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Journal articles on the topic 'Refined Zigzag Theory'

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Author: Grafiati

Published: 14 March 2023

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1

Iurlaro, Luigi, Marco Gherlone, Massimiliano Mattone, and Marco Di Sciuva. "Experimental assessment of the Refined Zigzag Theory for the static bending analysis of sandwich beams." Journal of Sandwich Structures & Materials 20, no. 1 (June 12, 2016): 86–105. http://dx.doi.org/10.1177/1099636216650614.

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In the present work, for the first time, the accuracy of the Refined Zigzag Theory in reproducing the static bending response of sandwich beams is experimentally assessed. The theory is briefly reviewed and an analytical solution of the equilibrium equations is presented for the boundary and loading conditions under investigation (four-point bending). The experimental campaign is described, including the material characterization and the bending tests. The experimentally measured deflections and axial strains are compared with those provided by Refined Zigzag Theory and by the Timoshenko Beam Theory with an ad hoc shear correction factor. The Refined Zigzag Theory is shown to be more accurate than the Timoshenko Beam Theory, in particular for beams with higher face-to-core thickness and stiffness ratios and with a reduced slenderness.

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2

Tessler, Alexander, Marco Di Sciuva, and Marco Gherlone. "A Refined Zigzag Beam Theory for Composite and Sandwich Beams." Journal of Composite Materials 43, no. 9 (January 29, 2009): 1051–81. http://dx.doi.org/10.1177/0021998308097730.

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3

Ghorbanpour-Arani, A., F. Kolahdouzan, and M. Abdollahian. "Nonlocal buckling of embedded magnetoelectroelastic sandwich nanoplate using refined zigzag theory." Applied Mathematics and Mechanics 39, no. 4 (February 20, 2018): 529–46. http://dx.doi.org/10.1007/s10483-018-2319-8.

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4

Wimmer, Heinz, Werner Hochhauser, and Karin Nachbagauer. "Refined Zigzag Theory: an appropriate tool for the analysis of CLT-plates and other shear-elastic timber structures." European Journal of Wood and Wood Products 78, no. 6 (August 28, 2020): 1125–35. http://dx.doi.org/10.1007/s00107-020-01586-x.

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Abstract Cross laminated timber (CLT), as a structural plate-like timber product, has been established as a load bearing product for walls, floor and roof elements. In a bending situation due to the transverse shear flexibility of the crossing layers, the warping of the cross section follows a zigzag pattern which should be considered in the calculation model. The Refined Zigzag Theory (RZT) can fulfill this requirement in a very simple and efficient way. The RZT, founded in 2007 by A. Tessler (NASA Langley Research Center), M. Di Sciuva and M. Gherlone (Politecnico Torino) is a very robust and accurate analysis tool, which can handle the typical zigag warping of the cross section by introducing only one additional kinematic degree of freedom in case of plane beams and two more in case of biaxial bending of plates. Thus, the RZT-kinematics is able to reflect the specific and local stress behaviour near concentrated loads in combination with a warping constraint, while most other theories do not. A comparison is made with different methods of calculation, as the modified Gamma-method, the Shear Analogy method (SA) and the First Order Shear Deformation Theory (FSDT). For a test example of a two-span continuous beam, an error estimation concerning the maximum bending stress is presented depending on the slenderness L/h and the width of contact area at the intermediate support. A stability investigation shows that FSDT provides sufficiently accurate results if the ratio of bending and shear stiffness is in a range as stated in the test example. It is shown that by a simple modification in the determination of the zigzag function, the scope can be extended to beams with arbitrary non-rectangular cross section. This generalization step considerably improves the possibilities for the application of RZT. Furthermore, beam structures with interlayer slip can easily be treated. So the RZT is very well suited to analyze all kinds, of shear-elastic structural element like CLT-plate, timber-concrete composite structure or doweled beam in an accurate and unified way.

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5

Flores, Fernando G., Sergio Oller, and Liz G. Nallim. "On the analysis of non-homogeneous laminates using the refined zigzag theory." Composite Structures 204 (November 2018): 791–802. http://dx.doi.org/10.1016/j.compstruct.2018.08.018.

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6

Ascione, Alessia, and Marco Gherlone. "Nonlinear static response analysis of sandwich beams using the Refined Zigzag Theory." Journal of Sandwich Structures & Materials 22, no. 7 (August 23, 2018): 2250–86. http://dx.doi.org/10.1177/1099636218795381.

