• Structural Engineering and Mechanics
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• v.90 no.1
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• pp.83-96
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• 2024

This paper suggests an analytical approach to investigate the free vibration and stability of functionally graded (FG) beams with both perfect and imperfect characteristics using a quasi-3D higher-order shear deformation theory (HSDT) with stretching effect. The study specifically focuses on FG beams resting on variable elastic foundations. In contrast to other shear deformation theories, this particular theory employs only four unknown functions instead of five. Moreover, this theory satisfies the boundary conditions of zero tension on the beam surfaces and facilitates hyperbolic distributions of transverse shear stresses without the necessity of shear correction factors. The elastic medium in consideration assumes the presence of two parameters, specifically Winkler-Pasternak foundations. The Winkler parameter exhibits variable variations in the longitudinal direction, including linear, parabolic, sinusoidal, cosine, exponential, and uniform, while the Pasternak parameter remains constant. The effective material characteristics of the functionally graded (FG) beam are assumed to follow a straightforward power-law distribution along the thickness direction. Additionally, the investigation of porosity includes the consideration of four different types of porosity distribution patterns, allowing for a comprehensive examination of its influence on the behavior of the beam. Using the virtual work principle, equations of motion are derived and solved analytically using Navier's method for simply supported FG beams. The accuracy is verified through comparisons with literature results. Parametric studies explore the impact of different parameters on free vibration and buckling behavior, demonstrating the theory's correctness and simplicity.

• Geomechanics and Engineering
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• v.37 no.5
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• pp.453-465
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• 2024

This paper presents a logarithmic shear deformation theory to study the thermal buckling response of power-law FG one-dimensional structures in thermal conditions with different boundary conditions. It is assumed that the functionally graded material and thermal properties are supposed to vary smoothly according to a contentious function across the vertical direction of the beams. A P-FG type function is employed to describe the volume fraction of material and thermal properties of the graded (1D) beam. The Ritz model is employed to solve the thermal buckling problems in immovable boundary conditions. The outcomes of the stability analysis of FG beams with temperature-dependent and independent properties are presented. The effects of the thermal loading are considered with three forms of rising: nonlinear, linear and uniform. Numerical results are obtained employing the present logarithmic theory and are verified by comparisons with the other models to check the accuracy of the developed theory. A parametric study was conducted to investigate the effects of various parameters on the critical thermal stability of P-FG beams. These parameters included support type, temperature fields, material distributions, side-to-thickness ratios, and temperature dependency.

• Journal of the Society of Naval Architects of Korea
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• v.29 no.4
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• pp.202-213
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• 1992

For the analysis and design of ship structures the generalized slope deflection method(GSDM) taking account of axial elongation effect as well as the bending and shearing deformation is developed. Using the span point concept, the existing slope deflection method is easy to transform the variable section to the equivalent uniform one under the bending moment and the shear force, but it is difficult to analyze the web frame with inclined members because the axial deformation effect is not considered. In the present method, the equilibrium conditions including all force components(i.e. axial force, shear force, bending moment) are formulated at the both ends of the variable section beam, such that the usual space frame stiffness equation which can be solved easily by the matrix method is derived. The accuracy and applicability of the present method is demonstrated by analyzing the ship web frame structures.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.18 no.4
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• pp.391-397
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• 2017

Recently, digital image correlation (DIC) techniques have been used to measure dynamic deformation during tensile testing. The standard tensile test method measures the average displacement of the relevant specimen to calculate the true stress-strain curve. Therefore, the validity of the true stress curve is restricted to the stress incurred within the uniform stretching interval, i.e., the maximum stress corresponds to the starting point of the necking deformation. Alternatively, if DIC is used, the effective range of the strain and strain rate can be extended to the breaking point of the tensile specimen, because of the feasibility of measuring the local strain over the entire area of interest. Because of these advantages, many optical 3D measurement systems have been introduced and used in research and industry. However, the conventional 3D measurement systems are exceedingly expensive and time consuming. In addition, these systems have the disadvantage of a very large equipment size which makes their transport difficult. In this study, a 2D image correction method employing a 2D DIC measurement method in conjunction with a numerical analysis method is developed using a smartphone. The results of the proposed modified 2D DIC method yielded higher accuracy than that obtained via the 3D measurement equipment. In conclusion, it was demonstrated that the proposed 2D DIC and calibration methods yield accurate measurement results with low time costs.

• Steel and Composite Structures
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• v.29 no.6
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• pp.785-802
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• 2018

In this paper, two different computational methods, called Rayleigh-Ritz and collocation are developed to estimate the ultimate strength of composite plates. Progressive damage behavior of moderately thick composite laminated plates is studied under in-plane compressive load and uniform lateral pressure. The formulations of both methods are based on the concept of the principle of minimum potential energy. First order shear deformation theory and the assumption of large deflections are used to develop the equilibrium equations of laminated plates. Therefore, Newton-Raphson technique will be used to solve the obtained system of nonlinear algebraic equations. In Rayleigh-Ritz method, two degradation models called complete and region degradation models are used to estimate the degradation zone around the failure location. In the second method, a new energy based collocation technique is introduced in which the domain of the plate is discretized into the Legendre-Gauss-Lobatto points. In this new method, in addition to the two previous models, the new model named node degradation model will also be used in which the material properties of the area just around the failed node are reduced. To predict the failure location, Hashin failure criteria have been used and the corresponding material properties of the failed zone are reduced instantaneously. Approximation of the displacement fields is performed by suitable harmonic functions in the Rayleigh-Ritz method and by Legendre basis functions (LBFs) in the second method. Finally, the results will be calculated and discussions will be conducted on the methods.

