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Journal articles on the topic 'Unsymmetrie'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Schmidt, Markus, Helmar Görls, and Winfried Plass. "Facile high-yield synthesis of unsymmetric end-off compartmental double Schiff-base ligands: easy access to mononuclear precursor and unsymmetric dinuclear complexes." RSC Advances 6, no. 79 (2016): 75844–54. http://dx.doi.org/10.1039/c6ra16870a.

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2

Wu, B., Q. A. Huang, D. Peng, X. Y. Yang, and Z. Feng. "The Analysis of a Cracked Material under Combined Unsymmetric Thermal Flux and Symmetric Linear Mechanical Loading." Mathematical Problems in Engineering 2021 (July 16, 2021): 1–8. http://dx.doi.org/10.1155/2021/5580908.

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An improved partially permeable crack model is put forward to deal with the problem of a single crack embedded in an orthotropic or isotropic material under combined unsymmetric thermal flux and symmetric linear mechanical loading. With the application of the Fourier transform technique (FTT), the thermoelastic field is given in a closed form. Numerical results show combined unsymmetric linear thermal flux, symmetric linear mechanical loading, and dimensionless thermal conductivity, and the coefficient has influences on fracture parameters. For the improved partially permeable crack, the mode II stress intensity factor and the energy release rate might be zero or positive under combined unsymmetric thermal flux and symmetric linear mechanical loading. Therefore, closure of the crack tip region need not be considered under combined unsymmetric thermal flux and symmetric linear mechanical loading when making use of fracture parameters as a criterion.

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3

Rao, G. Visweswara. "Dynamic Condensation and Synthesis of Unsymmetric Structural Systems." Journal of Applied Mechanics 69, no. 5 (August 16, 2002): 610–16. http://dx.doi.org/10.1115/1.1432988.

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In this paper model reduction of an unsymmetric and damped structural system is presented using a two-sided dynamic condensation technique. The method is an iterative one and essentially utilizes orthonormalized complex eigenvectors of the unsymmetric system. The eigensolution of the reduced order model with specified master degrees-of-freedom is obtained by Lanczos algorithm. The model reduction procedure is further utilized in substructure synthesis and eigenvalue analysis of large size unsymmetric systems. Application of the condensation technique is illustrated via two example problems of rotor bearing systems.

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4

Hu, Zhiguo, Zhibing Dong, Jun Liu, Wenjie Liu, and Xinling Zhu. "Synthesis of Unsymmetric Trisannelated Benzenes Using a SOCl2/EtOH Reagent." Journal of Chemical Research 2005, no. 9 (September 2005): 603–4. http://dx.doi.org/10.3184/030823405774308934.

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A simple and efficient method for the synthesis of unsymmetric trisannelated benzenes is presented. The dimers of cycloketones react with molecules of other cycloketones to form corresponding unsymmetric trisannelated benzenes in the presence of thionyl chloride in anhydrous ethanol.

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5

Li, Min, Bao Yan Zhang, and Xiang Bao Chen. "Distortion Simulation of Unsymmetrical Composite Laminates Using the Finite Element Analysis Method." Materials Science Forum 546-549 (May 2007): 1563–66. http://dx.doi.org/10.4028/www.scientific.net/msf.546-549.1563.

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Unsymmetric composite laminates were benefit to reducing the structure weight of some aircrafts. However, the cured unsymmetric laminates showed distortion at room temperature. Therefore, predicting the deformation before using the unsymmetrical composite is very important. In this study an attempt was made to predict the shapes of some unsymmetric cross-ply laminates using the finite element analysis (FEA). The bilinear shell-element was adopted in the process. Then the simulation results were compared with the experimental data. The studies we had performed showed that the theoretical calculation agreed well with the experimental results, the predicted shapes were similar to the real laminates, and the difference between the calculated maximum deflections and the experimental data were less than 5%. Hence the FEA method was suitable for predicting the warpage of unsymmetric laminates. The error analysis showed that the simulation results were very sensitive to the lamina thickness, 2 α and (T.

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6

Hasanzadeh, Majid, and Hossein Zareamoghadd. "An Iterative Method for Solving Unsymmetric System of Fuzzy Linear Equations." SIJ Transactions on Computer Science Engineering & its Applications (CSEA) 01, no. 05 (December 2, 2013): 39–43. http://dx.doi.org/10.9756/sijcsea/v1i5/0106550101.