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The Refined Zigzag Theory (RZT) is assessed for the buckling and nonlinear static response analysis of multilayered composite and sandwich beams. A nonlinear formulation of the RZT is developed taking into account geometric imperfections and nonlinearities using the Von Kármán nonlinear strain-displacement relations. FE analyses are conducted employing C0-beam elements based on the RZT and the Timoshenko Beam Theory (TBT) to model three sandwich beams with different core materials and slenderness ratios, in both simply supported and cantilever configurations. The reference solutions are obtained by high-fidelity FE commercial codes, Abaqus® and Nastran®. The first two buckling loads are evaluated for the beams without initial imperfections. Several shapes are then assumed as geometric imperfections to calculate the beams’ nonlinear response to axial-compressive loads. The comparisons show the very high accuracy of the RZT (comparable to high fidelity FE commercial codes) for both the buckling and nonlinear static analyses and its superior capability with respect to the TBT to deal with sandwich beams with low slenderness ratio and higher face-to-core stiffness ratio.

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7

Treviso, Alessandra, Domenico Mundo, and Michel Tournour. "Dynamic response of laminated structures using a Refined Zigzag Theory shell element." Composite Structures 159 (January 2017): 197–205. http://dx.doi.org/10.1016/j.compstruct.2016.09.026.

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8

Hasim, K. Ahmet. "Isogeometric static analysis of laminated composite plane beams by using refined zigzag theory." Composite Structures 186 (February 2018): 365–74. http://dx.doi.org/10.1016/j.compstruct.2017.12.033.

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9

Gherlone, Marco, Daniele Versino, and Vincenzo Zarra. "Multilayered triangular and quadrilateral flat shell elements based on the Refined Zigzag Theory." Composite Structures 233 (February 2020): 111629. http://dx.doi.org/10.1016/j.compstruct.2019.111629.

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10

Nallim, Liz G., Sergio Oller, Eugenio Oñate, and Fernando G. Flores. "A hierarchical finite element for composite laminated beams using a refined zigzag theory." Composite Structures 163 (March 2017): 168–84. http://dx.doi.org/10.1016/j.compstruct.2016.12.031.

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11

Fares, M. E., and M. Kh Elmarghany. "A refined zigzag nonlinear first-order shear deformation theory of composite laminated plates." Composite Structures 82, no. 1 (January 2008): 71–83. http://dx.doi.org/10.1016/j.compstruct.2006.12.007.

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12

Kutlu, Akif. "Mixed finite element formulation for bending of laminated beams using the refined zigzag theory." Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications 235, no. 7 (July 2021): 1712–22. http://dx.doi.org/10.1177/14644207211018839.

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This study presents a mixed finite element formulation for the stress analysis of laminated composite beams based on the refined zigzag theory. The Hellinger–Reissner variational principle is employed to obtain the first variation of the functional that is expressed in terms of displacements and stress resultants. Due to C0 continuity requirements of the formulation, linear shape functions are adopted to discretize the straight beam domain with two-noded finite elements. The proposed formulation is shear locking free from nature since it introduces displacement and stress resultant terms as independent field variables. A monolithic solution of the global finite element equations is preferred, hence the stress resultants are directly obtained from the solution of these equations. The in-plane strain measures of the beam are obtained directly at the nodes over the compliance matrix and stress resultants by avoiding error-prone spatial derivatives. Following, transverse shear stresses are calculated from the equilibrium equations at the post-processing level. This simple but effective finite element formulation is first verified and tested for convergence behavior. The robustness of the approach is shown through some examples and its accuracy in predicting the displacement and stress components is revealed.

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13

Iurlaro, Luigi, Alessia Ascione, Marco Gherlone, Massimiliano Mattone, and Marco Di Sciuva. "Free vibration analysis of sandwich beams using the Refined Zigzag Theory: an experimental assessment." Meccanica 50, no. 10 (April 3, 2015): 2525–35. http://dx.doi.org/10.1007/s11012-015-0166-4.

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14

Dorduncu, Mehmet. "Stress analysis of laminated composite beams using refined zigzag theory and peridynamic differential operator." Composite Structures 218 (June 2019): 193–203. http://dx.doi.org/10.1016/j.compstruct.2019.03.035.

