• Journal of Mechanical Science and Technology
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• 제14권6호
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• pp.666-674
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• 2000

Large deflection dynamic responses of laminated composite cylindrical shells under impact are analyzed by the geometrically nonlinear finite element method based on a generalized Sander's shell theory with the first order transverse shear deformation and the von-Karman large deflection assumption. A modified indentation law with inelastic indentation is employed for the contact force. The nonlinear finite element equations of motion of shell and an impactor along with the contact laws are solved numerically using Newmark's time marching integration scheme in conjunction with Akay type successive iteration in each step. The ply failure region of the laminated shell is estimated using the Tsai- Wu quadratic interaction criteria. Numerical results, including the contact force histories, deflections and strains are presented and compared with the ones by linear analysis. The effect of the radius of curvature on the composite shell behaviors is investigated and discussed.

• Structural Engineering and Mechanics
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• 제28권5호
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• pp.587-601
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• 2008

In this study, a numerical procedure based on the finite element method for materially and geometrically nonlinear analysis of reinforced and prestressed concrete slender columns with arbitrary section subjected to combined biaxial bending and axial load is developed. In order to overcome the low computer efficiency of the conventional section integration method in which the reinforced concrete section is divided into a large number of small areas, an efficient section integration method is used to determine the section tangent stiffness. In this method, the arbitrary shaped cross section is divided into several concrete trapezoids according to boundary vertices, and the contribution of each trapezoid to section stiffness is determined by integrating directly the trapezoid. The space frame flexural theory is utilized to derive the element tangent stiffness matrix. The nonlinear full-range member response is traced by an updated normal plane arc-length solution method. The analytical results agree well with the experimental ones.

• 전산구조공학
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• 제11권1호
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• pp.179-190
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• 1998

두개의 케이블요소를 이용한 3차원 케이블망의 정적 비선형 유한요소해석기법을 제시한다. 먼저, 공간 트러스요소와 탄성현수선 케이블요소(elastic catenary cable element)의 접선강도행렬과 질량행렬을 유도하는 과정을 간략히 요약한다. 지점 변위를 일으키고 자중을 받는 케이블망의 초기평형 상태를 결정하기 위하여, Newton-Raphson 반복법에 근거한 하중증분법과 현수케이블요소를 적용하는 경우에 viscous damping을 고려한 dynamic relaxation법을 제시한다. 또한 초기의 정적평형상태를 기준으로 추가하중에 대한 케이블망의 정적 비선형해석을 수행한다. 지점변위와 외력을 받는 케이블 구조에 대하여 비선형해석을 수행하고, 해석결과들을 기존의 문헌의 결과와 비교, 검토하므로써 본 논문에서 제시한 이론 및 해석방법의 타당성을 입증한다.

• 대한조선학회논문집
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• 제29권2호
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• pp.132-139
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• 1992

기하학적 비선형 해석과정에서 일반적인 방법으로는 연속적인 하중증분단계의 기하학적 변위증분에서 절점회전이 미소하다는 가정에 의해 제한되어 접선강성행렬을 유도하고 유한회전의 영향을 증분평형 방정식의 반복계산하는 과정에서 고려하는 방법이 사용되고 있다. 그리고 개선된 방법으로는 미소회전증분의 가정을 무시하고 유한회전증분의 영향을 고려하여 접선강성행렬을 유도하는 방법이 Surana, Onate 및 Dvorkin 등에 의해서 개발되었다. 유한 회전을 고려하는 방법에서 Surana는 비선형 절점 회전함수를 가정하여 강성메트릭스를 유도하였으며 Onate와 Dvorkin은 전체좌표에서 회전각에 대한 회전행렬의 2차항까지를 고려한 강성메트릭스를 유도하였다. 본 논문에서는 유한요소의 기하학적 위치를 나타내는 변위함수의 방향 벡터를 삼각함수로 표현하여 연속적인 하중증분 사이의 방향벡터 증분을Tayler의 급수로 2차항까지 전개하므로써 비선형 회전 증분을 고려한 쉘 요소를 개발하였다. 기하학적 비선형 해석과정은 연속체 운동의 증분이론을 도입하여 Total Lagrange(T.L.)수식과 Updated Lagrange(U.L.)수식으로 비선형 거동을 해석하였다.

