• Structural Engineering and Mechanics
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• 제63권4호
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• pp.439-446
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• 2017

This work proposes an original single variable shear deformation theory to study the buckling analysis of thick isotropic plates subjected to uniaxial and biaxial in-plane loads. This theory is built upon the classical plate theory (CPT) including the exponential function in terms of thickness coordinate to represent shear deformation effect and it involves only one governing differential equation. Efficacy of the present theory is confirmed through illustrative numerical examples. The obtained results are compared with those of other higher-order shear deformation plate theory results.

• Structural Engineering and Mechanics
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• 제65권1호
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• pp.9-17
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• 2018

This study concerns about calculating exact natural frequencies of frames using a single variable shear deformation theory (SVSDT) which considers the parabolic shear stress distribution across the cross section. Free vibration analyses are performed for multi-bay, multi-storey and multi-bay multi-storey type frame structures. Dynamic stiffness formulations are derived and used to obtain first five natural frequencies of frames. Different beam and column cross sections are considered to reveal their effects on free vibration analysis. The calculated natural frequencies are tabulated with the results obtained using Euler-Bernoulli Beam Theory (EBT) and Timoshenko Beam Theory (TBT). Moreover, the effects of inner and outer columns on natural frequencies are compared for multi-bay frames. Several mode shapes are plotted.

• Structural Engineering and Mechanics
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• 제74권1호
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• pp.33-54
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• 2020

The aim of this study is to calculate natural frequencies and harmonic responses of cracked frames with general boundary conditions by using transfer matrix method (TMM). The TMM is a straightforward technique to obtain harmonic responses and natural frequencies of frame structures as the method is based on constructing a relationship between state vectors of two ends of structure by a chain multiplication procedure. A single variable shear deformation theory (SVSDT) is applied, as well as, Timoshenko beam theory (TBT) and Euler-Bernoulli beam theory (EBT) for comparison purposes. Firstly, free vibration analysis of intact and cracked frames are performed for different crack ratios using TMM. The crack is modelled by means of a linear rotational spring that divides frame members into segments. The results are verified by experimental data and finite element method (FEM) solutions. The harmonic response curves that represent resonant and anti-resonant frequencies directly are plotted for various crack lengths. It is seen that the TMM can be used effectively for harmonic response analysis of cracked frames as well as natural frequencies calculation. The results imply that the SVSDT is an efficient alternative for investigation of cracked frame vibrations especially with thick frame members. Moreover, EBT results can easily be obtained by ignoring shear deformation related terms from governing equation of motion of SVSDT.

• Structural Engineering and Mechanics
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• 제73권2호
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• pp.109-121
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• 2020

This study aims to estimate crack location and crack length in damaged beam structures using transfer matrix formulations, which are based on analytical solutions of governing equations of motion. A single variable shear deformation theory (SVSDT) that considers parabolic shear stress distribution along beam cross-section is used, as well as, Timoshenko beam theory (TBT). The cracks are modelled using massless rotational springs that divide beams into segments. In the forward problem, natural frequencies of intact and cracked beam models are calculated for different crack length and location combinations. In the inverse approach, which is the main concern of this paper, the natural frequency values obtained from experimental studies, finite element simulations and analytical solutions are used for crack identification via plots of rotational spring flexibilities against crack location. The estimated crack length and crack location values are tabulated with actual data. Three different beam models that have free-free, fixed-free and simple-simple boundary conditions are considered in the numerical analyses.

• 한국정밀공학회지
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• 제21권6호
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• pp.109-116
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• 2004

In this study, when variable-amplitude load with various applying mode acts on the pre-crack tip, we examined how fatigue cracks behave. Hence aspects of the deformation caused by changing the applying mode of single overload and propagation behavior of fatigue crack were experimentally examined: What kinds of the deformation would be formed at pre-crack and its tip\ulcorner What aspects of the residual plastic deformation field would be formed in front of a crack\ulcorner How aspects of the plastic zone could be evaluated\ulcorner As applying mode of single overloading changes, the deformation caused by tensile and shear loading variously showed in each applying mode. The different aspects of deformation make influence on propagation behavior of cracks under constant-amplitude fatigue loading after overloading with various modes. We tried to examine the relationship between aspects of deformation and fatigue behavior by comparing the observed deformation at crack and crack propagation behavior obtained from fatigue tests.

• Structural Engineering and Mechanics
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• 제68권2호
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• pp.183-191
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• 2018

In this paper, harmonic responses of infilled multi-storey frames are obtained by using a single variable shear deformation theory (SVSDT) and dynamic stiffness formulations. Two different planar frame models are used which are fully infilled and soft storey. The infill walls are modeled by using equivalent diagonal strut approach. Firstly, free vibration analyses of bare frame and infilled frames are performed. The calculated natural frequencies are tabulated with finite element solution results. Then, harmonic response curves (HRCs) of frame models are plotted for different infill wall thickness values. All of the results are presented comparatively with Timoshenko beam theory results to reveal the effectiveness of SVSDT which considers the parabolic shear stress distribution along the frame member cross-sections.

