• 대한조선학회지
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• 제17권1호
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• pp.1-10
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• 1980

The nonlinear analysis of ship plating with flat bar stiffners has been carried out by the finite element method based on the load incremental approach. The large deflection analysis has been done by using the Lagrangian description. The elastoplastic analysis has been performed by adopting the flow theory of plasticity and the von Mises yield condition. The layered elements are used to show the process of yielding through the plate thickness in the elasto-plastic analysis. The following results are obtained; 1) According to the large deflection analysis, it is shown that the small deflection theory to the plate is applicable in the range of the lateral deflection-the thickness ratio $w/h{\leqq}0.3$ and ship plating in the range of $w/h{\leqq}0.5$. 2) By means of the elasto-plastic analysis, it is found that the maximum load-carrying capacity of the plate increases as much as 1.8 times of the initial yield load in the case of the simply supported condition and 2.2 times in the clamped condition. It is also shown that the maximum load-carrying capacity of ship plating increase as much as 4.3 times in the simply supported condition and 4.2 times in the clamped condition. This method would be applied and extended to solve combined nonlinear problems which involve both material nonlinearity and geometric nonlinearity.

• Steel and Composite Structures
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• 제42권1호
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• pp.23-32
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• 2022

In this paper, a nonlinear numerical method to solve the large deflection problem is introduced. And the non-dimensional load-deflection behavior of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) plates is parametrically investigated. The large deflection problem is formulated according to the von Kármán nonlinear theory and the (1,1,0)^* hierarchical model, and it is approximated by 2-D natural element method (NEM). The shear locking phenomenon is suppressed by the selectively reduced integration method. The nonlinear matrix equations are solved by combining the incremental loading scheme and the Newton-Raphson iteration method. The proposed method is validated from the benchmark experiments, where the propose method shows an excellent agreement with the reference methods. The nonlinear behavior of FG-CNTRC plates is evaluated in terms of the non-dimensional load-deflection curve, and it is parametrically investigated with respect to the existence/non-existence and gradient pattern of CNTs, the width-to-thickness and aspect ratios of plates and the type of boundary conditions. The non-dimensional central deflection is significantly reduced when CNTs and added, and it decreases with the volume fraction of CNTs. But, it shows a uniform increase in proportion to the width-to-thickness and aspect ratios. Both the gradient pattern of CNTs and the type of boundary conditions do also show the remarkable effects.

• Structural Engineering and Mechanics
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• 제67권3호
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• pp.255-265
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• 2018

The prestress force effect on the fundamental frequency and deflection shape of Prestressed Concrete I (PCI) beams was studied in this paper. Currently, due to the conflicts among existing theories, the analytical solution for properly considering the structural behavior of these prestressed members is not clear. A series of experiments were conducted on a large-scale PCI beam of high strength concrete with an eccentric straight unbonded tendon. Specifically, the simply supported PCI beam was subjected to free vibration and three-point bending tests with different prestress forces. Subsequently, the experimental data were compared with analytical results based on the Euler-Bernoulli beam theory. It was proved that the fundamental frequency of PCI beams is unaffected by the increasing applied prestress force, if the variation of the initial elastic modulus of concrete with time is considered. Vice versa, the relationship between the deflection shape and prestress force is well described by the magnification factor formula of the compression-softening theory assuming the secant elastic modulus.

• 대한기계학회논문집
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• 제10권6호
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• pp.976-981
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• 1986

본 연구에서는 판의 대변형이론을 도입하여 탱크저판의 두께, 탱크의 높이, 돌출부의 길이 등의 기하학적변수와 중심과 구석의 침하차를 무차원하여 이것들의 영 향으로 인한 처짐곡선과 반경 및 원주방향의 막력의 변화를 규명해보고자 한다. 또 한, 좌굴에 관한 8계미분방정식을 도입하여 셸 하단부의 전단력으로 인한 원통셸의 임 계좌굴력을 구하여 원통 셸의 안전성을 검토하고자 한다.

• Advances in Computational Design
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• 제7권2호
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• pp.99-112
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• 2022

This research has been devoted to examine nonlinear static bending analysis of smart beams with nano dimension exposed to thermal environment. The beam elastic properties are corresponding to piezo-magnetic material of different compositions. The large deflection analysis of the beam has been performed assuming that the beam is exposed to transverse uniform pressure. Based on the rule of Hamilton, the governing equations have been derived for a nonlocal thin beam and solved using differential quadrature method. Temperature variation effect on nonlinear deflection of the smart beams has been studied. Also, the beam deflection is shown to be affected by electric voltage, magnetic intensity and material composition.