• Steel and Composite Structures
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• v.29 no.3
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• pp.319-332
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• 2018

This paper investigates the free vibration of geometrically imperfect functionally graded car-bon nanotube-reinforced composite (FG-CNTRC) beams that are integrated with two sur-face-bonded piezoelectric layers and subjected to a combined action of a uniform temperature rise, a constant actuator voltage and an in-plane force. The material properties of FG-CNTRCs are assumed to be temperature-dependent and vary continuously across the thick-ness. A generic imperfection function is employed to simulate various possible imperfections with different shapes and locations in the beam. The governing equations that account for the influence of initial geometric imperfection are derived based on the first-order shear deformation theory. The postbuckling configurations of FG-CNTRC hybrid beams are determined by the differential quadrature method combined with the modified Newton-Raphson technique, after which the fundamental frequencies of hybrid beams in the postbuckled state are obtained by a standard eigenvalue algorithm. The effects of CNT distribution pattern and volume fraction, geometric imperfection, thermo-electro-mechanical load, as well as boundary condition are examined in detail through parametric studies. The results show that the fundamental frequency of an imperfect beam is higher than that of its perfect counterpart. The influence of geometric imperfection tends to be much more pronounced around the critical buckling temperature.

• Journal of Korean Society of Steel Construction
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• v.15 no.1
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• pp.33-40
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• 2003

There are two basic concepts about concerning the buckling analysis of a buried pipe. One concept considers the soil around the pipe asn elastic continuum mediaum. The other concept holds that the pipe is sup ported by an elastic spring, which replaces the effects of the surrounding soil (the Winkler model). Theise buckling analysis is based on plane analysis, without considering the corrugation effect and the length effect. This paper thus presents a parametric study using the Finite Element Method (FEM) for the Winker model and proposes a buckling strength formula after examining a 3D analysis considering the corrugation effect and the length effect, thatwhichhelp in estimating the critical buckling strength of such CSP

• Structural Engineering and Mechanics
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• v.62 no.5
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• pp.595-606
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• 2017

During their life span, post-tensioned concrete structures may be exposed to thermal loads. Therefore, there has been a growing interest in research on the advanced analysis and design of post-tensioned concrete slabs subjected to thermal loads. This paper investigates the structural behaviour of post-tensioned one-way spanning concrete slabs. A nonlinear finite element model for the analysis of post- tensioned unbonded and bonded concrete slabs at elevated temperatures was developed. The interface between the tendon and surrounding concrete was also modelled, allowing the tendon to retain its profile shape during the deformation of the slab. The load-deflection behaviour, load-force behaviour in the tendon, and the failure modes are presented. The numerical analysis was conducted by the finite element ANSYS software and was carried out on two different one-way concrete slabs chosen from literature. A parametric study was conducted to investigate the effect of several selected parameters on the overall behavior of post-tensioned one-way concrete slab. These parameters include the effect of tendon bonding, the effect of thermal loading and the effect of tendon profile. Comparison between uniform thermal loading and nonuniform thermal loading showed that restrained post tensioned slab with bottom surface hotter has smaller failure load capacity.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1996.04a
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• pp.819-823
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• 1996

In the large steel ingosts, void defects exhibiting microvoid shapes are inevitably formed in the V-segregation zone of the ingots during solidification. In the hot open-die forging process, material properties are improved by eliminating internal porosity. The void size is practically very small as compared with the huge large ingot. Thus, for deformation analysis of a large ingot, a massive number of elements are needed in order to describe a void surface and to uniform mesh sturcture. In the present work the Global/Local scheme has been introduced in order to reduce the computational time and to easily generate the mesh system as a void module of local mesh for obtaining the accurate solution around a void. The procedure of the global- local method consists of two steps. In the first step global analysis is carried out which seeks a reasonably good solution with a cpurse mesh system without describing a void. Then, a local analysis is performed locally with a fine mesh system under the size-criterion of a local region. The computational time has been greatly reduced. Though the work it has been shown that large ingot forging incorporation small voids can be effectively analyzed by using the proposed Global/Local scheme.

• Advances in Computational Design
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• v.2 no.3
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• pp.165-194
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• 2017

The present work proposes the thermo mechanically induced statistics of nonlinear transverse central deflection of elastically supported functionally graded (FG) plate subjected to static loadings with random system properties. The FG plate is supported on two parameters Pasternak foundation with Winkler cubic nonlinearity. The random system properties such as material properties of FG material, external loading and foundation parameters are assumed as uncorrelated random variables. The material properties are assumed as non-uniform temperature distribution with temperature dependent (TD) material properties. The basic formulation for static is based on higher order shear deformation theory (HSDT) with von-Karman nonlinear strain kinematics through Newton-Raphson method. A second order perturbation technique (SOPT) and direct Monte Carlo simulation (MCS) are used to compute the nonlinear governing equation. The effects of load parameters, plate thickness ratios, aspect ratios, volume fraction, exponent, foundation parameters, and boundary conditions with random system properties are examined through parametric studies. The results of present approaches are compared with those results available in the literature and by employing direct Monte Carlo simulation (MCS).