• Advances in aircraft and spacecraft science
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• 제1권2호
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• pp.145-175
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• 2014

The results of a series of numerical experiments are presented to verify some of the important developments made in the first part of this paper. Firstly, the static solution of an algebraic system obtained through Strong Formulation Finite Element Method (SFEM) is presented. Secondly, the stress and strain recovery procedure is descripted for the present technique. It will be clear that the present approach is suitable for any strong formulation finite element methodology, due to the presented general approach based on the unknown displacements and on the elasticity equations. Thirdly, the numerical solutions for some classical and other numerical results found in literature are exposed. Finally, an arbitrarily shaped composite plate is solved and good agreement is observed for all the presented cases.

• Advances in aircraft and spacecraft science
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• 제1권2호
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• pp.125-143
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• 2014

This paper provides a new technique for solving the static analysis of arbitrarily shaped composite plates by using Strong Formulation Finite Element Method (SFEM). Several papers in literature by the authors have presented the proposed technique as an extension of the classic Generalized Differential Quadrature (GDQ) procedure. The present methodology joins the high accuracy of the strong formulation with the versatility of the well-known Finite Element Method (FEM). The continuity conditions among the elements is carried out by the compatibility or continuity conditions. The mapping technique is used to transform both the governing differential equations and the compatibility conditions between two adjacent sub-domains into the regular master element in the computational space. The numerical implementation of the global algebraic system obtained by the technique at issue is easy and straightforward. The main novelty of this paper is the application of the stress and strain recovery once the displacement parameters are evaluated. Computer investigations concerning a large number of composite plates have been carried out. SFEM results are compared with those presented in literature and a perfect agreement is observed.

• Structural Engineering and Mechanics
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• 제11권2호
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• pp.221-236
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• 2001

A local point interpolation method (LPIM) is presented for the stress analysis of two-dimensional solids. A local weak form is developed using the weighted residual method locally in two-dimensional solids. The polynomial interpolation, which is based only on a group of arbitrarily distributed nodes, is used to obtain shape functions. The LPIM equations are derived, based on the local weak form and point interpolation. Since the shape functions possess the Kronecker delta function property, the essential boundary condition can be implemented with ease as in the conventional finite element method (FEM). The presented LPIM method is a truly meshless method, as it does not need any element or mesh for both field interpolation and background integration. The implementation procedure is as simple as strong form formulation methods. The LPIM has been coded in FORTRAN. The validity and efficiency of the present LPIM formulation are demonstrated through example problems. It is found that the present LPIM is very easy to implement, and very robust for obtaining displacements and stresses of desired accuracy in solids.

• Korean Journal of Mathematics
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• 제18권4호
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• pp.425-440
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• 2010

Using Green's theorem, elliptic boundary value problems can be converted to boundary integral equations. A numerical methods for boundary integral equations are boundary elementary method(BEM). BEM has advantages over finite element method(FEM) whenever the fundamental solutions are known. Helmholtz type equations arise naturally in many physical applications. In a boundary integral formulation for the exterior Neumann there occurs a hypersingular operator which exhibits a strong singularity like $\frac{1}{|x-y|^3}$ and hence is not an integrable function. In this paper we are going to remove this hypersingularity by reducing the regularity of test functions.

• Earthquakes and Structures
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• 제17권3호
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• pp.257-270
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• 2019

The purpose of this work is to analyze the bending behavior of laminated composite plates using the refined fourvariable theory and the finite element method approach using an ANSYS 12 computational code. The analytical model is based on the multilayer plate theory of shear deformation of the nth-order proposed by Xiang et al 2011 using the theory principle developed by Shimpi and Patel 2006. Unlike other theories, the number of unknown functions in the present theory is only four, while five or more in the case of other theories of shear deformation. The formulation of the present theory is based on the principle of virtual works, it has a strong similarity with the classical theory of plates in many aspects, it does not require shear correction factor and gives a parabolic description of the shear stress across the thickness while filling the condition of zero shear stress on the free edges. The analysis is validated by comparing results with those in the literature.

