• Steel and Composite Structures
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• 제49권4호
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• pp.419-430
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• 2023

This paper is aimed at investigating the effect of multiple longitudinal stiffeners on the patch loading resistance of slender steel plate girders. Firstly, a numerical study is conducted through geometrically and materially nonlinear analysis with imperfections included (GMNIA), the model is validated with experimental results taken from the literature. The structural responses of girders with multiple longitudinal stiffeners are compared to the one of girders with a single longitudinal stiffener. Thereafter, a patch loading resistance model is developed through machine learning (ML) using symbolic regression (SR). An extensive numerical dataset covering a wide range of bridge girder geometries is employed to fit the resistance model using SR. Finally, the performance of the SR prediction model is evaluated by comparison of the resistances predicted using available formulae from the literature.

• Structural Engineering and Mechanics
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• 제75권1호
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• pp.87-100
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• 2020

The present paper investigates the combination resonance behavior of imperfect spiral stiffened functionally graded (SSFG) cylindrical shells with internal and external functionally graded stiffeners under two-term large amplitude excitations. The structure is embedded within a generalized nonlinear viscoelastic foundation, which is composed of a two-parameter Winkler-Pasternak foundation augmented by a Kelvin-Voigt viscoelastic model with a nonlinear cubic stiffness, to account for the vibration hardening/softening phenomena and damping considerations. With regard to classical plate theory of shells, von-Kármán equation and Hook law, the relations of stress-strain are derived for shell and stiffeners. The spiral stiffeners of the cylindrical shell are modeled according to the smeared stiffener technique. According to the Galerkin method, the discretized motion equation is obtained. The combination resonance is obtained by using the multiple scales method. Finally, the influences of the stiffeners angles, foundation type, the nonlinear elastic foundation coefficients, material distribution, and excitation amplitude on the system resonances are investigated comprehensively.

• Structural Engineering and Mechanics
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• 제91권5호
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• pp.503-516
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• 2024

The present research examines the primary resonance (PR) behaviors of oblique stiffened multilayer functionally graded (OSMFG) shallow shells featuring an FG porous (FGP) core under an external excitation. The research considers two distinct types of FGP cores: one characterized by uniform porosity distribution (UPD) and the other by non-uniform porosity distribution (NPD) along the thickness direction. Furthermore, the study explores two types of shallow shells: one with external oblique stiffeners and one with internal oblique stiffeners, which might have angles that are similar or different from each other. Using the stress function alongside the first-order shear deformation theory (FSDT), the research establishes a nonlinear model for OSMFG shallow shells. The strain-displacement relationships are obtained utilizing FSDT and von-Kármán's geometric assumptions. The Galerkin approach is utilized to discretize the nonlinear governing equations, allowing for the analysis of stiffeners at varied angles. To validate the obtained results, a comparison is made not only with the findings of previous research but also with the response of PR obtained theoretically with the method of multiple scales, using the P-T method. Renowned for its superior accuracy and reliability, the P-T method is deemed an apt selection within this framework. Additionally, the study investigates how differences in material characteristics and stiffener angles affect the system's PR behaviors. The results of this study can be used as standards by engineers and researchers working in this area, and they can offer important information for the design and evaluation of the shell systems under consideration.

• Steel and Composite Structures
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• 제51권4호
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• pp.391-406
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• 2024

The present research investigates the combination resonance behaviors of porous FG shallow shells reinforced with oblique stiffeners and subjected to a two-term excitation. The oblique stiffeners considered in this research reinforce the shell internally and externally. To model the stiffeners, Lekhnitskii's smeared stiffeners technique is utilized. According to the first-order shear deformation theory (FSDT) and stress functions, a nonlinear model of the oblique stiffened shallow shell is established. With regard to the FSDT and von-Kármán nonlinear geometric assumptions, the stress-strain relationships for the present shell system are developed. Also, in order to discretize the nonlinear governing equations, the Galerkin method is implemented. To obtain the required relations for investigating the combination resonance theoretically, the method of multiple scales is applied. For verifying the results of the present research, generated results are compared with previous research. Additionally, a comparison with the P-T method is conducted to increase the validity of the generated results, as this method has illustrated advantages over other numerical methods in terms of accuracy and reliability. In this method, the piecewise constant argument is used jointly with the Taylor series expansion, which is why it is named the P-T method. The effects of stiffeners with different angles, and the effects of material parameters on the combination resonance behaviors of the present system are addressed. With the findings of this research, researchers and engineers in this field may use them as benchmarks for their design and research of porous FG shallow shells.

