• Title/Summary/Keyword: Fundamental Solutions

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Capabilities of 1D CUF-based models to analyse metallic/composite rotors

  • Filippi, Matteo;Carrera, Erasmo
    • Advances in aircraft and spacecraft science
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    • v.3 no.1
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    • pp.1-14
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    • 2016
  • The Carrera Unified Formulation (CUF) is here extended to perform free-vibrational analyses of rotating structures. CUF is a hierarchical formulation, which enables one to obtain refined structural theories by writing the unknown displacement variables using generic functions of the cross-section coordinates (x, z). In this work, Taylor-like expansions are used. The increase of the theory order leads to three-dimensional solutions while, the classical beam models can be obtained as particular cases of the linear theory. The Finite Element technique is used to solve the weak form of the three-dimensional differential equations of motion in terms of "fundamental nuclei", whose forms do not depend on the adopted approximation. Including both gyroscopic and stiffening contributions, structures rotating about either transversal or longitudinal axis can be considered. In particular, the dynamic characteristics of thin-walled cylinders and composite blades are investigated to predict the frequency variations with the rotational speed. The results reveal that the present one-dimensional approach combines a significant accuracy with a very low computational cost compared with 2D and 3D solutions. The advantages are especially evident when deformable and composite structures are analyzed.

SMA-based devices: insight across recent proposals toward civil engineering applications

  • Casciati, Sara
    • Smart Structures and Systems
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    • v.24 no.1
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    • pp.111-125
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    • 2019
  • Metallic shape memory alloys present fascinating physical properties such as their super-elastic behavior in austenite phase, which can be exploited for providing a structure with both a self-centering capability and an increased ductility. More or less accurate numerical models have been introduced to model their behavior along the last 25 years. This is the reason for which the literature is rich of suggestions/proposals on how to implement this material in devices for passive and semi-active control. Nevertheless, the thermo-mechanical coupling characterizing the first-order martensite phase transformation process results in several macroscopic features affecting the alloy performance. In particular, the effects of day-night and winter-summer temperature excursions require special attention. This aspect might imply that the deployment of some devices should be restricted to indoor solutions. A further aspect is the dependence of the behavior from the geometry one adopts. Two fundamental lacks of symmetry should also be carefully considered when implementing a SMA-based application: the behavior in tension is different from that in compression, and the heating is easy and fast whereas the cooling is not. This manuscript focuses on the passive devices recently proposed in the literature for civil engineering applications. Based on the challenges above identified, their actual feasibility is investigated in detail and their long term performance is discussed with reference to their fatigue life. A few available semi-active solutions are also considered.

Exact and approximate solutions for free vibrations of continuous partial-interaction composite beams

  • Sun, Kai Q.;Zhang, Nan;Zhu, Qun X.;Liu, Xiao
    • Steel and Composite Structures
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    • v.44 no.4
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    • pp.531-543
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    • 2022
  • An exact dynamic analytical method for free vibrations of continuous partial-interaction composite beams is proposed based on the Timoshenko beam theory. The main advantage of this method is that the independent shear deformations and rotary inertia of sub-beams are considered, which is more in line with the reality. Therefore, the accuracy of eigenfrequencies obtained by this method is significantly improved, especially for higher order modes, compared to the existing methods where the rotary angles of both sub-beams are assumed to be equal irrespective of the differences in the shear stiffness of each sub-beam. Furthermore, the solutions obtained by the proposed method are exact owing to no introduction of approximated displacement and force fields in the derivation. In addition, an exact analytical solution for the case of simply supported is obtained. Based on this, an approximate expression for the fundamental frequency of continuous partial-interaction composite beams is also proposed, which is useful for practical engineering applications. Finally, the practicability and effectiveness of the proposed method and the approximate expression are explored using numerical and experimental examples; The influence factors including the interfacial interaction, shear modulus ratio, span-to-depth ratio, and side-to-main span length ratio on the eigenfrequencies are presented and discussed in detail.

