• 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.

• Structural Engineering and Mechanics
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• v.89 no.1
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• pp.33-46
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• 2024

The present research delves into the analysis of nonlinear free and forced vibrations of porous functionally graded (FG) shallow shells reinforced with oblique stiffeners, which are embedded in a nonlinear elastic foundation (NEF) subjected to external excitation. Two distinct types of PFG shallow shells, characterized by even and uneven porosity distribution along the thickness direction, are considered in the research. In order to model the stiffeners, Lekhnitskii's smeared stiffeners technique is implemented. With the stress function and first-order shear deformation theory (FSDT), the nonlinear model of the oblique stiffened shallow shells is established. The strain-displacement relationships for the system are derived via the FSDT and utilization of the von-Kármán's geometric assumptions. To discretize the nonlinear governing equations, the Galerkin method is employed. The model such developed allows analysis of the effects of the stiffeners with various angles as desired, in addition to the quantitative investigation on the influence of the surrounding nonlinear elastic foundations. To numerically solve the problem of vibrations, the 4th-order P-T method is used, as this method, known for its enhanced accuracy and reliability, proves to be an effective choice. The validation of the present research findings includes a comprehensive comparison with outcomes documented in existing literature. Additionally, a comparative analysis of the numerical results against those obtained using the 4th Runge-Kutta method is performed. The impact of stiffeners with varying angles and material parameters on the vibration characteristics of the present system is also explored. The researchers and engineers working in this field may use the results of this study as benchmarks in their design and research for the considered shell systems.

• Bulletin of the Society of Naval Architects of Korea
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• v.20 no.4
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• pp.9-16
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• 1983

When the perforated panels are under in-plane shear loads, shear buckling analysis is also necessary because of the presence of stress concentration around holes. To constrain it, we need some reinforcement. The methods of reinforcement are attaching doubler around hole and stiffeners in the arbitary directions. In this paper, two kinds of methods mentioned above are investigated, it is also clarified that which of the two is the more effective reinforcement. For the sake of convenience those arbitary directions were selected parallel ($90^{\circ}$) and oblique ($135^{\circ}$) to the edge. From the results of the above investigation, following conclusion was obtained. In case of parallel stiffeners, doubler reinforcement gives higher buckling strength than stiffener, however, in case of oblique stiffeners, doubler reinforcement gives higher buckling strength than doubler when the external load direction is known.

• Transactions of the Korean Society of Mechanical Engineers
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• v.14 no.5
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• pp.1059-1068
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• 1990

The minimum weight design for the simply-supported eccentrically stiffened plates subjected to combined loads is studied according to the stiffening configuration. The optimal programming is accomplished by formulating the design requirements in terms of a mathematical programming problem, and by using the gradient projection algorithm. The Huber type equilibrium equation is used as the governing equation for the overall buckling. The overall buckling of stiffened plates and the local buckling of the unstiffened plate between stiffeners and the stiffeners themselves are used as behavior constraints. Results of design examples for the orthogonally stiffening case compared with those of the other study support that the present study is feasible. Design examples for the symmetrically oblique stiffening case are presented and the results indicate that a significant improvement in design efficiency may be achieved through symmetrically oblique stiffening compared to the orthogonal stiffening under the combined loading condition.

• Bulletin of the Society of Naval Architects of Korea
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• v.22 no.1
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• pp.9-20
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• 1985

Generally the stiffened plate in the ship structure is subjected to not only axial load but shear load. With respect to those combined loads buckling analysis in necessary. In this paper, buckling strength is analyzed by using Finite Element Method when the stiffened plate with hole is under loading conditions mentioned above. To obtain the higher buckling strength, we need some reinforcement. The methods of reinforcement are attaching doubler around hole and stiffeners in the arbitrary directions For the sake of convenience those arbitrary directions were selected paralleled($0^{\circ}C$), vertical($90^{\circ}C$)and oblique($45^{\circ}C$) to the edge. Two kinds of method mentioned above are investigated, it is clarified that which of the two is more effective reinforcement. From the viewpoint of buckling strength, following conclusions were obtained. When external load direction is unknown, doubler reinforcement is more effective than those of parallel and vertical stiffener. And oblique stiffener reinforcement is more effective than that of doubler when external load direction is know.