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15

Hasim, Kazim Ahmet, Adnan Kefal, and Erdogan Madenci. "Isogeometric plate element for unstiffened and blade stiffened laminates based on refined zigzag theory." Composite Structures 222 (August 2019): 110931. http://dx.doi.org/10.1016/j.compstruct.2019.110931.

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16

Hasim, K. A., and A. Kefal. "Isogeometric static analysis of laminated plates with curvilinear fibers based on Refined Zigzag Theory." Composite Structures 256 (January 2021): 113097. http://dx.doi.org/10.1016/j.compstruct.2020.113097.

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17

Dorduncu, Mehmet. "Peridynamic modeling of adhesively bonded beams with modulus graded adhesives using refined zigzag theory." International Journal of Mechanical Sciences 185 (November 2020): 105866. http://dx.doi.org/10.1016/j.ijmecsci.2020.105866.

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18

Flores, Fernando G. "Implementation of the refined zigzag theory in shell elements with large displacements and rotations." Composite Structures 118 (December 2014): 560–70. http://dx.doi.org/10.1016/j.compstruct.2014.07.034.

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19

Reid, Joel W., James A. Kaduk, and Lidia Matei. "The crystal structure of MoO2(O2)H2O." Powder Diffraction 33, no. 1 (February 14, 2018): 49–54. http://dx.doi.org/10.1017/s0885715618000118.

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The crystal structure of MoO2(O2)H2O has been solved by analogy with the WO2(O2)H2O structure and refined with synchrotron powder diffraction data obtained from beamline 08B1-1 at the Canadian Light Source. Rietveld refinement, performed with the software package GSAS, yielded monoclinic lattice parameters of a = 12.0417(4) Å, b = 3.87003(14) Å, c = 7.38390(24) Å, and β = 78.0843(11)° (Z = 4, space group P21/n). The structure is composed of double zigzag molybdate chains running parallel to the b-axis. The Rietveld refined structure was compared with density functional theory (DFT) calculations performed with CRYSTAL14, and show strong agreement with the DFT optimized structure.

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20

Di Sciuva, M., M. Gherlone, and M. Sorrenti. "Buckling analysis of angle-ply multilayered and sandwich plates using the enhanced Refined Zigzag Theory." Proceedings of the Estonian Academy of Sciences 71, no. 1 (2022): 84. http://dx.doi.org/10.3176/proc.2022.1.08.

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21

Ascione, Alessia, Marco Gherlone, and Adrian C. Orifici. "Nonlinear static analysis of composite beams with piezoelectric actuator patches using the Refined Zigzag Theory." Composite Structures 282 (February 2022): 115018. http://dx.doi.org/10.1016/j.compstruct.2021.115018.

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22

Iurlaro, Luigi, Marco Gherlone, and Marco Di Sciuva. "Bending and free vibration analysis of functionally graded sandwich plates using the Refined Zigzag Theory." Journal of Sandwich Structures & Materials 16, no. 6 (August 26, 2014): 669–99. http://dx.doi.org/10.1177/1099636214548618.

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23

Versino, Daniele, Marco Gherlone, and Marco Di Sciuva. "Four-node shell element for doubly curved multilayered composites based on the Refined Zigzag Theory." Composite Structures 118 (December 2014): 392–402. http://dx.doi.org/10.1016/j.compstruct.2014.08.018.

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24

Iurlaro, Luigi, Marco Gherlone, Marco Di Sciuva, and Alexander Tessler. "Refined Zigzag Theory for laminated composite and sandwich plates derived from Reissner’s Mixed Variational Theorem." Composite Structures 133 (December 2015): 809–17. http://dx.doi.org/10.1016/j.compstruct.2015.08.004.

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25

Versino, Daniele, Marco Gherlone, Massimiliano Mattone, Marco Di Sciuva, and Alexander Tessler. "C0 triangular elements based on the Refined Zigzag Theory for multilayer composite and sandwich plates." Composites Part B: Engineering 44, no. 1 (January 2013): 218–30. http://dx.doi.org/10.1016/j.compositesb.2012.05.026.

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26

Gherlone, Marco, Alexander Tessler, and Marco Di Sciuva. "C0 beam elements based on the Refined Zigzag Theory for multilayered composite and sandwich laminates." Composite Structures 93, no. 11 (October 2011): 2882–94. http://dx.doi.org/10.1016/j.compstruct.2011.05.015.

