• Steel and Composite Structures
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• 제20권2호
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• pp.379-397
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• 2016

Due to creep and shrinkage of the concrete core, concrete-filled steel tubular (CFST) arches continue to deform in the long-term under sustained loads. This paper presents analytical investigations of the effects of geometric nonlinearity on the long-term in-plane structural performance and stability of three-pinned CFST circular arches under a sustained uniform radial load. Non-linear long-term analysis is conducted and compared with its linear counterpart. It is found that the linear analysis predicts long-term increases of deformations of the CFST arches, but does not predict any long-term changes of the internal actions. However, non-linear analysis predicts not only more significant long-term increases of deformations, but also significant long-term increases of internal actions under the same sustained load. As a result, a three-pinned CFST arch satisfying the serviceability limit state predicted by the linear analysis may violate the serviceability requirement when its geometric nonlinearity is considered. It is also shown that the geometric nonlinearity greatly reduces the long-term in-plane stability of three-pinned CFST arches under the sustained load. A three-pinned CFST arch satisfying the stability limit state predicted by linear analysis in the long-term may lose its stability because of its geometric nonlinearity. Hence, non-linear analysis is needed for correctly predicting the long-term structural behaviour and stability of three-pinned CFST arches under the sustained load. The non-linear long-term behaviour and stability of three-pinned CFST arches are compared with those of two-pinned counterparts. The linear and non-linear analyses for the long-term behaviour and stability are validated by the finite element method.

• Structural Engineering and Mechanics
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• 제17권6호
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• pp.751-766
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• 2004

This paper extends the use of the hierarchic degenerated shell element to geometric non-linear analysis of composite laminated skew plates by the p-version of the finite element method. For the geometric non-linear analysis, the total Lagrangian formulation is adopted with moderately large displacement and small strain being accounted for in the sense of von Karman hypothesis. The present model is based on equivalent-single layer laminate theory with the first order shear deformation including a shear correction factor of 5/6. The integrals of Legendre polynomials are used for shape functions with p-level varying from 1 to 10. A wide variety of linear and non-linear results obtained by the p-version finite element model are presented for the laminated skew plates as well as laminated square plates. A numerical analysis is made to illustrate the influence of the geometric non-linear effect on the transverse deflections and the stresses with respect to width/depth ratio (a/h), skew angle (${\beta}$), and stacking sequence of layers. The present results are in good agreement with the results in literatures.

• 대한기계학회논문집A
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• 제28권4호
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• pp.467-474
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• 2004

A numerical method and algorithms is proposed to perform optimization of non-linear response structures. An analytical and numerical method based finite element method is also proposed for the transformation of non-linear response into linear response. Loads transformed from this method are defined as the equivalent linear loads. With the loads and the transformed response, linear static optimization is performed for nonlinear response structure with geometric and/or material non-linearity. The results of the optimization are compared with them of typical non-linear response optimization using finite difference method. The proposed method is very efficient and derives good solution.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2004년도 춘계학술대회
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• pp.999-1004
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• 2004

A numerical method and algorithms is proposed to perform optimization of non-linear response structures. An analytical and numerical method based finite element method is also proposed for the transformation of non-linear response into linear response. Loads transformed from this method are defined as the equivalent linear loads. With the loads and the transformed response, linear static optimization is performed for nonlinear response structure with geometric and/or material non-linearity. The results of the optimization are compared with them of typical non-linear response optimization using finite difference method. The proposed method is very efficient and derives good solution.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2001년도 추계학술대회논문집 I
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• pp.319-324
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• 2001

Free non-linear vibration of a rotating thin ring with a constant speed is analyzed when the ring has both the in-plane and out-of-plane motions. The geometric non-linearity of displacements is considered by adopting the Lagrange strain theory for the circumferential strain. By using Hamilton's principle, the coupled non-linear partial differential equations are derived, which describe the out-of-plane and in-plane bending, extensional and torsional motions. The natural frequencies are calculated from the linearized equations at various rotational speeds. Finally, the computation results from three non-linear models are compared with those from a linear model. Based on the comparison, this study recommends which model is appropriate to describe the non- linear behavior more precisely.

