• Structural Engineering and Mechanics
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• 제65권3호
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• pp.213-222
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• 2018

The purpose of this paper is to study free vibration analysis of thick plates resting on Winkler foundation using Mindlin's theory with shear locking free fourth order finite element, to determine the effects of the thickness/span ratio, the aspect ratio, subgrade reaction modulus and the boundary conditions on the frequency paramerets of thick plates subjected to free vibration. In the analysis, finite element method is used for spatial integration. Finite element formulation of the equations of the thick plate theory is derived by using higher order displacement shape functions. A computer program using finite element method is coded in C++ to analyze the plates free, clamped or simply supported along all four edges. In the analysis, 17-noded finite element is used. Graphs are presented that should help engineers in the design of thick plates subjected to earthquake excitations. It is concluded that 17-noded finite element can be effectively used in the free vibration analysis of thick plates. It is also concluded that, in general, the changes in the thickness/span ratio are more effective on the maximum responses considered in this study than the changes in the aspect ratio.

• Korean Journal of Mathematics
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• 제26권3호
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• pp.467-481
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• 2018

In this paper we present a postprocessing scheme for the Raviart-Thomas mixed finite element approximation of the second order elliptic eigenvalue problem. This scheme is carried out by solving a primal source problem on a higher order space, and thereby can improve the convergence rate of the eigenfunction and eigenvalue approximations. It is also used to compute a posteriori error estimates which are asymptotically exact for the $L^2$ errors of the eigenfunctions. Some numerical results are provided to confirm the theoretical results.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2007년도 정기 학술대회 논문집
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• pp.663-668
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• 2007

An enhanced first shear deformation theory for composite plate is developed. The detailed process is as follows. Firstly, the theory is formulated by modifying higher order zigzag theory. That is, the higher order theory is separated into the warping function representing the higher order terms and lower order terms. Secondly, the relationships between higher order zig-zag field and averaged first shear deformation field based on the Reissner-Mindlin's plate theory are derived. Lastly, the effective shear modulus is calculated by minimizing error between higher order energy and first order energy. Then the governing equation of FSDT is solved by substituting shear modulus into effective shear modulus. The recovery processing with the nodal unknown obtained from governing equation is performed. The accuracy of the present proposed theory is demonstrated through numerical examples. The proposed method will serve as a powerful tool in the prediction of laminated composite plate.

• Structural Engineering and Mechanics
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• 제34권6호
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• pp.703-718
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• 2010

In classical higher-order discontinuous boundary element formulation for two-dimensional elastostatics, interpolation functions for different boundary variables (i.e., boundary displacements and tractions) are assumed to be the same. However, there is a derivational relationship between these variables. This paper presents a boundary element formulation, called Mixed Boundary Element Formulation, for two dimensional elastostatic problems in which above mentioned relationship is taking into account. The formulations are performed by using discontinuous first and second-order mixed boundary elements. Based on the formulations presented in this study, two computer softwares are developed and verified through some example problems. The results show that the present formulation is credible.

• Structural Engineering and Mechanics
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• 제73권1호
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• pp.97-108
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• 2020

This study presents a 4 node, 11 DOF/node plate element based on higher order shear deformation theory for lamina composite plates. The theory accounts for parabolic distribution of the transverse shear strain through the thickness of the plate. Differential field equations of composite plates are obtained from energy methods using virtual work principle. Differential field equations of composite plates are obtained from energy methods using virtual work principle. These equations were transformed into the operator form and then transformed into functions with geometric and dynamic boundary conditions with the help of the Gâteaux differential method, after determining that they provide the potential condition. Boundary conditions were determined by performing variational operations. By using the mixed finite element method, plate element named HOPLT44 was developed. After coding in FORTRAN computer program, finite element matrices were transformed into system matrices and various analyzes were performed. The current results are verified with those results obtained in the previous work and the new results are presented in tables and graphs.

• Structural Engineering and Mechanics
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• 제19권6호
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• pp.749-755
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• 2005

In this work, thermo-elastic stability behavior of laminated cross-ply elliptical cylindrical shells subjected to uniform temperature rise is studied employing the finite element approach based on higher-order theory that accounts for the transverse shear and transverse normal deformations, and nonlinear in-plane displacement approximations through the thickness with slope discontinuity at the layer interfaces. The combined influence of higher-order shear deformation, shell geometry and non-circularity on the prebuckling thermal stress distribution and critical temperature parameter of laminated elliptical cylindrical shells is examined.

• Advances in materials Research
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• 제6권4호
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• pp.349-361
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• 2017

The nonlinear thermal buckling load parameter of the laminated composite panel structure is investigated numerically using the higher-order theory including the stretching effect through the thickness and presented in this research article. The large geometrical distortion of the curved panel structure due to the elevated thermal loading is modeled via Green-Lagrange strain field including all of the higher-order terms to achieve the required generality. The desired solutions are obtained numerically using the finite element steps in conjunction with the direct iterative method. The concurrence of the present nonlinear panel model has been established via adequate comparison study with available published data. Finally, the effect of different influential parameters which affect the nonlinear buckling strength of laminated composite structure are examined through numerous numerical examples and discussed in details.

• Geomechanics and Engineering
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• 제11권1호
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• pp.95-116
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• 2016

A novel higher order shear-deformable beam model, which provides linear variation of transversal normal strain and quadratic variation of shearing strain, is proposed to describe the beam resting on foundation. Then, the traditional two-parameter Pasternak foundation model is modified to capture the effects of the axial deformation of beam. The Masing's friction law is incorporated to deal with nonlinear interaction between the foundation and the beam bottom, and the nonlinear properties of the beam material are also considered. To solve the mathematical problem, a displacement-based finite element is formulated, and the reliability of the proposed model is verified. Finally, numerical examples are presented to study the effects of the interfacial friction between the beam and foundation, and the mechanical behavior due to the tensionless characteristics of the foundation is also examined. Numerical results indicate that the effects of tensionless characteristics of foundation and the interfacial friction have significant influences on the mechanical behavior of the beam-foundation system.

• Structural Engineering and Mechanics
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• 제54권3호
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• pp.393-417
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• 2015

In this paper an 8-node quadrilateral assumed stress hybrid Mindlin plate element with $39{\beta}$ is presented. The formulation is based on complementary energy principle. The proposed element is free of shear locking and is capable of passing all the patch tests, especially the non-zero constant shear enhanced patch test. To accomplish this purpose, special attention is devoted to selecting boundary displacement interpolation and stress approximation in domain. The arbitrary order Timoshenko beam function is successfully used to derive the boundary displacement interpolation. According to the equilibrium equations, an appropriate stress approximation is rationally derived. Particularly, in order to improve element's accuracy, the assumed stress field is derived by employing $39{\beta}$ rather than conventional $21{\beta}$. The resulting element can be adopted to analyze both moderately thick and thin plates, and the convergence for the very thin case can be ensured theoretically. Excellent element performance is demonstrated by a wide of experimental evaluations.

• 한국해양공학회지
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• 제31권3호
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• pp.189-195
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• 2017

A three-dimensional higher order boundary element method based on the B-spline is presented. The method accurately models piecewise continuous bodies and induced velocity potentials using B-spline tensor product representations, and it is capable of obtaining accurate pointwise values for the potential and its derivatives, especially in the trailing edge and tip region of the lift generating body, which may be difficult or impossible to evaluate with constant panel methods. In addition, we implement a wake roll-up and examine the tip vortex formation in the near wake region. The results are compared with existing numerical results and the results of experiments performed out at the cavitation tunnel of Chungnam National University.