• Advances in nano research
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• v.15 no.1
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• pp.75-89
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• 2023

In this paper, Bishop theory performs longitudinal vibration analysis of Nano-beams. Its governing equation, due to integrated displacement field and more considered primarily effects compared with other theories, enjoys fully completed status, and more reliable results as well. This article aims to find how Bishop theory and Two-phase elasticity work together. In other words, whether Bishop theory will be compatible with Two-phase local/nonlocal elasticity. Hamilton's principle is employed to derive governing equation of motion, and then the 6th order of Generalized Differential Quadrature Method (GDQM) as a constructive numerical method is utilized to attain the discretized two-phase formulation. To acquire a proper verification procedure, exact solution is prepared to be compared with current results. Furthermore, the effects of key parameters on the objective are investigated.

• Earthquakes and Structures
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• v.26 no.4
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• pp.299-309
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• 2024

The present paper develops application of third-order shear deformation theory (TSDT) and modified couple stress theory (MCST) to size-dependent bending analysis of a functionally graded cylindrical micro-shell. The radial and axial displacement components are described based on TSDT for more accurate analysis. The effect of small scales is accounted based on MCST. The principle of virtual work is used for derivation of bending governing equations. The solution is presented for a simply-supported boundary condition to account the influence of various important parameters such as micro length scale parameter, in-homogeneous index and some dimensionless geometric parameters such as length to radius and length to thickness ratios on the bending results. A comparative analysis is presented to examine the effect of order of employed shear deformation theory on the axial and radial displacements.

• Journal of the Korean Society of Propulsion Engineers
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• v.21 no.6
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• pp.64-72
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• 2017

The longitudinal dynamic instability which can occur in the fueling process of a space launch vehicle is called pogo. It is caused by coupling between the fuselage and propulsion system and they would be formed as a closed-loop system. so that the amplitude of the response may increase or decrease. In this paper, a mathematical model which is applicable to the systematic pogo analysis of a general launch vehicle is developed for an example of space shuttle. The formulations are composed of the linearized second-order differential equation for the propulsion system, and of the pressure, weight displacement, and generalized displacement. Those are important parameters for pogo analysis, are derived through eigenvalue analysis. By the formulation suggested in this paper, it is expected that mathematical modeling method of the pogo system can be obtained and systematic pogo stability analysis for any launch vehicle will be enabled.

• Journal of the Korean Society for Advanced Composite Structures
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• v.1 no.2
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• pp.29-35
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• 2010

In addition to the Young's modulus, the Poisson's ratio is also at the center of attention in the field stochastic finite element analysis since the parameters play an important role in determining structural behavior. Accordingly, the sole effect of this parameter on the response variability is of importance from the perspective of estimation of uncertain response. To this end, a formulation to determine the response variability in laminate composite plates due to the spatial randomness of Poisson's ratio is suggested. The independent contributions of random Poisson's ratiocan be captured in terms of sub-matrices which include the effect of the random parameter in the same order, which can be attained by using the Taylor's series expansion about the mean of the parameter. In order to validate the adequacy of the proposed formulation, several example analyses are performed, and then the results are compared with Monte Carlo simulation (MCS). A good agreement between the suggested scheme and MCS is observed showing the adequacy of the scheme.

• Structural Engineering and Mechanics
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• v.68 no.4
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• pp.409-421
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• 2018

In the present paper, functionally graded (FG) materials are presented to investigate the bending analysis of simply supported plates. It is assumed that the material properties of the plate vary through their length according to the power-law form. The displacement field of the present model is selected based on quasi-3D hyperbolic shear deformation theory. By splitting the deflection into bending, shear and stretching parts, the number of unknowns and equations of motion of the present formulation is reduced and hence makes them simple to use. Governing equations are derived from the principle of virtual displacements. Numerical results for deflections and stresses of powerly graded plates under simply supported boundary conditions are presented. The accuracy of the present formulation is demonstrated by comparing the computed results with those available in the literature. As conclusion, this theory is as accurate as other shear deformation theories and so it becomes more attractive due to smaller number of unknowns. Some numerical results are provided to examine the effects of the material gradation, shear deformation on the static behavior of FG plates with variation of material stiffness through their length.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.32 no.4
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• pp.18-23
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• 2004