• Coupled systems mechanics
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• 제12권4호
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• pp.391-407
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• 2023

This paper presents a static study of a rectangular functional graded material (FGM) plate, simply supported on its four edges, adopting a refined higher order theory that looks for, only,four unknowns,without taking into account any corrective factor of the deformation energy with the satisfaction of the zero shear stress conditions on the upper and lower faces of the plate. We will have determined the contribution of these stresses in the transverse deflection of the plate, as well as their effects on the axial stress within the interfaces between the layers(to avoid any problem of imperfections such as delamination) and on the top and bottom edges of the plate in order to take into account the fatigue phenomenon when choosing the distribution law of the properties used during the design of the plate. A numerical statement, in percentage, of the contribution of the shear effect is made in order to show the reliability of the adopted theory. We will also have demonstrated the need to add the shear effect when the aspect ratio is small or large. Code routines are programmed to obtain numerical results illustrating the validity of the model proposed in the theory compared to those available in the literature.

• Structural Engineering and Mechanics
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• 제19권4호
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• pp.413-423
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• 2005

This paper presents the solution of large static deflection due to uniformly distributed self weight and the critical or maximum applied uniform loading that a simply supported beam with variable-arc-length can resist. Two analytical approaches are presented and validated experimentally. The first approach is a finite-element discretization of the span length based on the variational formulation, which gives the solution of large static sag deflections for the stable equilibrium case. The second approach is the shooting method based on an elastica theory formulation. This method gives the results of the stable and unstable equilibrium configurations, and the critical uniform loading. Experimental studies were conducted to complement the analytical results for the stable equilibrium case. The measured large static configurations are found to be in good agreement with the two analytical approaches, and the critical uniform self weight obtained experimentally also shows good correlation with the shooting method.

• 한국공간구조학회논문집
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• 제6권4호
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• pp.53-61
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• 2006

본 연구에서는 임의의 반복하중 작용시 강구조물에 발생하는 대변형 및 반복소성거동을 정확히 예측하기 위하여 유한변위이론과 반복소성이력모델을 적용한 3차원 탄소성 유한요소 해석기법을 개발하였다. 반복소성이력모델은 강재의 단조재하실험 및 반복하중실험 결과에 기초하여 정식화되었다. 개발된 해석기법의 정도는 Bilinear모델 및 미소변위이론을 적용한 해석기법 및 실험결과와 비교하여 검증하였다. 본 연구에서 개발한 유한변위이론과 반복소성이력모델을 적용한 3차원 유한요소 해석기법이 임의의 반복하중을 받는 원형강교각의 대변형 및 반복소성거동을 정확히 예측할 수 있음을 알 수 있었다.

• Structural Engineering and Mechanics
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• 제20권4호
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• pp.405-420
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• 2005

In this paper, a hybrid/mixed nonlinear shell element is developed in polar coordinate system based on Hellinger/Reissner variational principle and the large-deflection theory of plate. A numerical solution scheme is formulated using the hybrid/mixed finite element method (HMFEM), in which the nodal values of bending moments and the deflection are the unknown discrete parameters. Stability of the present element is studied. The large-deflection analyses are performed for simple supported and clamped circular plates under uniformly distributed and concentrated loads using HMFEM and the traditional displacement finite element method. A parametric study is also conducted in the research. The accuracy of the shell element is investigated using numerical computations. Comparisons of numerical solutions are made with theoretical results, finite element analysis and the available numerical results. Excellent agreements are shown.

• Structural Engineering and Mechanics
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• 제1권1호
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• pp.87-102
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• 1993

A $C^{\circ}$ continuous finite element formulation of a higher order displacement theory is presented for predicting linear and geometrically non-linear in the sense of von Karman transient responses of composite and sandwich plates. The displacement model accounts for non-linear cubic variation of tangential displacement components through the thickness of the laminate and the theory requires no shear correction coefficients. In the time domain, the explicit central difference integrator is used in conjunction with the special mass matrix diagonalization scheme which conserves the total mass of the element and included effects due to rotary inertia terms. The parametric effects of the time step, finite element mesh, lamination scheme and orthotropy on the linear and geometrically non-linear responses are investigated. Numerical results for central transverse deflection, stresses and stress resultants are presented for square/rectangular composite and sandwich plates under various boundary conditions and loadings and these are compared with the results from other sources. Some new results are also tabulated for future reference.