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7

Murray, Darryl V., and Oliver J. Myers. "Modeling Bistable Composite Laminates for Piezoelectric Morphing Structures." ISRN Materials Science 2013 (April 29, 2013): 1–12. http://dx.doi.org/10.1155/2013/428624.

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A sequential modeling effort for bistable composite laminates for piezoelectric morphing structures is presented. Thin unsymmetric carbon fiber composite laminates are examined for use of morphing structures using piezoelectric actuation. When cooling from the elevated cure temperature to room temperature, these unsymmetric composite laminates will deform. These postcure room temperature deformation shapes can be used as morphing structures. Applying a force to these deformed laminates will cause them to snap through to another shape. This bistability arises from the fabrication process of the thin unsymmetric laminates. The snap through force studied here will be controlled by using piezoelectricity. Macrofiber composite (MFC) actuators are used for piezoelectric actuation. In this research, an analytical modeling method is presented to accurately depict the piezoelectric morphing structures. Sequential numerical modeling of the cure process to account for residual stresses and postcured shapes and piezoelectric morphing structure is done to predict the piezoelectric actuated displacements of the thin unsymmetric composite laminates. Analytical and numerical models are compared to experimental methods and results.

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8

Schmittel, Michael, and Andreas Haeuseler. "Access to Unsymmetric Binaphthols through Oxidative Coupling of Silicon Bisnaphtholates." Zeitschrift für Naturforschung B 58, no. 2-3 (March 1, 2003): 211–16. http://dx.doi.org/10.1515/znb-2003-2-302.

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The oxidative coupling of various symmetric (5 -7) as well as unsymmetric silicon bisnaphtholates (11, 12), initiated by different oxidants (iron(III), cerium(IV), copper(II) or hypervalent iodine), furnishes the corresponding symmetric and unsymmetric binaphthols 13 - 17. The coupling reaction of the substrates follows strictly an intramolecular pathway.

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9

de la Torre, Gema, and Tomás Torres. "Synthetic advances in phthalocyanine chemistry." Journal of Porphyrins and Phthalocyanines 06, no. 04 (April 2002): 274–84. http://dx.doi.org/10.1142/s1088424602000324.

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A brief overview is presented on the status of the synthesis of unsymmetric phthalocyanines and related compounds. The main aim of this paper is to describe the key problems and the interest in synthesizing new functionalized unsymmetric phthalocyanine systems. Some phthalocyanine homologues and analogues like subphthalocyanines and expanded phthalocyanines are also treated.

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10

Arisawa, Mieko, Masahiko Yamaguchi, Saori Tanii, Takaya Tougo, and Kiyofumi Horiuchi. "Thieme Chemistry Journals Awardees – Where Are They Now? Rhodium-Catalyzed Synthesis of Unsymmetric Di(heteroaryl) Ethers Using Heteroaryl Exchange Reaction." Synlett 28, no. 13 (April 27, 2017): 1601–7. http://dx.doi.org/10.1055/s-0036-1588801.

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Unsymmetric di(heteroaryl) ethers were synthesized by the rhodium-catalyzed heteroaryl exchange reaction of heteroaryl aryl ethers and heteroaryl esters at equilibrium. Diverse unsymmetric di(heteroaryl) ethers containing five- and six-membered heteroarenes were obtained. Di(heteroaryl) ethers can be synthesized starting from diaryl ethers, because heteroaryl aryl ethers are obtained by the heteroaryl exchange reaction of diaryl ethers.

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11

Yusof, Zarina, Zainudin A. Rasid, Mohamad Zaki Hassan, SM Sapuan, Shamsul Sarip, Hafizal Yahaya, and Fitri Yakub. "The parametric instability improvement of fully anisotropic composite plates with embedded shape memory alloy." Advanced Composites Letters 29 (January 1, 2020): 2633366X1989940. http://dx.doi.org/10.1177/2633366x19899405.