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27

Eijo, A., E. Oñate, and S. Oller. "A four-noded quadrilateral element for composite laminated plates/shells using the refined zigzag theory." International Journal for Numerical Methods in Engineering 95, no. 8 (May 20, 2013): 631–60. http://dx.doi.org/10.1002/nme.4503.

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28

Chen, Chung-De. "A distributed parameter electromechanical model for bimorph piezoelectric energy harvesters based on the refined zigzag theory." Smart Materials and Structures 27, no. 4 (March 7, 2018): 045009. http://dx.doi.org/10.1088/1361-665x/aaa725.

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29

Tessler, Alexander. "Refined zigzag theory for homogeneous, laminated composite, and sandwich beams derived from Reissner’s mixed variational principle." Meccanica 50, no. 10 (July 8, 2015): 2621–48. http://dx.doi.org/10.1007/s11012-015-0222-0.

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30

Farhatnia, F., and M. Sarami. "Finite Element Approach of Bending and Buckling Analysis of FG Beams Based on Refined Zigzag Theory." Universal Journal of Mechanical Engineering 7, no. 4 (July 2019): 147–58. http://dx.doi.org/10.13189/ujme.2019.070402.

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31

Oñate, E., A. Eijo, and S. Oller. "Simple and accurate two-noded beam element for composite laminated beams using a refined zigzag theory." Computer Methods in Applied Mechanics and Engineering 213-216 (March 2012): 362–82. http://dx.doi.org/10.1016/j.cma.2011.11.023.

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32

Chen, Chung-De, and Po-Wen Su. "An analytical solution for vibration in a functionally graded sandwich beam by using the refined zigzag theory." Acta Mechanica 232, no. 11 (October 11, 2021): 4645–68. http://dx.doi.org/10.1007/s00707-021-03063-9.

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33

Dorduncu, Mehmet. "Stress analysis of sandwich plates with functionally graded cores using peridynamic differential operator and refined zigzag theory." Thin-Walled Structures 146 (January 2020): 106468. http://dx.doi.org/10.1016/j.tws.2019.106468.

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34

Iurlaro, L., M. Gherlone, and M. Di Sciuva. "The (3,2)-Mixed Refined Zigzag Theory for generally laminated beams: Theoretical development and C0 finite element formulation." International Journal of Solids and Structures 73-74 (November 2015): 1–19. http://dx.doi.org/10.1016/j.ijsolstr.2015.07.028.

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35

Sorrenti, M., M. Di Sciuva, and A. Tessler. "A robust four-node quadrilateral element for laminated composite and sandwich plates based on Refined Zigzag Theory." Computers & Structures 242 (January 2021): 106369. http://dx.doi.org/10.1016/j.compstruc.2020.106369.

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36

Di Sciuva, Marco, Marco Gherlone, Luigi Iurlaro, and Alexander Tessler. "A class of higher-order C0 composite and sandwich beam elements based on the Refined Zigzag Theory." Composite Structures 132 (November 2015): 784–803. http://dx.doi.org/10.1016/j.compstruct.2015.06.071.

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37

Barut, A., E. Madenci, and A. Tessler. "C0-continuous triangular plate element for laminated composite and sandwich plates using the {2,2} – Refined Zigzag Theory." Composite Structures 106 (December 2013): 835–53. http://dx.doi.org/10.1016/j.compstruct.2013.07.024.

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38

Reid, Joel W., James A. Kaduk, and Lidia Matei. "The crystal structure of MoO2(O2)(H2O)·H2O." Powder Diffraction 34, no. 1 (February 7, 2019): 44–49. http://dx.doi.org/10.1017/s0885715619000095.

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The crystal structure of MoO2(O2)(H2O)·H2O has been solved using parallel tempering with the FOX software package and refined using synchrotron powder diffraction data obtained from beamline 08B1-1 at the Canadian Light Source. Rietveld refinement, performed with the software package GSAS, yielded monoclinic lattice parameters of a = 17.3355(5) Å, b = 3.83342(10) Å, c = 6.55760(18) Å, and β = 91.2114(27)° (Z = 4, space group I2/m). The structure is composed of double zigzag molybdate chains running parallel to the b-axis. The Rietveld refined structure was compared with density functional theory (DFT) calculations performed with CRYSTAL14, and shows comparable agreement with two DFT optimized structures of similar energy, which differ by the location of the molybdate coordinated water molecule. The true structure is likely a disordered combination of the two DFT optimized structures.