Simulating vibration of single-walled carbon nanotube using Rayleigh-Ritz's method

  • Hussain, Muzamal;Naeem, Muhammad Nawaz;Taj, Muhammad;Tounsi, Abdelouahed
    • Advances in nano research
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    • v.8 no.3
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    • pp.215-228
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    • 2020
  • In this paper, a new method based on the Sander theory is developed for SWCNTs to predict the vibrational behavior of length and ratio of thickness-to-radius according to various end conditions. The motion equation for this system is developed using Rayleigh-Ritz's method. The proposed model shows the vibration frequencies of armchair (5, 5), (7, 7), (9, 9), zigzag (12, 0), (14, 0), (19, 0) and chiral (8, 3), (10, 2), (14, 5) under different support conditions namely; SS-SS, C-F, C-C, and C-SS. The solutions of frequency equations have been given for different boundary condition, which have been given in several graphs. Several parameters of nanotubes with characteristic frequencies are given and vary continuously in length and ratio of thickness-to-radius. It has been illustrated that an enhancing the length of SWCNTs results in decreasing of the frequency range. It was demonstrated by increasing of the height-to-radius ratio of CNTs, the fundamental natural frequency would increase. Moreover, effects of length and ratio of height-to-radius with different boundary conditions have been investigated in detail. It was found that the fundamental frequencies of C-F are always lower than that of other conditions, respectively. In addition, the existence of boundary conditions has a significant impact on the vibration of SWCNTs. To generate the fundamental natural frequencies of SWCNTs, computer software MATLAB engaged. The numerical results are validated with existing open text. Since the percentage of error is negligible, the model has been concluded as valid.

A Study on the Fundamental Direction of Design in an Aged Society (고령 사회를 대비한 디자인 기초방향 연구)

  • 윤태호
    • Archives of design research
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    • v.16 no.4
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    • pp.91-100
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    • 2003
  • The population is aging rapidly in Korea. From that point of view, 'aging' becomes our reality, and the progression of aging brings about far-reaching changes throughout the whole country. The developed countries are making vigorous preparations for aging now, but our country has not been doing well. So it is necessary to research the counter plan for aging. As an aged society is coming dose at hand, we need the urgent overall countermeasures to decrease the difficulties and troubles the elderly are suffering in their daily lives. This thesis studied the documents and literatures on the fundamental direction of design in preparation for an aged society. The fundamental direction of design needs the conversion to the view that will enable society to cope with the problems of aging. One of solutions for them is Universal Design. Universal Design should be embodied with synthetic and diversified approaches and strategies. 1 expect the healthy aged society with Universal Design mind to build the society where everyone can live together.

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Efficiency Evaluation of Harmony Search Algorithm according to Constraint Handling Techniques : Application to Optimal Pipe Size Design Problem (제약조건 처리기법에 따른 하모니써치 알고리즘의 효율성 평가 : 관로 최소비용설계 문제의 적용)

  • Yoo, Do Guen;Lee, Ho Min;Lee, Eui Hoon;Kim, Joong Hoon
    • Journal of the Korea Academia-Industrial cooperation Society
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    • v.16 no.7
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    • pp.4999-5008
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    • 2015
  • The application of efficient constraint handling technique is fundamental method to find better solutions in engineering optimization problems with constraints. In this research four of constraint handling techniques are used with a meta-heuristic optimization method, harmony search algorithm, and the efficiency of algorithm is evaluated. The sample problem for evaluation of effectiveness is one of the typical discrete problems, optimal pipe size design problem of water distribution system. The result shows the suggested constraint handling technique derives better solutions than classical constraint handling technique with penalty function. Especially, the case of ${\varepsilon}$-constrained method derives solutions with efficiency and stability. This technique is meaningful method for improvement of harmony search algorithm without the need for development of new algorithm. In addition, the applicability of suggested method for large scale engineering optimization problems is verified with application of constraint handling technique to big size problem has over 400 of decision variables.

Numerical Evaluation of Fundamental Finite Element Models in Bar and Beam Structures (Bar와 Beam 구조물의 기본적인 유한요소 모델의 수치해석)

  • Ryu, Yong-Hee;Ju, Bu-Seog;Jung, Woo-Young;Limkatanyu, Suchart
    • Journal of the Korean Society for Advanced Composite Structures
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    • v.4 no.1
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    • pp.1-8
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    • 2013
  • The finite element analysis (FEA) is a numerical technique to find solutions of field problems. A field problem is approximated by differential equations or integral expressions. In a finite element, the field quantity is allowed to have a simple spatial variation in terms of linear or polynomial functions. This paper represents a review and an accuracy-study of the finite element method comparing the FEA results with the exact solution. The exact solutions were calculated by solid mechanics and FEA using matrix stiffness method. For this study, simple bar and cantilever models were considered to evaluate four types of basic elements - constant strain triangle (CST), linear strain triangle (LST), bi-linear-rectangle(Q4),and quadratic-rectangle(Q8). The bar model was subjected to uniaxial loading whereas in case of the cantilever model moment loading was used. In the uniaxial loading case, all basic element results of the displacement and stress in x-direction agreed well with the exact solutions. In the moment loading case, the displacement in y-direction using LST and Q8 elements were acceptable compared to the exact solution, but CST and Q4 elements had to be improved by the mesh refinement.

