• 한국전산구조공학회논문집
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• 제19권3호
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• pp.223-231
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• 2006

본 연구에서는 복합적층 절판 구조물을 고차 전단변형이론을 이용하여 길이변화에 의한 거동 특성을 해석한다. 고차 전단변형이론을 적용하기 위하여 잘 알려진 Lagrangian 및 Hermite 보간함수를 병용한 방법은 다소 복잡하고 4절점 요소에만 적용할 수 있으며, 3절점 요소에 적용할 경우 매우 복잡하게 된다. 이러한 단점 및 복잡성을 피하기 위하여 Lagrangian 보간함수만을 사용한 고차 전단변형이론을 이용하며 복합적층 절판 구조물의 해석과정의 편의성 및 정확성을 위하여 면내 회전각 자유도를 추가한다. 그러므로 한 요소 당 4개의 절점이 있으며, 한 절점 당 10개의 자유도를 가지게 된다. 기존의 절판 구조물은 길이 변화에 대한 영향을 고려한 경우가 적으므로 본 연구에서는 이를 중심 변수로 설정하여 다양한 매개변수 연구를 수행한다. 본 연구에서는 길이 변화에 따라 예측하기 힘든 복잡한 거동을 보이는 복합적층 절판 구조물의 거동특성을 분석하여 합리적인 설계가 가능하고자 한다.

• Steel and Composite Structures
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• 제32권3호
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• pp.293-304
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• 2019

In the present paper, the element free Galerkin (EFG) method is developed for geometrically nonlinear analysis of deep beams considering small scale effect. To interpret the behavior of structure at the nano scale, the higher-order gradient elasticity nonlocal theory is taken into account. The radial point interpolation method with high order of continuity is used to construct the shape functions. The nonlinear equation of motion is derived using the principle of the minimization of total potential energy based on total Lagrangian approach. The Newmark method with the small time steps is used to solve the time dependent equations. At each time step, the iterative Newton-Raphson technique is applied to minimize the residential forces caused by the nonlinearity of the equations. The effects of nonlocal parameter and aspect ratio on stiffness and dynamic parameters are discussed by numerical examples. This paper furnishes a ground to develop the EFG method for large deformation analysis of structures considering small scale effects.

• 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.