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39

Ascione, Alessia, Adrian C. Orifici, and Marco Gherlone. "Experimental and Numerical Investigation of the Refined Zigzag Theory for Accurate Buckling Analysis of Highly Heterogeneous Sandwich Beams." International Journal of Structural Stability and Dynamics 20, no. 07 (July 2020): 2050078. http://dx.doi.org/10.1142/s0219455420500789.

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The Refined Zigzag Theory (RZT) is a structural theory developed for the analysis of composite multilayer and sandwich beams. However, the accuracy of RZT for buckling analysis of sandwich beams has not been experimentally investigated, and for RZT and Timoshenko Beam Theory (TBT) the effect of the degree of heterogeneity on their accuracy requires further study. The aim of this work was to validate the use of the RZT for predicting the critical buckling loads of sandwich beams, even with highly heterogeneous material properties, and to assess the use of the TBT for the same application. Buckling experiments were conducted on five foam-core sandwich beams, which varied in geometry and included highly heterogeneous configurations. For each beam, two finite element (FE) models were analyzed using RZT- and TBT-beam FEs. The comparison between the numerical and the experimental results highlighted a major capability of RZT to correctly predict the critical buckling load for all the beams considered. The dependence of the TBT results on the beam characteristics was further investigated through a parametric analysis, which showed the dominant effect to be a close to linear relationship between the TBT error and the beam face-to-core thickness ratio. The work demonstrated the outstanding accuracy of the RZT predictions, including the superior capabilities with respect to TBT, and has application for rapid and accurate analysis of industrial structures.

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40

Honda, Shinya, Takahito Kumagai, Kazuya Tomihashi, and Yoshihiro Narita. "Frequency maximization of laminated sandwich plates under general boundary conditions using layerwise optimization method with refined zigzag theory." Journal of Sound and Vibration 332, no. 24 (November 2013): 6451–62. http://dx.doi.org/10.1016/j.jsv.2013.07.010.

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41

Eijo, A., E. Oñate, and S. Oller. "Delamination in laminated plates using the 4-noded quadrilateral QLRZ plate element based on the refined zigzag theory." Composite Structures 108 (February 2014): 456–71. http://dx.doi.org/10.1016/j.compstruct.2013.09.052.

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42

Dorduncu, Mehmet, and M. Kemal Apalak. "Elastic flexural analysis of adhesively bonded similar and dissimilar beams using refined zigzag theory and peridynamic differential operator." International Journal of Adhesion and Adhesives 101 (September 2020): 102631. http://dx.doi.org/10.1016/j.ijadhadh.2020.102631.

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43

Singh, S. K., and A. Chakrabarti. "Static, Vibration and Buckling Analysis of Skew Composite and Sandwich Plates Under Thermo Mechanical Loading." International Journal of Applied Mechanics and Engineering 18, no. 3 (August 1, 2013): 887–98. http://dx.doi.org/10.2478/ijame-2013-0053.

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Abstract Static, vibration and buckling behavior of laminated composite and sandwich skew plates is studied using an efficient C0 FE model developed based on refined higher order zigzag theory. The C0 FE model satisfies the interlaminar shear stress continuity at the interfaces and zero transverse shear stress conditions at plate top and bottom. In this model, the first derivatives of transverse displacement have been treated as independent variables to overcome the problem of C1 continuity associated with the plate theory. The C0 continuity of the present element is compensated in the stiffness matrix formulation by adding a suitable term. In order to avoid stress oscillations observed in the displacement based finite element, the stress field derived from temperature is made consistent with the total strain field by using field consistent approach. Numerical results are presented for different static, vibration and buckling problems by applying the FE model under thermo mechanical loading, where a nine noded C0 continuous isoparametric element is used. It is observed that there are very few results available in the literature on laminated composite and sandwich skew plates based on refined theories. As such many new results are also generated for future reference

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44

Di Sciuva, M., and M. Sorrenti. "Bending, free vibration and buckling of functionally graded carbon nanotube-reinforced sandwich plates, using the extended Refined Zigzag Theory." Composite Structures 227 (November 2019): 111324. http://dx.doi.org/10.1016/j.compstruct.2019.111324.

