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DEM Simulation of Macro and Micro-scale Behavior of Granular Materials during Loading and Unloading

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Year : March 30, 2022 | Volume : 09 | Issue : 01 | Page : 26-38

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Md. Mahmud Sazzad
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    1. Professor,Rajshahi University of Engineering & Technology,,Bangladesh
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    Abstract

    n The present paper aims at comparing the simulated stress-strain behavior of granular materials quantitatively with the experiment and exploring the evolution of the micro-scale behaviors during loading and unloading using the discrete element method (DEM). A numerical sample consisting of 9826 randomly generated spheres similar to the experiment was prepared. The numerically prepared isotropic sample was subjected to loading and unloading under strain controlled condition. It is noticed that the simulated stress-strain behavior agrees well with the experimental stress-strain behavior during loading and unloading. The evolution of micro-scale parameters is studied by varying the maximum applied strain. The evolution pattern of coordination number and slip coordination number depends on the maximum applied strain during loading and unloading. Slip coordination number evolves differently during loading from coordination number, but it evolves in a similar manner during unloading. The ratio of strong contacts to all contacts increases abruptly on reversal of loading, which is opposite to what is observed for coordination number and slip coordination number. The deviatoric fabric considering strong contacts mimics the deviatoric stress regardless of the values of maximum applied strain during loading and unloading. Fabric ratio can be linearly correlated to the stress ratio during loading and unloading regardless of the values of maximum applied strain when the contact normal vectors only at strong contacts are considered.n

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    Keywords: Quantitative validation, Micro-scale quantities, Deviatoric fabric, DEM, Loading and Unloading.

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    How to cite this article:n Md. Mahmud Sazzad DEM Simulation of Macro and Micro-scale Behavior of Granular Materials during Loading and Unloading joge March 30, 2022; 09:26-38

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    How to cite this URL: Md. Mahmud Sazzad DEM Simulation of Macro and Micro-scale Behavior of Granular Materials during Loading and Unloading joge March 30, 2022n {cited March 30, 2022};09:26-38. Available from: https://journals.stmjournals.com/joge/article=March 30, 2022/view=90812/

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    1. Azéma, E., Radjai, F., Peyroux, R., and Saussine, G. (2007). Force transmission in a packing of pentagonal particles. Physical Review E, 76 (1), 01130. DOI: 10.1103/PhysRevE.76.011301.
    2. Azéma, E., Radjai, F., and Saussine, G. (2009). Quasistatic rheology, force transmission and fabric properties of a packing of irregular polyhedral particles. Mechanics of Materials, 41(6), 729-741. DOI: 10.1016/j.mechmat.2009.01.021.
    3. Cui, L. (2006). Developing a virtual test environment for granular materials using discrete element modeling. PhD Thesis, University College Dublin, Ireland.
    4. Cui, L., O’Sullivan, C., and O’Neil, S. (2007). An analysis of the triaxial apparatus using a mixed boundary three-dimensional discrete element model.” Geotechnique, 57(10), 831–844, DOI: 10.1680/geot.2007.57.10.831.
    5. Cundall, PA., and Strack, ODL. (1979). A discrete numerical model for granular assemblies. Geotechnique, 29(1), 47-65. DOI: 10.1680/geot.1979.29.1.47.
    6. Jiang, MJ., Yu, H-S., and Harris, D. (2005). A novel discrete model for granular material incorporating rolling resistance. Computers and Geotechnics, 32(5), 240-357, DOI: 10.1016/j.compgeo.2005.05.001.
    7. Kuhn, MR. (1999). Structured deformation in granular materials. Mechanics of Materials, 31(6), 407-429. DOI: 10.1016/S0167-6636(99)00010-1.
    8. Kuhn, MR. (2003). Smooth convex three-dimensional particle for the discrete element method. Journal of Engineering Mechanics, 129(5), 539-547. DOI: 10.1061/(ASCE)0733-9399(2003)129:5(539).
    9. Kuhn, MR., Renken, HE., Mixsell, AD., and Kramer, SL. (2014). Investigation of cyclic liquefaction with discrete element simulations. Journal of Geotechnical and Geoenvironmental Engineering, 140(12), 1-13. DOI: 10.1061/(ASCE)GT.1943-5606.0001181.
    10. Ng, T-T. (2001). Fabric evolution of ellipsoidal arrays with different particle shapes. Journal of Engineering Mechanics, 127(10), 994-999, DOI: 10.1061/(ASCE)0733-9399(2001)127:10(994).
    11. Ng, T-T., and Dobry, R. (1994). Numerical simulations of monotonic and cyclic loading of granular soil. Journal of Geotechnical Engineering, 120(2), 388-403. DOI: 10.1061/(ASCE)0733-9410(1994)120:2(388).
    12. Nouguier-Lehon, C., Cambou, B., Vincens, E. (2003). “Influence of particle shape and angularity on the behavior of granular materials: a numerical analysis.” International Journal of Numerical Analytical Methods in Geomechanics, 27(14), 1207-1226. DOI: 10.1002/nag.314.
    13. Oda, M., Nemat-Nasser, S., and Konishi, J. (1985). Stress-induced anisotropy in granular masses. Soils and Foundations, 25(3), 85-97. DOI: 10.3208/sandf1972.25.3_85.
    14. O’Sullivan, C., Bray, J., and Riemer, M. (2004). An examination of the response of regularly packed specimens of spherical particles using physical tests and discrete element simulations. Journal of Engineering Mechanics, 130(10), 1140–1150. DOI: 10.1061/(ASCE)0733-9399(2004)130:10(1140).
    15. O’Sullivan, C., Cui, L. and O’Neill, SC. (2008). Discrete element analysis of the response of granular materials during cyclic loading. Soils and Foundations, 48(4), 511-530, DOI: 10.3208/sandf.48.511.
    16. Ouadfel, H., and Rothenburg, L. (2001). Stress-force-fabric relationship for assemblies of ellipsoids. Mechanics of Materials, 33(4), 201–221. DOI: 10.1016/S0167-6636(00)00057-0.
    17. Radjai, F., Wolf, DE., Jean, M., and Moreau, JJ. (1998). Bimodal character of stress transmission in granular packings. Physical Review Letter, 80(1), 61–64. DOI: 10.1103/PhysRevLett.80.61.
    18. Rothenburg, L., and Bathurst, RJ. (1989). Analytical study of induced anisotropy in idealized granular materials. Geotechnique, 39(4), DOI: 601–614, DOI: 10.1680/geot.1989.39.4.601.
    19. Sazzad, MM., and Suzuki, K. (2010). Micromechanical behavior of granular materials with inherent anisotropy under cyclic loading using 2D DEM., Granular Matter, 12(6), 597–605, DOI: 10.1007/s10035-010-0200-0.
    20. Sazzad, M., and Suzuki, K. (2011). Effect of interparticle friction on the cyclic behavior of granular materials using 2D DEM. Journal of Geotechnical and Geoenvironmental Engineering, 137(5), 545-549. DOI: 10.1061/(ASCE)GT.1943-5606.0000441.
    21. Sazzad, MM. (2014). Micro-scale behavior of granular materials during cyclic loading. Particuology, 16, 132-141. DOI: 10.1016/j.partic.2013.12.005.
    22. Sazzad, MM., Sayera, K., Shaha, RK., and Islam, MS. (2015). “Macro and micro responses of granular materials under plane strain compression by 3D DEM.”, International Journal of Advanced Structures and Geotechnical Engineering, 4(2), 114-119.
    23. Sazzad, MM. (2016). Micro-scale responses of granular materials at different confining pressures using DEM. Acta Geotechnica. Slovenica, 13(1), 26-36.
    24. Sazzad, MM., Sneha, E., and Rouf, RB. (2017). Comparison of stress-stain behavior of CTC test using DEM simulation. International Conference on Planning, Architecture and Civil Engineering, Bangladesh, pp. 194-199.
    25. Sazzad, MM (2019) Effect of intermediate principal stress on the behavior of granular materials at a low mean stress by DEM. Geotechnical and Geological Engineering, 37(5), DOI: 4539–4550. DOI: 10.1007/s10706-019-00929-7 .
    26. Yang, Y., Fei, W., Yu., H-S., Ooi, J., and Rotter, M. (2015). Experimental study of anisotropy and non-coaxiality of granular solids, Granular Matter, 17(2), 189–196. DOI: 10.1007/s10035-015-0551-7.