A simple quasi-3D HSDT for the dynamics analysis of FG thick plate on elastic foundation

  • Boukhlif, Zoulikha;Bouremana, Mohammed;Bourada, Fouad;Bousahla, Abdelmoumen Anis;Bourada, Mohamed;Tounsi, Abdelouahed;Al-Osta, Mohammed A.
    • Steel and Composite Structures
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    • v.31 no.5
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    • pp.503-516
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    • 2019
  • This work presents a dynamic investigation of functionally graded (FG) plates resting on elastic foundation using a simple quasi-3D higher shear deformation theory (quasi-3D HSDT) in which the stretching effect is considered. The culmination of this theory is that in addition to taking into account the effect of thickness extension (${\varepsilon}_z{\neq}0$), the kinematic is defined with only 4 unknowns, which is even lower than the first order shear deformation theory (FSDT). The elastic foundation is included in the formulation using the Pasternak mathematical model. The governing equations are deduced through the Hamilton's principle. These equations are then solved via closed-type solutions of the Navier type. The fundamental frequencies are predicted by solving the eigenvalue problem. The degree of accuracy of present solutions can be shown by comparing it to the 3D solution and other closed-form solutions available in the literature.

Anion Effects on Changes in Viscoelasticity of Polypyrrole during Electrochemical Growth in Neutral Aqueous Solutions (중성 수용액에서 폴리피롤의 전기화학적 성장시 발생하는 점탄성 변화에 미치는 음이온 효과)

  • Bae Sang-Eun;Lee Seung-Yong;Paek Se-Hwan;Kim Young-Sang;Lee Chi-Woo
    • Journal of the Korean Electrochemical Society
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    • v.2 no.2
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    • pp.66-69
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    • 1999
  • A large number of works have been Performed to understand the electrochemical growth of Polypynole on conducting substrates in aqueous as well as in nonaqueous solutions. Recently most researches with Polypyrrole have tended to be directed toward technological applications, but many fundamental physical and chemical properties of Polypyrrole remain unknown. In Particular, microrheological Property of polypyrrole has been largely neglected until the advanced electrochemical quartz crystal microbalance technique was introduced recently. To study anion effects on microrheolosical Property of Polypyrrole, we investigated changes in viscoelasticity of Polypyrrole during electrochemical growth in neutral aqueous solutions by means of in siか electrochemical quartz crystal oscillator method. The results showed that the films of Polypyrrole synthesized in $KPF_6\;and\;KCIO_4$ were more viscoelastic than the ones in $KCI,\;KNO_3,\;KBr,\;KBF_4,\;K_2SO_4$, sodium tosylate (NaOTs), and sodium dodecyl sulfate (SDS). The growth rate of Polypyrrole in SDS was faster than that in the others utilized. Polypyrroles synthesized in buffered neutral solutions were more elastic than those in unbuffered neutral solutions.

Hierarchical theories for a linearised stability analysis of thin-walled beams with open and closed cross-section

  • Giunta, Gaetano;Belouettar, Salim;Biscani, Fabio;Carrera, Erasmo
    • Advances in aircraft and spacecraft science
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    • v.1 no.3
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    • pp.253-271
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    • 2014
  • A linearised buckling analysis of thin-walled beams is addressed in this paper. Beam theories formulated according to a unified approach are presented. The displacement unknown variables on the cross-section of the beam are approximated via Mac Laurin's polynomials. The governing differential equations and the boundary conditions are derived in terms of a fundamental nucleo that does not depend upon the expansion order. Classical beam theories such as Euler-Bernoulli's and Timoshenko's can be retrieved as particular cases. Slender and deep beams are investigated. Flexural, torsional and mixed buckling modes are considered. Results are assessed toward three-dimensional finite element solutions. The numerical investigations show that classical and lower-order theories are accurate for flexural buckling modes of slender beams only. When deep beams or torsional buckling modes are considered, higher-order theories are required.