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45

Ghorbanpour Arani, A., M. Mosayyebi, F. Kolahdouzan, R. Kolahchi, and M. Jamali. "Refined zigzag theory for vibration analysis of viscoelastic functionally graded carbon nanotube reinforced composite microplates integrated with piezoelectric layers." Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering 231, no. 13 (September 14, 2016): 2464–78. http://dx.doi.org/10.1177/0954410016667150.

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Damped free vibration of carbon nanotube reinforced composite microplate bounded with piezoelectric sensor and actuator layers are investigated in this study. For the mathematical modeling of sandwich structure, the refined zigzag theory is applied. In addition, to present a realistic model, the material properties of system are supposed as viscoelastic based on Kelvin–Voigt model. Distributions of single-walled carbon nanotubes along the thickness direction of the viscoelastic carbon nanotube reinforced composite microplate are considered as four types of functionally graded distribution patterns. The viscoelastic functionally graded carbon nanotube reinforced composite microplate subjected to electromagnetic field is embedded in an orthotropic visco-Pasternak foundation. Hamilton’s principle is employed to establish the equations of motion. In order to calculate the frequency and damping ratio of sandwich plate, boundary condition of plate is assumed as simply-supported and an exact solution is used. The effects of some significant parameters such as damping coefficient of viscoelastic plates, volume fraction of carbon nanotubes, different types of functionally graded distributions of carbon nanotubes, magnetic field, and external voltage on the damped free vibration of system are investigated. Results clarify that considering viscoelastic property for system to achieve accurate results is essential. Furthermore, the effects of volume fraction and distribution type of carbon nanotubes are remarkable on the vibration of sandwich plate. In addition, electric and magnetic fields are considerable parameters to control the behavior of viscoelastic carbon nanotube reinforced composite microplate. It is hoped that the results of this study could be applied in design of nano/micromechanical sensor and actuator systems.

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46

Dey, S., T. Mukhopadhyay, S. Naskar, TK Dey, HD Chalak, and S. Adhikari. "Probabilistic characterisation for dynamics and stability of laminated soft core sandwich plates." Journal of Sandwich Structures & Materials 21, no. 1 (June 1, 2017): 366–97. http://dx.doi.org/10.1177/1099636217694229.

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This paper presents a generic multivariate adaptive regression splines-based approach for dynamics and stability analysis of sandwich plates with random system parameters. The propagation of uncertainty in such structures has significant computational challenges due to inherent structural complexity and high dimensional space of input parameters. The theoretical formulation is developed based on a refined C0 stochastic finite element model and higher-order zigzag theory in conjunction with multivariate adaptive regression splines. A cubical function is considered for the in-plane parameters as a combination of a linear zigzag function with different slopes at each layer over the entire thickness while a quadratic function is assumed for the out-of-plane parameters of the core and constant in the face sheets. Both individual and combined stochastic effect of skew angle, layer-wise thickness, and material properties (both core and laminate) of sandwich plates are considered in this study. The present approach introduces the multivariate adaptive regression splines-based surrogates for sandwich plates to achieve computational efficiency compared to direct Monte Carlo simulation. Statistical analyses are carried out to illustrate the results of the first three stochastic natural frequencies and buckling load.

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47

Sorrenti, M., M. Di Sciuva, J. Majak, and F. Auriemma. "Static Response and Buckling Loads of Multilayered Composite Beams Using the Refined Zigzag Theory and Higher-Order Haar Wavelet Method." Mechanics of Composite Materials 57, no. 1 (March 2021): 1–18. http://dx.doi.org/10.1007/s11029-021-09929-2.

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48

Kutlu, Akif, Mehmet Dorduncu, and Timon Rabczuk. "A novel mixed finite element formulation based on the refined zigzag theory for the stress analysis of laminated composite plates." Composite Structures 267 (July 2021): 113886. http://dx.doi.org/10.1016/j.compstruct.2021.113886.

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49

Dorduncu, Mehmet, Akif Kutlu, and Erdogan Madenci. "Triangular C0 continuous finite elements based on refined zigzag theory {2,2} for free and forced vibration analyses of laminated plates." Composite Structures 281 (February 2022): 115058. http://dx.doi.org/10.1016/j.compstruct.2021.115058.

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50

Chen, Chung-De, and Wei-Lian Dai. "The analysis of mode II strain energy release rate in a cracked sandwich beam based on the refined zigzag theory." Theoretical and Applied Fracture Mechanics 107 (June 2020): 102504. http://dx.doi.org/10.1016/j.tafmec.2020.102504.

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