• Title/Summary/Keyword: higher order solution

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Is it shear locking or mesh refinement problem?

  • Ozdemir, Y.I.;Ayvaz, Y.
    • Structural Engineering and Mechanics
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    • v.50 no.2
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    • pp.181-199
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    • 2014
  • Locking phenomenon is a mesh problem and can be staved off with mesh refinement. If the studier is not preferred going to the solution with increasing mesh size or the computer memory can stack over flow than using higher order plate finite element or using integration techniques is a solution for this problem. The purpose of this paper is to show the shear locking phenomenon can be avoided by increase low order finite element mesh size of the plates and to study shear locking-free analysis of thick plates using Mindlin's theory by using higher order displacement shape function and to determine the effects of various parameters such as the thickness/span ratio, mesh size on the linear responses of thick plates subjected to uniformly distributed loads. A computer program using finite element method is coded in C++ to analyze the plates clamped or simply supported along all four edges. In the analysis, 4-, 8- and 17-noded quadrilateral finite elements are used. It is concluded that 17-noded finite element converges to exact results much faster than 8-noded finite element, and that it is better to use 17-noded finite element for shear-locking free analysis of plates.

Stability analysis of functionally graded heterogeneous piezoelectric nanobeams based on nonlocal elasticity theory

  • Ebrahimi, Farzad;Barati, Mohammad Reza
    • Advances in nano research
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    • v.6 no.2
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    • pp.93-112
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    • 2018
  • An analytical solution of the buckling governing equations of functionally graded piezoelectric (FGP) nanobeams obtained by using a developed third-order shear deformation theory is presented. Electro-mechanical properties of FGP nanobeam are supposed to change continuously in the thickness direction based on power-law model. To capture the small size effects, Eringen's nonlocal elasticity theory is adopted. Employing Hamilton's principle, the nonlocal governing equations of a FG nanobeams made of piezoelectric materials are obtained and they are solved using Navier-type analytical solution. Results are provided to show the effect of different external electric voltage, power-law index, nonlocal parameter and slenderness ratio on the buckling loads of the size-dependent FGP nanobeams. The accuracy of the present model is verified by comparing it with nonlocal Timoshenko FG beams. So, this study makes the first attempt for analyzing buckling behavior of higher order shear deformable FGP nanobeams.

SOLUTION OF TENTH AND NINTH-ORDER BOUNDARY VALUE PROBLEMS BY HOMOTOPY PERTURBATION METHOD

  • Mohyud-Din, Syed Tauseef;Yildirim, Ahmet
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.14 no.1
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    • pp.17-27
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    • 2010
  • In this paper, we apply homotopy perturbation method (HPM) for solving ninth and tenth-order boundary value problems. The suggested algorithm is quite efficient and is practically well suited for use in these problems. The proposed iterative scheme finds the solution without any discretization, linearization or restrictive assumptions. Several examples are given to verify the reliability and efficiency of the method. The fact that the proposed homotopy perturbation method solves nonlinear problems without using Adomian's polynomials can be considered as a clear advantage of this technique over the decomposition method.

A dynamic analysis of three-dimensional functionally graded beams by hierarchical models

  • Giunta, Gaetano;Koutsawa, Yao;Belouettar, Salim;Calvi, Adriano
    • Smart Structures and Systems
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    • v.13 no.4
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    • pp.637-657
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    • 2014
  • This paper presents a dynamic analysis of three-dimensional beams. Structures made of functionally graded materials are considered. Several higher-order as well as classical theories are derived by means of a compact notation for the a-priori expansion order of the displacement field over the beam cross-section. The governing differential equations and boundary conditions are obtained in a condensed nuclear form that does not depend on the kinematic hypotheses. The problem is, then, exactly solved in space by means of a Navier-type solution, whereas time integration is performed by means of Newmark's solution scheme. Slender and short simply supported beams are investigated. Results are validated towards three-dimensional FEM results obtained via the commercial software ANSYS. Numerical investigations show that good accuracy can be obtained through the proposed formulation provided that the appropriate expansion order is considered.

Solubilization of Ibuprofen in Aqueous Solution (이부프로펜의 가용화)

  • Lee, Jang-Won;Park, Eun-Seok;Chi, Sang-Cheol
    • Journal of Pharmaceutical Investigation
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    • v.27 no.4
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    • pp.279-286
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    • 1997
  • In order to formulate 2% ibuprofen solution, the effects of various solublizing agents, such as cosolvents (propylene glycol, polyethylene glycol, glycerin), a complexing agent $(CELDEX{\circledR}\;CH20)$, surfactants $(Poloxamers\;and\;Cremophor{\circledR}\;RH40)$ on the solubility of ibuprofen in aqueous solution were evaluated. Among them, Poloxamer 407 and $Cremophor{\circledR}$ RH40 showed the excellent capacity on the solubilization of ibuprofen. After 2% ibuprofen solution of choice were administered orally to rats, in reference to a 2% ibuprofen syrup in the market, the pharmacokinetic parameters were determined. The absorption rate of ibuprofen from the solution was higher than that from the suspension.