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The parametric resonance or instability challenge in designing laminated composite is crucial in areas such as aeronautical and marine where structures experience dynamic loading. Shape memory alloy (SMA), a type of smart material, has been used to improve the structural behaviours of composite plate using its well-known property of shape memory effect. It is also known that mechanical couplings that exist in unsymmetric composite can increase the instability of the composite. In this study, the SMA property has been exploited to generate recovery stress in the composite to improve its parametric instability problem. The unsymmetric composites were embedded with SMA fibres, and the formulation for the dynamic instability of this composites was developed using finite element method. The third-order shear deformation theory of composite was applied. The results were initially validated for the case of composite without SMA. Following that, the parametric instability behaviour of unsymmetric composites was studied under the effect of several parameters. It was found that the mechanical couplings that exist in the unsymmetric composite have increased the instability of the composite, but the presence of the SMA can significantly reduce this instability.

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12

Prokopuk, Nicholas, Andrew Chafin, Richard Gilardi, and Jeffrey R. Deschamps. "Unsymmetric diruthenium complexes." Inorganica Chimica Acta 365, no. 1 (January 2011): 439–46. http://dx.doi.org/10.1016/j.ica.2010.09.059.

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13

Jiang, Guoqing, Ting Dong, and Zhenkun Guo. "Nonlinear Dynamics of an Unsymmetric Cross-Ply Square Composite Laminated Plate for Vibration Energy Harvesting." Symmetry 13, no. 7 (July 14, 2021): 1261. http://dx.doi.org/10.3390/sym13071261.

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The nonlinear behaviors and energy harvesting of an unsymmetric cross-ply square composite laminated plate with a piezoelectric patch is presented. The unsymmetric cross-ply square composite laminated plate has two stable equilibrium positions by applying thermal stress, thus having snap-through with larger amplitude between the two stable equilibrium positions relative to the general laminated plate. Based on the von-Karman large deformation theory, the nonlinear electromechanical coupling equations of motion of the unsymmetric composite laminated plate with a piezoelectric patch are derived by using Hamilton’s principle. The influence of the base excitation amplitude on nonlinear behaviors and energy harvesting are investigated. For different base excitation amplitudes, the motions of the system demonstrate periodic motion, quasi-periodic motion, chaotic motion and snap-through, and two single-well chaotic attractors and a two-well chaos attractor coexist. Moreover, the power generation efficiency is optimal when the excitation amplitude is in a certain range due to its own unique nonlinear characteristics. The unsymmetric cross-ply square composite laminated plate subjected to thermal stress can actually be called a kind of bistable composite shell structure that has a broad application prospect in combination with morphing aircraft, large deployable antenna and solar panel, which are very likely to have nonlinear vibration.

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14

Bříza, Tomáš, Zdeněk Kejík, Jarmila Králová, Pavel Martásek, and Vladimír Král. "Synthesis of unsymmetric cyanine dye via merocyanine and their interaction with DNA." Collection of Czechoslovak Chemical Communications 74, no. 7-8 (2009): 1081–90. http://dx.doi.org/10.1135/cccc2009034.

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An effective method has been developed for synthesis of neutral merocyanine dye 4 from (4-nitrophenyl)malondialdehyde. Merocyanine 4 was used as a basic building block for preparation of unsymmetric cyanine dyes 9 and 10, both derived from the same aromatic malondialdehyde. With the cyanine 10, pH-dependent affinity to DNA has been studied. Unsymmetric cyanine dye 10 has been compared with symmetric dye 8. The corresponding binding constants (K) have been calculated for various pH.

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15

Shirzadi, Ahmad, and Leevan Ling. "Convergent Overdetermined-RBF-MLPG for Solving Second Order Elliptic PDEs." Advances in Applied Mathematics and Mechanics 5, no. 1 (February 2013): 78–89. http://dx.doi.org/10.4208/aamm.11-m11168.

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AbstractThis paper deals with the solvability and the convergence of a class of unsymmetric Meshless Local Petrov-Galerkin (MLPG) method with radial basis function (RBF) kernels generated trial spaces. Local weak-form testings are done with step-functions. It is proved that subject to sufficiently many appropriate testings, solvability of the unsymmetric RBF-MLPG resultant systems can be guaranteed. Moreover, an error analysis shows that this numerical approximation converges at the same rate as found in RBF interpolation. Numerical results (in double precision) give good agreement with the provided theory.