• 한국구조물진단유지관리공학회 논문집
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• 제15권2호
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• pp.125-135
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• 2011

유연도법 기반의 공식화에서는 변위영역의 형상함수를 라그랑지언(Lagrangian)보간법에 의한 곡률로부터 횡방향 변위를 유도한다. 곡률변위보간법으로 유도한 매트릭스를 사용한 기하학적 비선형 해석방법과 강성도법을 기반으로 한 비선형 기존의 유한요소 해석 프로그램의 결과를 비교하여 적용이 가능함을 확인하였고, Spacone의 이론을 확장시켜 기하학적 비선형 거동을 예측할 수 있는 유연도법의 알고리즘을 제안하였다. 예제를 통하여 실제 문제에 대한 기하학적 비선형 해석을 수행하였다.

• Structural Engineering and Mechanics
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• 제68권3호
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• pp.299-312
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• 2018

In this paper, an extended finite element method is proposed to analyze both geometric and material non-linear behavior of general Functionally Graded Material (FGM) plate-shell type structures. A user defined subroutine (UMAT) is developed and implemented in Abaqus/Standard to study the elastoplastic behavior of the ceramic particle-reinforced metal-matrix FGM plates-shells. The standard quadrilateral 4-nodes shell element with three rotational and three translational degrees of freedom per node, S4, is extended in the present study, to deal with elasto-plastic analysis of geometrically non-linear FGM plate-shell structures. The elastoplastic material properties are assumed to vary smoothly through the thickness of the plate-shell type structures. The nonlinear approach is based on Mori-Tanaka model to underline micromechanics and locally determine the effective FGM properties and self-consistent method of Suquet for the homogenization of the stress-field. The elasto-plastic behavior of the ceramic/metal FGM is assumed to follow Ludwik hardening law. An incremental formulation of the elasto-plastic constitutive relation is developed to predict the tangent operator. In order to to highlight the effectiveness and the accuracy of the present finite element procedure, numerical examples of geometrically non-linear elastoplastic functionally graded plates and shells are presented. The effects of the geometrical parameters and the volume fraction index on nonlinear responses are performed.

• Steel and Composite Structures
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• 제18권1호
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• pp.51-69
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• 2015

In recent years, the use of fiber reinforced polymer composites has increased because of their unique features. They have been used widely in the aircraft and space industries, medical and sporting goods and automotive industries. Thanks to their beneficial and various advantages over traditional materials such as high strength, high rigidity, low weight, corrosion resistance, low maintenance cost, aesthetic appearance and easy demountable or moveable construction. In this paper, it is aimed to determine and compare the geometrically nonlinear static and dynamic analysis results of footbridges using steel and glass fiber reinforced polymer composite (GFRP) materials. For this purpose, Halgavor suspension footbridge is selected as numerical examples. The analyses are performed using three identical footbridges, first constructed from steel, second built only with GFRP material and third made of steel- GFRP material, under static and dynamic loadings using finite element method. In the finite element modeling and analyses, SAP2000 program is used. Geometric nonlinearities are taken into consideration in the analysis using P-Delta criterion. The numerical results have indicated that the responses of the three bridges are different and that the response values obtained for the GFRP composite bridge are quite less compared to the steel bridge. It is understood that GFRP material is more useful than the steel for the footbridges.