• Smart Structures and Systems
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• 제8권5호
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• pp.433-447
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• 2011

The present paper addresses the nonlinear response of a FG square plate with two smart layers as a sensor and actuator under pressure. Geometric nonlinearity was considered in the strain-displacement relation based on the Von-Karman assumption. All the mechanical and electrical properties except Poisson's ratio can vary continuously along the thickness of the plate based on a power function. Electric potential was assumed as a quadratic function along the thickness direction and trigonometric function along the planar coordinate. By evaluating the mechanical and electrical energy, the total energy equation can be minimized with respect to amplitude of displacements and electrical potential. The effect of non homogenous index was investigated on the responses of the system. Obtained results indicate that with increasing the non homogenous index, the displacements and electric potential tend to an asymptotic value. Displacements and electric potential can be presented in terms of planar coordinate system. A linear analysis was employed and then the achieved results are compared with those results that are obtained using the nonlinear analysis. The effect of the geometric nonlinearity is investigated by using the comparison between the linear and nonlinear results. Displacement-load and potential-load curves verified the necessity of a nonlinear analysis rather than a linear analysis. Improvement of the previous results (by the linear analysis) through employing a nonlinear analysis can be presented as novelty of this study.

• 대한기계학회논문집A
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• 제28권12호
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• pp.2012-2018
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• 2004

The vibration of a semi-circular pipe conveying fluid is studied when the pipe is clamped at both ends. To consider the geometric nonlinearity, this study adopts the Lagrange strain theory for large deformation and the extensible dynamics based on the Euler-Bernoulli beam theory for slenderness assumption. By using the Hamilton principle, the non-linear partial differential equations are derived for the in-plane motions of the pipe, considering the fluid inertia forces as a kind of non-conservative forces. The linear and non-linear terms in the governing equations are compared with those in the previous study, and some significant differences are discussed. To investigate the dynamic characteristics of the system, the discretized equations of motion are derived from the Galerkin method. The natural frequencies varying with the flow velocity are computed from the two cases, which one is the linear problem and the other is the linearized problem in the neighborhood of the equilibrium position. Finally, the time responses at various flow velocities are directly computed by using the generalized-$\alpha$ method. From these results, we should consider the geometric nonlinearity to analyze dynamics of a semi-circular pipe conveying fluid more precisely.

• 한국지진공학회논문집
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• 제5권5호
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• pp.1-11
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• 2001

파랑하중 및 지진하중을 받는 스틸자켓 해양구조물의 기하학적 비선형성을 고려한 정적 및 동적해석을 위한 주처리 및 전/후처리 프로그램을 개발하고 이를 이용한 해석결과를 제시한다. 본 논문에서는 스틸자켓을 기하학적 비선형성을 고려한 공간뼈대구조로 모델링하여, 유체 동하중은 선형파이론과 Stokes 5차이론에 의하여 구해진 파의 속도와 가속도를 이용하여 Morison 방정식에 근거한 파력을 계산한다. JONSWAP 스펙트럼을 이용하여 특정 유효파공의 크기에 따라 불규칙파를 생성하며, 지진하중은 인공지진 가속도 프로그램(SIMQKE)을 이용하여 목표응답스펙트럼에 맞는 다양한 형태의 인공지진 가속도를 이용하여 동적해석법을 제시한다. 선형 동적 해석을 위하여 직접 적분법과 모드 중첩법을 사용하며, 비선형 동적해석시에는 직접 적분법을 적용한다. 또한, 스틸자켓의 극한거동을 추적하기 위하여 뼈대구조의 소성힌지 해석법을 적용한다. 연계논문 에서는 전/후처리 프로그램의 내용을 설명하고 해양환경하중을 받는 스틸자켓의 정적 및 동적해석 결과를 제시한다.

• 한국복합재료학회:학술대회논문집
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• 한국복합재료학회 2004년도 춘계학술발표대회 논문집
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• pp.87-90
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• 2004

In this paper, geometrically non-linear finite element analyses were performed to study the mechanical behavior of the material system of the envelope of stratospheric airships. The microstructure of the load­bearing plain weave layer was identified and modeled. The Updated Lagrangian formulation was employed to consider the geometric non-linearity as well as the induced structural non-linearity for the fiber tows. The stress-strain behavior was predicted and the effective elastic modulus was calculated by numerical experiments. It was found the non-linear stress-strain curves were largely different from those by linear analysis with much higher non-linear elastic moduli. The difference was more distinguishable when the tow waviness was smaller.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2006년도 정기 학술대회 논문집
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• pp.623-630
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• 2006

In this paper, a geometric nonlinear analysis procedure of beam-column element including multi-noded cable element is presented. For this, first a stiffness matrix about beam-column element which considers the second effect of initial force supposing the curved shape at each time step with Hermitian polynomials as the shape function is derived and second, tangent stiffness matrix about multi-noded cable element being too. To verify geometric nonlinearity of this newly developed multi-noded cable-truss element, IPS(Innovative Prestressed Support) system using this theory is analysed by geometric nonlinear method and the results are compared with those by linear analysis.