• Coupled systems mechanics
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• v.10 no.1
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• pp.79-102
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• 2021

In this paper we deal with instability problems of structures under nonconservative loading. It is shown that such class of problems should be analyzed in dynamics framework. Next to analytic solutions, provided for several simple problems, we show how to obtain the numerical solutions to more complex problems in efficient manner by using the finite element method. In particular, the numerical solution is obtained by using a modified Euler-Bernoulli beam finite element that includes the von Karman (virtual) strain in order to capture linearized instabilities (or Euler buckling). We next generalize the numerical solution to instability problems that include shear deformation by using the Timoshenko beam finite element. The proposed numerical beam models are validated against the corresponding analytic solutions.

• Structural Engineering and Mechanics
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• v.59 no.2
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• pp.343-371
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• 2016

In this paper thermo-mechanical vibration analysis of a porous functionally graded (FG) Timoshenko beam in thermal environment with various boundary conditions are performed by employing a semi analytical differential transform method (DTM) and presenting a Navier type solution method for the first time. The temperature-dependent material properties of FG beam are supposed to vary through thickness direction of the constituents according to the power-law distribution which is modified to approximate the material properties with the porosity phases. Also the porous material properties vary through the thickness of the beam with even and uneven distribution. Two types of thermal loadings, namely, uniform and linear temperature rises through thickness direction are considered. Derivation of equations is based on the Timoshenko beam theory in order to consider the effect of both shear deformation and rotary inertia. Hamilton's principle is applied to obtain the governing differential equation of motion and boundary conditions. The detailed mathematical derivations are presented and numerical investigations are performed while the emphasis is placed on investigating the effect of several parameters such as porosity distributions, porosity volume fraction, thermal effect, boundary conditions and power-low exponent on the natural frequencies of the FG beams in detail. It is explicitly shown that the vibration behavior of porous FG beams is significantly influenced by these effects. Numerical results are presented to serve benchmarks for future analyses of FG beams with porosity phases.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.11 no.11
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• pp.4635-4642
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• 2010

Latex modification of concrete provides the material with higher flexural strength, as well as high bond strength and reduced water permeability. One of the most advantages of the very early-strength latex-modified concrete (VES-LMC) could be the similar contraction and expansion behaviour to normal concrete substrate, which enable to ensure long-term performance. The purpose of this study was to parametric nonlinear flexural nonlinear analysis of RC beam rehabilitated by VES-LMC. The results were as follows; The flexural nonlinear analysis model of RC beam overlaid by VES-LMC in ABAQUS was proposed to predict the load-deflection response, interfacial stress, and ultimate strength. The proposed FE analysis model was verified by comparison of an experimental data and the FE analysis results. The FE analysis results showed that yield point as well as flexural stiffness increased as the depth increased; the stiffness of beam overall increased as the bond stiffness became larger; the bond strength between two different materials is a key factor in composite beam. A parametric study showed that an overlay thickness was a main influencing factor to the behavior of RC beam overlaid by VES-LMC.

• Composites Research
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• v.22 no.5
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• pp.24-29
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• 2009

In this paper, a post-tensioned reinforced concrete slab was analyzed by the specially orthotropic laminates theory. Both the geometrical and material property of the cross section of the slab was considered symmetrically with respect to the neutral surface so that the bending extension coupling stiffness, $B_{ij}=0$, and $D_{16}=D_{26}=0$. Reinforced concrete slab behave as specially orthotropic plates. In general, the analytical solution for such complex systems is very difficult to obtain. Thus, finite difference method was used for analysis of the problem. In this paper, the finite difference method and the beam theory were used for analysis. The result of beam analysis was modified to obtain the solution of the plate analysis.

• Advances in materials Research
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• v.12 no.2
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• pp.133-159
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• 2023

In this paper, a size-dependent dynamic investigation of a porous metal foams microbeamsis presented. The novelty of this study is to use a metal foam microbeam that contain porosities based on the refined high order shear deformation beam model, with sinusoidal shear strain function, and the modified strain gradient theory (MSGT) for the first time. The Lagrange's principle combined with differential quadrature hierarchicalfinite element method (DQHFEM) are used to obtain the porous microbeam governing equations. The solutions are presented for the natural frequencies of the porous and homogeneoustype microbeam. The obtained results are validated with the analytical methods found in the literature, in order to confirm the accuracy of the presented resolution method. The influences of the shape of porosity distribution, slenderness ratio, microbeam thickness, and porosity coefficient on the free vibration of the porous microbeams are explored in detail. The results of this paper can be used in various design formetallic foammicro-structuresin engineering.