• Steel and Composite Structures
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• 제35권1호
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• pp.77-92
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• 2020

The present paper outlined a procedure for geometrically nonlinear dynamic analysis of functionally graded graphene platelets-reinforced (GPLR-FG) nanocomposite cylinder subjected to mechanical shock loading. The governing equation of motion for large deformation problems is derived using meshless local Petrov-Galerkin (MLPG) method based on total lagrangian approach. In the MLPG method, the radial point interpolation technique is employed to construct the shape functions. A micromechanical model based on the Halpin-Tsai model and rule of mixture is used for formulation the nonlinear functionally graded distribution of GPLs in polymer matrix of composites. Energy dissipation in analyses of the structure responding to dynamic loads is considered using the Rayleigh damping. The Newmark-Newton/Raphson method which is an incremental-iterative approach is implemented to solve the nonlinear dynamic equations. The results of the proposed method for homogenous material are compared with the finite element ones. A very good agreement is achieved between the MLPG and FEM with very fine meshing. In addition, the results have demonstrated that the MLPG method is more effective method compared with the FEM for very large deformation problems due to avoiding mesh distortion issues. Finally, the effect of GPLs distribution on strength, stiffness and dynamic characteristics of the cylinder are discussed in details. The obtained results show that the distribution of GPLs changed the mechanical properties, so a classification of different types and volume fraction exponent is established. Indeed by comparing the obtained results, the best compromise of nanocomposite cylinder is determined in terms of mechanical and dynamic properties for different load patterns. All these applications have shown that the present MLPG method is very effective for geometrically nonlinear analyses of GPLR-FG nanocomposite cylinder because of vanishing mesh distortion issue in large deformation problems. In addition, since in proposed method the distributed nodes are used for discretization the problem domain (rather than the meshing), modeling the functionally graded media yields to more accurate results.

• Steel and Composite Structures
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• 제15권5호
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• pp.481-505
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• 2013

This paper focuses on thermal post-buckling analysis of functionally graded beams with temperature dependent physical properties by using the total Lagrangian Timoshenko beam element approximation. Material properties of the beam change in the thickness direction according to a power-law function. The beam is clamped at both ends. In the case of beams with immovable ends, temperature rise causes compressible forces and therefore buckling and post-buckling phenomena occurs. It is known that post-buckling problems are geometrically nonlinear problems. Also, the material properties (Young's modulus, coefficient of thermal expansion, yield stress) are temperature dependent: That is the coefficients of the governing equations are not constant in this study. This situation suggests the physical nonlinearity of the problem. Hence, the considered problem is both geometrically and physically nonlinear. The considered highly non-linear problem is solved considering full geometric non-linearity by using incremental displacement-based finite element method in conjunction with Newton-Raphson iteration method. In this study, the differences between temperature dependent and independent physical properties are investigated for functionally graded beams in detail in post-buckling case. With the effects of material gradient property and thermal load, the relationships between deflections, critical buckling temperature and maximum stresses of the beams are illustrated in detail in post-buckling case.

• Structural Engineering and Mechanics
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• 제44권1호
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• pp.109-125
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• 2012

Post-buckling behavior of Timoshenko beams subjected to uniform temperature rising with temperature dependent physical properties are studied in this paper by using the total Lagrangian Timoshenko beam element approximation. The beam is clamped at both ends. In the case of beams with immovable ends, temperature rise causes compressible forces end therefore buckling and post-buckling phenomena occurs. It is known that post-buckling problems are geometrically nonlinear problems. Also, the material properties (Young's modulus, coefficient of thermal expansion, yield stress) are temperature dependent: That is the coefficients of the governing equations are not constant in this study. This situation suggests the physical nonlinearity of the problem. Hence, the considered problem is both geometrically and physically nonlinear. The considered highly non-linear problem is solved considering full geometric non-linearity by using incremental displacement-based finite element method in conjunction with Newton-Raphson iteration method. The beams considered in numerical examples are made of Austenitic Stainless Steel (316). The convergence studies are made. In this study, the difference between temperature dependent and independent physical properties are investigated in detail in post-buckling case. The relationships between deflections, thermal post-buckling configuration, critical buckling temperature, maximum stresses of the beams and temperature rising are illustrated in detail in post-buckling case.