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On the Strengthening mechanisms of INCONEL 690 (인코넬 690의 강화기구에 관한 연구)

  • 허무영;박용수;안성욱
    • Transactions of Materials Processing
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    • v.6 no.3
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    • pp.213-220
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    • 1997
  • The microstructure of the inconel 690 alloy was varied by the solution treatment and the thermal treatment. The specimens having different microstructures were examined in order to understand the strengthening mechanism of the inconel 690. The level of supersaturation of carbon in the solid solution was increased by applying a longer solution treatment at 115$0^{\circ}C$. As increased carbon content in the solid solution, more carbides precipitated during the thermal treatment at $700^{\circ}C$. Since the carbides played a role of obstacle on the movement of dislocations, a higher tensile strength was obtained in the sample having a large number of carbider. The accumulation of dislocations at the grain boundary carbides caused the development of intergranular fracture which led to a lower elongation.

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Analysis of laminated and sandwich spherical shells using a new higher-order theory

  • Shinde, Bharti M.;Sayyad, Atteshamudin S.
    • Advances in aircraft and spacecraft science
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    • v.7 no.1
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    • pp.19-40
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    • 2020
  • In the present study, a fifth-order shear and normal deformation theory using a polynomial function in the displacement field is developed and employed for the static analysis of laminated composite and sandwich simply supported spherical shells subjected to sinusoidal load. The significant feature of the present theory is that it considers the effect of transverse normal strain in the displacement field which is eliminated in classical, first-order and many higher-order shell theories, while predicting the bending behavior of the shell. The present theory satisfies the zero transverse shear stress conditions at the top and bottom surfaces of the shell. The governing equations and boundary conditions are derived using the principle of virtual work. To solve the governing equations, the Navier solution procedure is employed. The obtained results are compared with Reddy's and Mindlin's theory for the validation of the present theory.

Assessment of geometric nonlinear behavior in composite beams with partial shear interaction

  • Jie Wen;Abdul Hamid Sheikh;Md. Alhaz Uddin;A.B.M. Saiful Islam;Md. Arifuzzaman
    • Steel and Composite Structures
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    • v.48 no.6
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    • pp.693-708
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    • 2023
  • Composite beams, two materials joined together, have become more common in structural engineering over the past few decades because they have better mechanical and structural properties. The shear connectors between their layers exhibit some deformability with finite stiffness, resulting in interfacial shear slip, a phenomenon known as partial shear interaction. Such a partial shear interaction contributes significantly to the composite beams. To provide precise predictions of the geometric nonlinear behavior shown by two-layered composite beams with interfacial shear slips, a robust analytical model has been developed that incorporates the influence of significant displacements. The application of a higher-order beam theory to the two material layers results in a third-order adjustment of the longitudinal displacement within each layer along the depth of the beam. Deformable shear connectors are employed at the interface to represent the partial shear interaction by means of a sequence of shear connectors that are evenly distributed throughout the beam's length. The Von-Karman theory of large deflection incorporates geometric nonlinearity into the governing equations, which are then solved analytically using the Navier solution technique. Suggested model exhibits a notable level of agreement with published findings, and numerical outputs derived from finite element (FE) model. Large displacement substantially reduces deflection, interfacial shear slip, and stress values. Geometric nonlinearity has a significant impact on beams with larger span-to-depth ratio and a greater degree of shear connector deformability. Potentially, the analytical model can accurately predict the geometric nonlinear responses of composite beams. The model has a high degree of generality, which might aid in the numerical solution of composite beams with varying configurations and shear criteria.

New Material Architecture and Its Process Integration for a-Si TFT Array Manufacturing

  • Song, Jean-Ho;Park, Hong-Sick;Kim, Sang-Gab;Cho, Hong-Je;Jeong, Chang-Oh;Kang, Sung-Chul;Kim, Chi-Woo;Chung, Kyu-Ha
    • 한국정보디스플레이학회:학술대회논문집
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    • 2002.08a
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    • pp.552-555
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    • 2002
  • In order to achieve higher performance and low cost a-Si TFT-LCD panel, new material architecture and its process integration for a-Si TFT array manufacturing method were developed. Material combination of low resistant dry-etchable metal and new pixel electrode under currently adopted 4 mask process made it possible to get more-simplified manufacturing method and better device performance for the a-Si TFT-LCD application. Proposed 4 mask process architecture with optimized wet etchants and dry etching process was applicable to various devices such as notebook, monitor and TV.

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Study on the Leaching Characteristics of Simulated Nuclear Waste Glass with variable Composition (핵폐기용 모의글라스의 조성변화에 따른 용출특성에 관한 연구)

  • 한호현;이승한;류수착;류봉기
    • Journal of the Korean institute of surface engineering
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    • v.28 no.5
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    • pp.259-266
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    • 1995
  • In order to manufacture an attractive waste glass for the permanent and secure disposal of high-level radioactive waste, the complex composition of the simulated nuclear waste glass PNL-7668 was simplified to a composition of sodium borosilicate glass. The substitutions of $Fe_2O_3$ and $Al_2O_3$ were added to examine on the leaching characteristics of simulated nuclear waste glass with variable composition. The leach tests for these glasses were performed according to 'MCC-1, Static Leach Test Procedure' in acid and basic solution. In this study, for the $Al_2O_3$-containing glasses, Na ion release from these glasses was higher in acid solution than in basic solution. As the content of $Fe_2O_3$ was increased in glasses, Na ion release was increased in acid solution, in spite of decrease of amount of total mass diminution.

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