat, Reynolds number and Mach number). The material properties (i.e., coefficient of thermal expansion and modulus of elasticity) are temperature-dependent. The equations are derived using the principle of virtual displacement. Furthermore, based on the definitions of virtual work, the potential and kinetic energy of the final relations in the integral form, and the governing nonlinear differential equations are obtained after fractional integration. This problem is solved using two approaches. The frequency analysis and flutter are studied in the first approach by transferring the handle of ordinary differential equations to the state space, calculating the system Jacobin matrix and analyzing the eigenvalue to determine the instability conditions. The second approach discusses the nonlinear frequency analysis and nonlinear flutter using the semi-analytical solution of governing differential equations based on the weighted residual method. The partial differential equations are converted to ordinary differential equations, after which they are solved based on the Runge-Kutta fourth- and fifth-order methods. The comparison between the results of frequency and flutter analysis of curved plate is linearly and nonlinearly performed for the first time. The results show that the plate curvature has a profound impact on the instability boundary of the plate under supersonic aerodynamic loading. The flutter boundary decreases with growing thermal load and increases with growing curvature.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.14 no.1
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• pp.43-56
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• 2010

The representative numerical algorithms to solve the time dependent Navier-Stokes equations are projection type methods. Lots of projection schemes have been developed to find more accurate solutions. But most of projection methods [4, 11] suffer from inconsistency and requesting unknown datum. E and Liu in [5] constructed the gauge method which splits the velocity $u=a+{\nabla}{\phi}$ to make consistent and to replace requesting of the unknown values to known datum of non-physical variables a and ${\phi}$. The errors are evaluated in [9]. But gauge method is not still obvious to find out suitable combination of discrete finite element spaces and to compute boundary derivative of the gauge variable ${\phi}$. In this paper, we define 4 gauge algorithms via combining both 2 decomposition operators and 2 boundary conditions. And we derive variational derivative on boundary and analyze numerical results of 4 gauge algorithms in various discrete spaces combinations to search right discrete space relation.

• Proceedings of the Korean Society For Composite Materials Conference
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• 2003.04a
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• pp.143-146
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• 2003

A finite element based on the efficient higher order zig-zag theory with multiple delaminations Is developed to refine the predictions of frequency and mode shapes. Displacement field through the thickness are constructed by superimposing linear zig-zag field to the smooth globally cubic varying field. The layer-dependent degrees of freedom of displacement fields are expressed in terms of reference primary degrees of freedom by applying interface continuity conditions including delaminated interfaces as well as free hounding surface conditions of transverse shear stresses. Thus the proposed theory is not only accurate but also efficient. This displacement field can systematically handle the number, shape, size, and locations of delaminations. Throught the dynamic version of variational approach, the dynamic equilibrium equations and variationally consistent boundary conditions are obtained. Through the natural frequency analysis and time response analysis of composite plate with multiple delaminations, the accuracy and efficiency of the present finite element are demonstrated. The present finite element is suitable in the predictions of the dynamic response of the thick composite plate with multiple delaminations.

• Journal of Powder Materials
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• v.4 no.2
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• pp.83-89
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• 1997

A finite element analysis to solve the coupled thermomechanical problem in the plane strain upsetting of the porous metals was performed. The analysis was formulated using the yield function advanced by Lee and kim and developed using the thermo-elasto-plastic time integration procedure. The density and temperature dependent thermal and mechanical properties of porous metals were considered. The internal heat generation by the plastic deformation and the changing thermal boundary conditions corresponding to the geometry were incorporated in the program. The distributions of the stress, strain, pressure, density and temperature were predicted during the free resting period, deformation period and dwelling period of the forging process.

• Proceedings of the Korea Concrete Institute Conference
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• 2005.11a
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• pp.205-208
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• 2005

A single span-to-depth ratio function is proposed for control of deflection in one-way concrete construction. The equation can be applied to one-way slabs, beams, and flat plates. Effects of cracking, time-dependent deformation, boundary conditions, applied loading, and target deflection-to-span ratio are taken into account.