• Steel and Composite Structures
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• v.49 no.4
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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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• v.75 no.1
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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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• v.91 no.5
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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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• v.51 no.4
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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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• v.37 no.1
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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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• v.84 no.6
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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.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.39 no.3
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• pp.261-268
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• 2011

Generally, modeling procedure of cross section of composite rotor blade is complicated and time-consuming, because it is made up of various stiffeners and multiple layers of composite materials. For efficient modeling of cross section of composite rotor blade, a modeling program so called KSec2D, which provides a user friendly GUI, is developed by using a 2D modeling algorithm based on set operation. By the developed program KSec2D, a modeling of complicated cross section of rotor blade is carried out. Through the demonstration, the usefulness of developed program in modeling procedure of cross section of composite rotor blade is verified.

• Journal of Ship and Ocean Technology
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• v.3 no.1
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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.

• Journal of Korean Society of Steel Construction
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• v.21 no.3
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• pp.321-330
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• 2009

This paper presents numerical analysis results for the lateral-torsional buckling (LTB) strength of steel I-girder bridges. Current Korean and AASHTO design specifications for LTB consider the buckling strength of a single girder with both its ends constrained. The I-girder bridges are composed of more than one girder, and the girders are interconnected with intermediate cross-beams or cross-frames. Therefore, it should be required to evaluate the effects of cross-beam stiffness and the interactionof girders on LTB strength. It is also necessary to consider the effects of transverse web stiffeners on LTB strength. By considering these parameters, a series of four-girder systemswere numerically modeled using 3D shell elements to estimate the LTB strength while considering initial imperfections and residual stresses.