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16

Dang, Jeremy D., Mabel V. Fulford, Brett A. Kamino, Andrew S. Paton, and Timothy P. Bender. "Process for the synthesis of symmetric and unsymmetric oxygen bridged dimers of boron subphthalocyanines (μ-oxo-(BsubPc)2s)." Dalton Transactions 44, no. 9 (2015): 4280–88. http://dx.doi.org/10.1039/c4dt02624a.

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17

Eskandari, Roozbeh, Jeremy P. Hess, and Gregory P. Tochtrop. "Synthesis of α,β-unsaturated epoxy ketones utilizing a bifunctional sulfonium/phosphonium ylide." Chemical Communications 57, no. 58 (2021): 7136–39. http://dx.doi.org/10.1039/d1cc02475b.

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18

Griffiths, D. V. "Seepage beneath unsymmetric cofferdams." Géotechnique 44, no. 2 (June 1994): 297–305. http://dx.doi.org/10.1680/geot.1994.44.2.297.

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19

Künzi, Hans-Peter A., Mark Sioen, and Filiz Yıldız. "Unsymmetric T0-quasi-metrics." Topology and its Applications 279 (July 2020): 107249. http://dx.doi.org/10.1016/j.topol.2020.107249.

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20

Yuan, Zhenyi, Yongjun Wang, Junbiao Wang, Shengmin Wei, Tianjiao Liu, Yujin Cai, Junjie He, and Wang Wang. "A model on the curved shapes of unsymmetric laminates including tool-part interaction." Science and Engineering of Composite Materials 25, no. 1 (January 26, 2018): 1–8. http://dx.doi.org/10.1515/secm-2015-0215.

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AbstractThe room-temperature shape of unsymmetric laminate due to the residual stress developed during the curing process has been investigated in the past decades. The factors influencing the residual stress of unsymmetric laminate, including moisture, fiber orientation, aspect ratio and ply thickness, have been widely investigated. Another mechanism that can generate residual stress is the interaction between the tool and the composite part during heating-up process. In this work, the effects resulting from the interaction between laminate and tool during the heating-up phase were considered. By introducing an interfacial shear stress due to tool-part interaction, an analytical model based on the Extended Classical Lamination Theory of Dano and Hyer was proposed to predict the room-temperature shapes of cross-ply unsymmetric laminates. The interfacial shear stress, which was correlated with experimental results, was introduced to tailor the amount of residual stress transferred from the tool. The model was validated with experimental data provided in the literature. It is shown that this model which takes the tool-part interaction into consideration could predict part processing deformations more accurately.

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21

Hedberg Wallenstein, Joachim, Lisa A. Fredin, Martin Jarenmark, Maria Abrahamsson, and Petter Persson. "Chemical consequences of pyrazole orientation in RuII complexes of unsymmetric quinoline–pyrazole ligands." Dalton Transactions 45, no. 29 (2016): 11723–32. http://dx.doi.org/10.1039/c6dt01070a.

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22

Luo, Jianhui, and Hae Chang Gea. "Modal Sensitivity Analysis of Coupled Acoustic-Structural Systems." Journal of Vibration and Acoustics 119, no. 4 (October 1, 1997): 545–50. http://dx.doi.org/10.1115/1.2889760.

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Modal analysis of coupled acoustic-structural systems leads to unsymmetric eigenproblem of special form which introduce different left and right eigenvectors. In this paper, the relation between left and right eigenvectors is first established by symmetrization of the unsymmetric eigensystem, and then Nelson’s method is extended to coupled acoustic-structural systems for calculating the sensitivities of the eigenvalues and eigenvectors. The method only needs to calculate the sensitivities of the right eigenvectors and can treat the Helmholtz resonance mode naturally. Numerical examples of an acoustic box model solved by the proposed approach are compared with finite difference approach and good agreement is noted.

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23

Zhang, Yindi, Xi Chen, Dongdong Song, Daokun Zhong, Xiaolong Yang, Yuanhui Sun, Boao Liu, Guijiang Zhou, and Zhaoxin Wu. "Unsymmetric 2-phenylpyridine (ppy)-type cyclometalated Ir(iii) complexes bearing both 5,9-dioxa-13b-boranaphtho[3,2,1-de]anthracene and phenylsulfonyl groups for tuning optoelectronic properties and electroluminescence abilities." Inorganic Chemistry Frontiers 7, no. 8 (2020): 1651–66. http://dx.doi.org/10.1039/c9qi01388a.