• Steel and Composite Structures
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• 제37권1호
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• pp.51-73
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• 2020

The present paper investigates the simultaneous resonance behavior of spiral stiffened multilayer functionally graded (SSMFG) cylindrical shells with internal and external functionally graded stiffeners under the two-term large amplitude excitations. The structure is embedded within a generalized nonlinear viscoelastic foundation which is composed of a two-parameter Winkler-Pasternak foundation augmented by a Kelvin-Voigt viscoelastic model with a nonlinear cubic stiffness. The cylindrical shell has three layers consist of ceramic, FGM, and metal. The exterior layer of the cylindrical shell is rich ceramic while the interior layer is rich metal and the functionally graded material layer is located between these layers. With regard to classical shells theory, von-Kármán equation, and Hook law, the relations of stress-strain are derived for shell and stiffeners. The spiral stiffeners of the cylindrical shell are modeled according to the smeared stiffener technique. According to the Galerkin method, the discretized motion equation is obtained. The simultaneous resonance is obtained using the multiple scales method. Finally, the influences of different material and geometrical parameters on the system resonances are investigated comprehensively.

• Structural Engineering and Mechanics
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• 제84권6호
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• pp.767-782
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• 2022

In this paper, the nonlinear vibration behavior of the spiral stiffened multilayer functionally graded (SSMFG) cylindrical shells exposed to the thermal environment and a uniformly distributed harmonic loading using a semi-analytical method is investigated. The cylindrical shell is surrounded by a nonlinear viscoelastic foundation consisting of a two-parameter Winkler-Pasternak foundation augmented by a Kelvin-Voigt viscoelastic model with a nonlinear cubic stiffness. The distribution of temperature and material constitutive of the stiffeners are continuously changed through the thickness direction. The cylindrical shell has three layers consisting of metal, FGM, and ceramic. The interior layer of the cylindrical shell is rich in metal, while the exterior layer is rich in ceramic, and the FG material is located between two layers. The nonlinear vibration problem utilizing the smeared stiffeners technique, the von Kármán equations, and the Galerkin method has been solved. The multiple scales method is utilized to examine the nonlinear vibration behavior of SSMFG cylindrical shells. The considered resonant case is 1:3:9 internal resonance and subharmonic resonance of order 1/3. The influences of different material and geometrical parameters on the vibration behavior of SSMFG cylindrical shells are examined. The results show that the angles of stiffeners, temperature, and elastic foundation parameters have a strong effect on the vibration behaviors of the SSMFG cylindrical shells.

• 한국항공우주학회지
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• 제39권3호
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• pp.261-268
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• 2011

복합재료 로터 블레이드는 각종 보강재와 더불어 적층된 형태로 구성되어 있어 그 단면 구조가 매우 복잡하고, 이로 인해 모델링에 어려움이 존재한다. 본 논문에서는 효율적인 로터 블레이드 단면 모델링을 위해 집합 연산에 기반 한 2차원 모델링 알고리듬을 활용하여 그래픽 사용자 환경을 갖춘 프로그램 KSec2D를 구현하였다. 구현된 프로그램을 이용하여 복잡한 로터 블레이드 단면 형상 모델링을 수행하고 이를 통해 복합재료 로터블레이드 모델링 시 개발된 프로그램의 유용성을 확인하였다.

• Journal of Ship and Ocean Technology
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• 제3권1호
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• pp.27-41
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• 1999

The objective of the paper is to study the impact of changing the traditional hull design of bulk carriers by providing them with a double hull while keeping the same deadweight. It is demonstrated that by introducing the double hull the structural reliability is increased throughout the entire life and also the extend of the needed repair is reduced. The results are obtained with recently developed mathematical tools for the reliability assessment of ship hulls subjected to the existence of multiple cracks both in the stiffeners and in the plating and it models the crack growth process. The effect of corrosion is represented as time dependent. The long-term stress range acting on the elements is defined as a function of the local transverse pressure of the internal cargo and outside sea water combined with the stresses resulting from the longitudinal bending of the hull, which is a combined with the stresses resulting from the longitudinal bending of the hull, which is a combineation of horizontal and vertical bending moments. The effect of maintenance actions is modelled as a stochastic process. The results show that a different design of the midship section improves the structural safety and also the economy with respect to structural repair of bulk carriers.

• 한국강구조학회 논문집
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• 제21권3호
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• pp.321-330
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• 2009

본 연구에서는 I-단면 플레이트거더교의 횡비틀림 좌굴강도 평가를 위한 해석적 연구를 수행하였다. 현재 국내 및 AASHTO 설계 기준에서 횡비틀림 좌굴강도는 양단의 변위가 구속된 단일 거더의 좌굴강도 식을 근거로 하고 있다. 그러나, I-단면 강교의 주거더는 한 개 이상으로 구성되고 중간가로보 또는 수직브레이싱으로 서로 연결되므로, 가로보의 휨강성과 주거더의 상호 효과를 고려한 횡좌굴강도의 평가가 필요하다. 또한, 중간가로보가 부착되는 수직보강재의 강성이 복부판의 뒤틀림과 연계하여 횡좌굴강도에 미치는 영향의 평가가 필요하다. 이에, 4-거더교에서 중간가로보 및 수직보강재의 소요 강성을 평가하기 위해 초기처짐 및 잔류응력을 고려한 3차원 쉘요소 모델을 이용하여 재료 및 기하 비선형해석을 수행하고 그 결과를 제시하였다.