• Smart Structures and Systems
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• v.19 no.3
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• pp.309-322
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• 2017

In this paper, the buckling, and free vibration analysis of tapered functionally graded carbon nanotube reinforced composite (FG-CNTRC) micro Reddy beam under longitudinal magnetic field using finite element method (FEM) is investigated. It is noted that the material properties of matrix is considered as Poly methyl methacrylate (PMMA). Using Hamilton's principle, the governing equations of motion are derived by applying a modified strain gradient theory and the rule of mixture approach for micro-composite beam. Micro-composite beam are subjected to longitudinal magnetic field. Then, using the FEM, the critical buckling load, and natural frequency of micro-composite Reddy beam is solved. Also, the influences of various parameters including ${\alpha}$ and ${\beta}$ (the constant coefficients to control the thickness), three material length scale parameters, aspect ratio, different boundary conditions, and various distributions of CNT such as uniform distribution (UD), unsymmetrical functionally graded distribution of CNT (USFG) and symmetrically linear distribution of CNT (SFG) on the critical buckling load and non-dimensional natural frequency are obtained. It can be seen that the non-dimensional natural frequency and critical buckling load decreases with increasing of ${\beta}$ for UD, USFG and SFG micro-composite beam and vice versa for ${\alpha}$. Also, it is shown that at the specified value of ${\alpha}$ and ${\beta}$, the dimensionless natural frequency and critical buckling load for SGT beam is more than for the other state. Moreover, it can be observed from the results that employing magnetic field in longitudinal direction of the micro-composite beam increases the natural frequency and critical buckling load. On the other hands, by increasing the imposed magnetic field significantly increases the stability of the system that can behave as an actuator.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.11
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• pp.2922-2931
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• 1994

We propose a modified 6-node element, where the sampling point of Gauss quadrature moved in the thickness direction. The modified 6-node element has been applied to static problems and forced motion analyses. In this study, this method is extended to the finite element analysis of the natural frequencies of two dimensional problems. We also propose a modified 16-node element for three dimensional problems, which behaves much like a 20-node element with smaller degree of freedom. The modified 6-node and 16-node elements have been applied to the modal analyses of beams and plates, respectively. The results agree well with the results of the 8-node or 20-node element models.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.19 no.2
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• pp.191-197
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• 2010

In spite of a large amount of previous research, detail study on modified mass in proportional damping system is not well understood. It is common to predict structural dynamic design parameters due to the change of mass, but to predict the amount of modified mass and the location where the mass is being modified are rarely found in previous literature. Such inverse problem required detail analytical study in order to understand structural modification in proportional damping system. This paper predicts the modified mass and the modified mass location in proportional damping system using sensitivity coefficients and iterative method. The sensitivity coefficients are obtained from the change of eigenvectors due to mass modification. This method is applied to a horizontal beam and three degree of freedoms system. To validate the predicted changing mass and its location, the obtained results are compared to the reanalysis result which shows good agreement.

• Proceedings of the Korea Concrete Institute Conference
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• 2004.11a
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• pp.425-428
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• 2004

Nonlinear finite element analysis is conducted to predict the structural behavior of precast concrete column and steel beam connected by using bolted connections. The Nonlinear FEM program is based on the modified compression field theory which has good accuracy in the concrete structures. The link element is properly used to model the discontinuity between precast concrete column and steel beam. Predictions from the proposed model are compared with experimental results and it is concluded that structural behaviors of the composite structures, such as strength capacity, crack pattern and failure mode, can be predicted quite successfully.

• Computers and Concrete
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• v.30 no.3
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• pp.185-196
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• 2022

In this paper, the dynamic characteristics of a composite cylindrical beam made of a mechanism of carbon dioxide absorption coated on the tube core are investigated based on the classical beam theory coupled with the modified couple stress theory. The composite tube structures are assumed to be uniform along the tube length, and the energy method regarding the Hamilton principle is utilized for generating the governing equations. A powerful numerical solution, the generalized differential quadrature method (GDQM), is employed to solve the differential equations. The carbon dioxide trapping mechanism is a composite consisting of a polyacrylonitrile substrate and a cross-link polydimethylsiloxane gutter layer. Methacrylate, poly (ethylene glycol), methyl ether methacrylate, and three pedant methacrylates are all taken into account as potential mechanisms for capturing carbon dioxide. The application of the present study is helpful in the design and production of microelectromechanical systems (MEMS) and the different valuable parameters, such as the length-scale parameter, rate of section change, aspect ratio, etc., are presented in detail.