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24

Zhang, Zuolun, Zheng Wang, Martin Haehnel, Antonius Eichhorn, Robert M. Edkins, Andreas Steffen, Anke Krueger, Zhenyang Lin, and Todd B. Marder. "Synthesis and fluxional behaviour of novel chloroborole dimers." Chemical Communications 52, no. 62 (2016): 9707–10. http://dx.doi.org/10.1039/c6cc04831e.

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25

Wang, Jian, Shuang Luo, Jing Li, and Qiang Zhu. "A room-temperature synthesis of 2,2′-bisoxazoles through palladium-catalyzed oxidative coupling of α-isocyanoacetamides." Org. Chem. Front. 1, no. 11 (2014): 1285–88. http://dx.doi.org/10.1039/c4qo00250d.

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26

Ji, Meishan, Zhen Wu, and Chen Zhu. "Visible-light-induced consecutive C–C bond fragmentation and formation for the synthesis of elusive unsymmetric 1,8-dicarbonyl compounds." Chemical Communications 55, no. 16 (2019): 2368–71. http://dx.doi.org/10.1039/c9cc00378a.

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27

Zhang, Zhen, Zongyang Li, Bin Fu, and Zhenhua Zhang. "Palladium-catalyzed cross-coupling reaction of azides with isocyanides." Chemical Communications 51, no. 91 (2015): 16312–15. http://dx.doi.org/10.1039/c5cc05981j.

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28

Verma, Pramod Kumar, Andreas Steinbacher, Federico Koch, Patrick Nuernberger, and Tobias Brixner. "Monitoring ultrafast intramolecular proton transfer processes in an unsymmetric β-diketone." Physical Chemistry Chemical Physics 17, no. 13 (2015): 8459–66. http://dx.doi.org/10.1039/c4cp05811a.

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29

Pankova, Alena S., Mikhail A. Samartsev, Igor A. Shulgin, Pavel R. Golubev, Margarita S. Avdontceva, and Mikhail A. Kuznetsov. "Synthesis of thiazolidines via regioselective addition of unsymmetric thioureas to maleic acid derivatives." RSC Adv. 4, no. 93 (2014): 51780–86. http://dx.doi.org/10.1039/c4ra07840c.

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30

Zhang, Y., and F. L. Matthews. "Large Deflection Behavior of Simply Supported Laminated Panels Under In-Plane Loading." Journal of Applied Mechanics 52, no. 3 (September 1, 1985): 553–58. http://dx.doi.org/10.1115/1.3169100.

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An analysis is presented for nonbifurcational behavior of flat and curved panels of unsymmetrically laminated composite materials under in-plane loading, either compression or shear. A pair of governing equations in the von Karman sense are solved in conjunction with simply supported boundaries. A series of computations is carried out for panels having different curvatures, different lay-ups, and different materials. The results show that during loading, lateral deflection is involved in panels with unsymmetric cross-ply layers under compression or in those with unsymmetric angle-ply layers under shear. This effect increases deflection of the flat plates under loading and reduces resistance of curved panels against collapse.

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31

Meng, Qianli, Frank R. Fronczek, and M. Graça H. Vicente. "Synthesis and spectroscopic properties of β,β′-dibenzo-3,5,8-triaryl-BODIPYs." New Journal of Chemistry 40, no. 7 (2016): 5740–51. http://dx.doi.org/10.1039/c5nj03324a.

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32

Ibrahim, Yehia A., Nouria A. Al-Awadi, Talal F. Al-Azemi, and Elizabeth John. "Improved microwave synthesis of unsymmetrical N,N'-diaryl-1,2-aminoethane and imidazolidinium salts as precursors of N-heterocyclic carbenes." RSC Adv. 4, no. 73 (2014): 38869–76. http://dx.doi.org/10.1039/c4ra06128d.