In this paper, material non-linear behavior of PZT wafer(3203HD, CTS) under high electric field and stress is experimentally investigated and the non-linearity of the PZT wafer is numerically simulated. Empirical functions that can represent the non-linear behavior of the PZT wafer have been extracted based on the measured piezo-strain under stress. The functions are implemented in an incremental finite element formulation for material non-linear analysis. New definition of the piezoelectric constant and the incremental strain are incorporated into the finite element formulation for a better reproduction of the non-linear behavior. With the new definition of the in incremental piero-strain the measured non-linear behavior of the PZT wafer has been accurately reproduced even for high electric field. For validation of the measured non-linear characteristics and the proposed approach, a PZT bimorph beam actuator has been numerically and experimentally tested. The predicted actuation displacement, based on the material nonlinear finite element analysis, showed a good agreement with the measured one.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.19 no.2 s.72
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• pp.151-160
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• 2006

In this study, we propose a new efficient 2-noded hybrid-mixed element for curved beam vibrationshaving a uniform and non-uniform cross section. The present element considering transverse shear strain is based on Hellinger-Reissner variational principle and 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 then the nodeless degrees are condensed out by the Guyan reduction. In the performance evaluation process of the present field-consistent higher-order element, we carefully examine the effects of field consistency and the role of higher-order interpolation functions on the hybrid-mixed formulation. Several benchmark tests confirm e superior behavior of the present hybrid-mixed element for curved beam vibrations.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.30 no.1
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• pp.1-6
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• 2017

This paper presents development of the nine-node co-rotational(CR) planar element applicable for elastoplastic and contact analysis. The CR formulation is one of the efficient geometrically nonlinear formulations. It is based on the assumptions of small strain and large displacement. Further, it is extended to both elastoplastic analysis and contact analysis in this paper. For accurate plastic analysis, nine-node quadrilateral element, which can provide accurate stress prediction, is chosen. Bi-linear hardening rule based on Newton- Raphson return-mapping is employed. Also, Lagrange multiplier is used in order for constraints regarding the contact analysis. The present development is validated via the time transient problems. The present results are compared with those obtained by the other existing software.

• Journal of the Korean Geotechnical Society
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• v.27 no.3
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• pp.75-83
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• 2011

Emerging issues related with fully coupled Thermo-Hydro-Mechanical (THM) behavior of unsaturated soil demand the development of a numerical tool in diverse geo-mechanical and geo-environmental areas. This paper presents general governing equations for coupled THM processes in unsaturated porous media. Coupled partial differential equations are derived from three mass balances equations (solid, water, and air), energy balance equation, and force equilibrium equation. With Galerkin formulation and time integration of these governing equations, finite element code is developed to find nonlinear solution of four main variables (displacement-u, gas pressure-$P_g$), liquid pressure-$P_1$), and temperature-T) using Newton's iterative scheme. Three cases of numerical simulations are conducted and discussed: one-dimensional drainage experiments (u-$P_g-P_1$), thermal consolidation (u-$P_1$-T), and effect of pile on surrounding soil due to surface temperature variation (u-$P_1$-T).

• Computational Structural Engineering
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• v.11 no.1
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• pp.191-204
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• 1998

The general formulation for free vibration and stability analysis of unsymmetric thin-wared space frames is presented in case where the shear deformation effects are neglected. The kinetic and total potential energies are derived by applying the extended virtual work principle, introducing displacement parameters defined at the arbitrarily chosen axis and including warping deformation and second order terms of finite semitangential rotations. In formulating the finite element procedure, cubic Hermitian polynomials are utilized as shape functions of the two node space frame element. Mass, elastic stiffness, and geometric stiffness matrices for the unsymmetric thin-walled section are evaluated, and load-correction stiffness matrices for off-axis distributed loadings are considered. In order to illustrate the accuracy and practical usefulness of this formulation, finite element solutions for the free vibration and stability problems of thin-walled beam-columns and space frames are presented and compared with available solutions.