• Steel and Composite Structures
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• 제47권3호
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• pp.365-374
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• 2023

This paper presents a new scheme for constructing locking-free finite elements in thick and thin plates, called Discrete Shear Gap element (DSG), using multiphase material topology optimization for triangular elements of Reissner-Mindlin plates. Besides, common methods are also presented in this article, such as quadrilateral element (Q4) and reduced integration method. Moreover, when the plate gets too thin, the transverse shear-locking problem arises. To avoid that phenomenon, the stabilized discrete shear gap technique is utilized in the DSG3 system stiffness matrix formulation. The accuracy and efficiency of DSG are demonstrated by the numerical examples, and many superior properties are presented, such as being a strong competitor to the common kind of Q4 elements in the static topology optimization and its computed results are confirmed against those derived from the three-node triangular element, and other existing solutions.

• Steel and Composite Structures
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• 제48권1호
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• pp.73-88
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• 2023

This paper presents a novel implicit level set method for topology optimization of functionally graded (FG) structures with pre-existing discontinuities (pre-cracks) using radial basis functions (RBF). The mathematical formulation of the optimization problem is developed by incorporating RBF-based nodal densities as design variables and minimizing compliance as the objective function. To accurately capture crack-tip behavior, crack-tip enrichment functions are introduced, and an eXtended Finite Element Method (X-FEM) is employed for analyzing the mechanical response of FG structures with strong discontinuities. The enforcement of boundary conditions is achieved using the Hamilton-Jacobi method. The study provides detailed mathematical expressions for topology optimization of systems with defects using FG materials. Numerical examples are presented to demonstrate the efficiency and reliability of the proposed methodology.

• Structural Engineering and Mechanics
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• 제87권2호
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• pp.173-189
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• 2023

For a given structural geometry, the stiffness and damping parameters of the soil and the dynamic response of the structure may change in the face of an equivalent linear soil behavior caused by a strong earthquake. Therefore, the influence of equivalent linear soil behavior on the impedance functions form and the seismic response of the soil-structure system has been investigated. Through the substructure method, the seismic response of the selected structure was obtained by an analytical formulation based on the dynamic equilibrium of the soil-structure system modeled by an analog model with three degrees of freedom. Also, the dynamic response of the soil-structure system for a nonlinear soil behavior and for the two types of impedance function forms was also analyzed by 2D finite element modeling using ABAQUS software. The numerical results were compared with those of the analytical solution. After the investigation, the effect of soil nonlinearity clearly showed the critical role of soil stiffness loss under strong shaking, which is more complex than the linear elastic soil behavior, where the energy dissipation depends on the seismic motion amplitude and its frequency, the impedance function types, the shear modulus reduction and the damping increase. Excellent agreement between finite element analysis and analytical results has been obtained due to the reasonable representation of the model.

• 대한기계학회논문집
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• 제16권5호
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• pp.829-837
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• 1992

본 연구에서는 열간박판압연공정에서의 소성유동, 롤압력, 온도분포를 예측하 기 위한 새로운 방법을 제안하고 있다. 제안된 방법은 유한요소 수식화에 바탕을 두 고 있으며 박판의 소성유동과 온도판의 소성유동과 롤-박판 접촉면에서의 롤압력을 예 측하기 위하여 Hwang등이 제안한 벌칙 강소성 유한요소 수식화기법을 제시하였으며 제 안된 방법에 대한 해의 정확도는 문헌에서의 이론해와 시뮬레이션 결과를 비교하여 확 인하였다. 또한 박판에서의 온도장, 속도장과 롤에서의 온도장의 연계해석을 위한 반복계산방법이 제안되었다. 제안된 방법들을 이용하여 다양한 공정에 대한 시뮬레 이션을 수생하였으며 다양한 공정조건에 대한 롤-박판 시스템의 열적특성과 롤간극에 서 박판의 유동특성을 조사하였다.

• International Journal of Aeronautical and Space Sciences
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• 제14권1호
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• pp.19-29
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• 2013

This paper deals with the study of buckling, vibration, and parametric instability characteristics in a damaged cross-ply and angle-ply laminated plate like beam under in-plane harmonic loading, using the finite element approach. Damage is modelled using an anisotropic damage formulation, based on the concept of reduction in stiffness. The effect of damage on free vibration and buckling characteristics of a thin plate like beam has been studied. It has been observed that damage shows a strong orthogonality and in general deteriorates the static and dynamic characteristics. For the harmonic type of loading, analysis was carried out on a thin plate like beam by solving the governing differential equation which is of Mathieu-Hill type, using the method of multiple scales (MMS). The effects of damage and its location on dynamic stability characteristics have been presented. The results indicate that, compared to the undamaged plate like beam, heavily damaged beams show steeper deviations in simple and combination resonance characteristics.