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33

Antonangelo, A. R., K. C. M. Westrup, L. A. Burt, C. Grazia Bezzu, T. Malewschik, G. S. Machado, F. S. Nunes, N. B. McKeown, and S. Nakagaki. "Synthesis, crystallographic characterization and homogeneous catalytic activity of novel unsymmetric porphyrins." RSC Adv. 7, no. 80 (2017): 50610–18. http://dx.doi.org/10.1039/c7ra08734a.

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34

Yoshida, Suguru. "Sequential conjugation methods based on triazole formation and related reactions using azides." Organic & Biomolecular Chemistry 18, no. 8 (2020): 1550–62. http://dx.doi.org/10.1039/c9ob02698c.

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35

Kutsumizu, Shoichi, Yutaro Yamada, Tadashi Sugimoto, Nina Yamada, Taro Udagawa, and Yohei Miwa. "Systematic exploitation of thermotropic bicontinuous cubic phase families from 1,2-bis(aryloyl)hydrazine-based molecules." Physical Chemistry Chemical Physics 20, no. 12 (2018): 7953–61. http://dx.doi.org/10.1039/c7cp08345a.

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36

Aoshima, Kenta, Marina Ide, and Akinori Saeki. "Organic photovoltaics of diketopyrrolopyrrole copolymers with unsymmetric and regiorandom configuration of the side units." RSC Advances 8, no. 53 (2018): 30201–6. http://dx.doi.org/10.1039/c8ra05903a.

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Diketopyrrolopyrroles with unsymmetric side aromatics of benzene and (thiophene or thienothiophene) were copolymerized with 2-dimensional benzodithiophene, and their solar cell devices were characterized.

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37

Itazaki, Masumi, Shinya Katsube, Masahiro Kamitani, and Hiroshi Nakazawa. "Synthesis of vinylphosphines and unsymmetric diphosphines: iron-catalyzed selective hydrophosphination reaction of alkynes and vinylphosphines with secondary phosphines." Chemical Communications 52, no. 15 (2016): 3163–66. http://dx.doi.org/10.1039/c5cc10185a.

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38

Fukazawa, Aiko, Junichi Usuba, Raúl A. Adler, and Shigehiro Yamaguchi. "Synthesis of seminaphtho-phospha-fluorescein dyes based on the consecutive arylation of aryldichlorophosphines." Chemical Communications 53, no. 61 (2017): 8565–68. http://dx.doi.org/10.1039/c7cc04323f.

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39

Hsieh, M. C., and Chyanbin Hwu. "Explicit Expressions of the Fundamental Elasticity Matrices of Stroh-Like Formalism for Symmetric/Unsymmetric Laminates." Journal of Mechanics 18, no. 3 (September 2002): 109–18. http://dx.doi.org/10.1017/s1727719100002070.

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AbstractBased upon our recent development of Stroh-like forma lism for symmetric/unsymmetric laminates, most of the relations for bending problems can be organized into the forms of Stroh formalism for two-dimensional problems. Through the use of Stroh-like formalism, the fundamental elasticity matrices Ni, S, H and L appear frequently in the real form solutions of plate bending problems. Therefore, the determination of these matrices becomes important in the analysis of plate bending problems. In this paper, by following the approach for two-dimensional problems, we obtain the explicit expressions of the fundamental elasticity matrices for symmetric and unsymmetric laminates, which are all expressed in terms of the extensional, bending and coupling stiffnesses of the composite laminates.

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40

Takahashi, Keisuke, Shingo Ito, Ryo Shintani, and Kyoko Nozaki. "Selective synthesis of unsymmetric dibenzo[a,e]pentalenes by a rhodium-catalysed stitching reaction." Chemical Science 8, no. 1 (2017): 101–7. http://dx.doi.org/10.1039/c6sc04560j.

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41

Pang, Shaofeng, Youquan Deng, and Feng Shi. "Synthesis of unsymmetric tertiary amines via alcohol amination." Chemical Communications 51, no. 46 (2015): 9471–74. http://dx.doi.org/10.1039/c5cc02205c.

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42

Uesaka, Akihiro, Isao Hara, Tomoya Imai, Junji Sugiyama, and Shunsaku Kimura. "Unsymmetric vesicles with a different design on each side for near-infrared fluorescence imaging of tumor tissues." RSC Advances 5, no. 19 (2015): 14697–703. http://dx.doi.org/10.1039/c4ra15635h.