• Structural Engineering and Mechanics
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• 제67권3호
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• pp.291-300
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• 2018

In this work, a new trigonometry theory of shear deformation is developed for the static analysis of thick isotropic beams. The number of variables used in this theory is identical to that required in the theory of Euler-Bernoulli, sine function is used in the displacement field in terms of the coordinates of the thickness to represent the effects of shear deformation. The advantage of this theory is that shear stresses can be obtained directly from the relationships constitute, while respecting the boundary conditions at the free surface level of the beam. Therefore, this theory avoids the use of shear correction coefficients. The differential equilibrium equations are obtained using the principle of virtual works. A thick isotropic beam is considered, whose numerical study to show the effectiveness of this theory.

• Advances in nano research
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• 제10권1호
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• pp.15-24
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• 2021

Microtubules (MTs) are the main part of the cytoskeleton in living eukaryotic cells. In this article, a mechanical model of MT buckling, considering the modified strain gradient theory, is analytically examined. The MT is assumed as a cylindrical beam and a new single variable trigonometric beam theory is developed in conjunction with a modified strain gradient model. The main benefit of the present formulation is shown in its new kinematic where we found only one unknown as the Euler-Bernoulli beam model, which is even less than the Timoshenko beam model. The governing equations are deduced by considering virtual work principle. The effectiveness of the present method is checked by comparing the obtained results with those reported by other higher shear deformation beam theory involving a higher number of unknowns. It is shown that microstructure-dependent response is more important when material length scale parameters are closer to the outer diameter of MTs. Also, it can be confirmed that influences of shear deformation become more considerable for smaller shear modulus and aspect ratios.

• Steel and Composite Structures
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• 제48권5호
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• pp.583-597
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• 2023

This paper introduces a novel approach to multi-material topology optimization (MTO) targeting in-plane bi-directional functionally graded (IBFG) non-uniform thickness Reissner-Mindlin plates, employing an alternative active phase approach. The mathematical formulation integrates a first shear deformation theory (FSDT) to address compliance minimization as the objective function. Through an alternating active-phase algorithm in conjunction with the block Gauss-Seidel method, the study transforms a multi-phase topology optimization challenge with multi-volume fraction constraints into multiple binary phase sub-problems, each with a single volume fraction constraint. The investigation focuses on IBFG materials that incorporate adequate local bulk and shear moduli to enhance the precision of material interactions. Furthermore, the well-established mixed interpolation of tensorial components 4-node elements (MITC4) is harnessed to tackle shear-locking issues inherent in thin plate models. The study meticulously presents detailed mathematical formulations for IBFG plates in the MTO framework, underscored by numerous numerical examples demonstrating the method's efficiency and reliability.

• 한국구조물진단유지관리공학회 논문집
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• 제28권1호
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• pp.39-45
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• 2024

경주 및 포항지진으로 인한 지하매설배관의 파열 및 누수가 발생하여 내진 안전성 확보의 중요성이 증대되고 있다. 배관시스템의 내진 확보를 위해 금속 벨로우즈 신축관이음이 적용되고 있다. 금속 벨로우즈는 일련의 주름 형상으로 제작되어 비교적 낮은 강성으로 유연하게 변형으로부터 대응한다. 금속 벨로우즈의 목적에 따라 다양한 주름 형상과 겹 수로 제작되고 이와 관련한 다양한 연구가 수행되었다. 하지만 산높이가 복합적인 벨로우즈의 전단 거동에 대한 내진성능을 평가한 연구는 미비하다. 따라서 본 연구는 복합적인 산 높이로 구현된 벨로우즈의 전단 내진성능을 분석하기 위한 단조하중실험, 점증반복하중실험 및 피로반복실험을 수행하였다. 실험은 한 겹 및 세 겹으로 제작된 벨로우즈를 대상으로 수행하였으며, 한 겹 보다 세 겹으로 제작된 벨로우즈의 최대 변형 및 피로 수명이 높은 것으로 평가되었다. 하지만 세 겹의 벨로우즈는 내압에 비해 높은 강성으로 주름산의 변형이 더 낮은 변위에서 발생하며, 복합적인 주름산의 높이와 관련하여 특정 조건에서는 누수가 빠르게 발생하였다. 피로 수명은 낮은 변형률에서 많은 겹 수의 벨로우즈가 높게 평가되었고, 높은 변형률에서는 동일한 피로 수명으로 수렴하였다.