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43

Li, Zhi, Song Cen, and Chenfeng Li. "Extension of the unsymmetric 8-node hexahedral solid element US-ATFH8 to geometrically nonlinear analysis." Engineering Computations 38, no. 8 (July 13, 2021): 3219–53. http://dx.doi.org/10.1108/ec-04-2020-0203.

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Purpose The purpose of this paper is to extend a recent unsymmetric 8-node, 24-DOF hexahedral solid element US-ATFH8 with high distortion tolerance, which uses the analytical solutions of linear elasticity governing equations as the trial functions (analytical trial function) to geometrically nonlinear analysis. Design/methodology/approach Based on the assumption that these analytical trial functions can still properly work in each increment step during the nonlinear analysis, the present work concentrates on the construction of incremental nonlinear formulations of the unsymmetric element US-ATFH8 through two different ways: the general updated Lagrangian (UL) approach and the incremental co-rotational (CR) approach. The key innovation is how to update the stresses containing the linear analytical trial functions. Findings Several numerical examples for 3D structures show that both resulting nonlinear elements, US-ATFH8-UL and US-ATFH8-CR, perform very well, no matter whether regular or distorted coarse mesh is used, and exhibit much better performances than those conventional symmetric nonlinear solid elements. Originality/value The success of the extension of element US-ATFH8 to geometrically nonlinear analysis again shows the merits of the unsymmetric finite element method with analytical trial functions, although these functions are the analytical solutions of linear elasticity governing equations.

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44

Wang, Fuyuan, Jinhai Shen, Guolin Cheng, and Xiuling Cui. "Practical access to 1,3,5-triarylbenzenes from chalcones and DMSO." RSC Advances 5, no. 89 (2015): 73180–83. http://dx.doi.org/10.1039/c5ra13137e.

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We presents a practical access to 1,3,5-triarylbenzenes from chalcones and DMSO. This protocol could simultaneously provide symmetric and unsymmetric 1,3,5-triarylbenzenes under metal-free reaction conditions.

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45

Yu, Xiaoli, Duo-Sheng Wang, Zhaojun Xu, Bobin Yang, and Dawei Wang. "The synthesis of unsymmetric diamides through Rh-catalyzed selective C–H bond activation of amides with isocyanates." Organic Chemistry Frontiers 4, no. 6 (2017): 1011–18. http://dx.doi.org/10.1039/c6qo00793g.

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46

Chahinian, Leon. "Jacobi method for unsymmetric eigenproblems." Journal of Guidance, Control, and Dynamics 14, no. 3 (May 1991): 674–77. http://dx.doi.org/10.2514/3.20692.

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47

Douglas, Judy E., and Zhi Yuan Wang. "Unsymmetric 1,4-naphthylene-containing polysulfones." Macromolecular Rapid Communications 17, no. 11 (November 1996): 795–803. http://dx.doi.org/10.1002/marc.1996.030171107.

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48

Lagace, Paul A., David W. Jensen, and Douglas C. Finch. "Buckling of unsymmetric composite laminates." Composite Structures 5, no. 2 (January 1986): 101–23. http://dx.doi.org/10.1016/0263-8223(86)90030-9.

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49

Mao, Zhengzhou, Zhaoyang Wang, Wenjie Mei, and Kai Yang. "Synthesis of Novel Unsymmetric Bisbenzimidazoles." Chinese Journal of Chemistry 28, no. 5 (June 8, 2010): 818–24. http://dx.doi.org/10.1002/cjoc.201090152.

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50

McCarney, Eoin P., Chris S. Hawes, Salvador Blasco, and Thorfinnur Gunnlaugsson. "Synthesis and structural studies of 1,4-di(2-pyridyl)-1,2,3-triazole dpt and its transition metal complexes; a versatile and subtly unsymmetric ligand." Dalton Transactions 45, no. 25 (2016): 10209–21. http://dx.doi.org/10.1039/c6dt01416j.

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Abstract:

Structural analysis of the 1,4-di(2-pyridyl)-1,2,3-triazole ligand and its transition metal complexes of varying lability demonstrate the coordination chemistry selectivity of this subtly unsymmetric ligand.

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