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    Journal of Geotechnical Engineering

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    Volume 09
    Issue 01
    Received March 3, 2022
    Accepted March 21, 2022
    Published March 30, 2022

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    Effect of Particle Size of Sand on the Interface Shear Behavior of Sand and Non-woven Geotextile

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    By [foreach 286]u00a0

    u00a0Mahmud Sazzad, Rima Parvin,

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    nJanuary 9, 2023 at 4:38 am

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    Soil-geosynthetic interface is the weakest zone for shear failure. It is influenced by size, shape, density and water content of sand. It is also influenced by the properties of geosynthetic such as texture and structure. This paper explores the influence of the size of sand on the behavior of sand-geotextile interface. Three types of sands namely coarse, medium and fine sand and non-woven geotextile were used in this study. Several interface direct shear tests on these materials were performed using a direct shear box modified for interface testing. The test results depict that the peak interfacial friction angles between the sand particles and geosynthetic material (geotextile) depend on the relative size of sand particles. The interfacial friction angle for fine sand is higher than that of the coarse sand with the non-woven geotextile. Interfacial strength efficiency of fine sand is 19.45% greater than that of coarse sand and is 11.38% greater than that of medium sand for the same type of geosynthetic material. Interfacial friction angle between sand and non-woven geotextile is 0.70 to 0.90 times of sand to sand friction angle for dry condition.

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    Volume :u00a0u00a08 | Issue :u00a0u00a03 | Received :u00a0u00a0September 21, 2021 | Accepted :u00a0u00a0October 9, 2021 | Published :u00a0u00a0November 30, 2021n[if 424 equals=”Regular Issue”][This article belongs to Journal of Geotechnical Engineering(joge)] [/if 424][if 424 equals=”Special Issue”][This article belongs to Special Issue Effect of Particle Size of Sand on the Interface Shear Behavior of Sand and Non-woven Geotextile under section in Journal of Geotechnical Engineering(joge)] [/if 424]
    Keywords Size of sand, interfacial friction angle, sand-geotextile interface, direct shear test

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    1. Yetimoglu T, Salbas O. A study on shear strength of sands reinforced with randomly distributed discrete fibers. Geotextiles and Geomembranes. 2003; 21(2):103–10p.
    2. Palmeira EM. Soil-geosynthetic interaction: Modelling and analysis. Geotextiles and Geomembranes. 2009; 27(5):368–90p.
    3. Lee KM, Manjunath VR. Soil-geotextile interface friction by direct shear tests. Canadian Geotechnical Journal. 2000; 37(1): 238-52p.
    4. Anubhav, Basudhar PK. Interface behavior of woven geotextile with rounded and angular particle sand. Journal of Materials in Civil Engineering. 2013; 25(12):1970–74p.
    5. Tuna SC, Altun S. Mechanical behaviour of sand-geotextile interface. Scientia Iranica, 2012; 19(4): 1044–51p.
    6. Vangla P, Gali ML. Effect of particle size of sand and surface asperities of reinforcement on their interface shear behaviour. Geotextiles and Geomembranes. 2016; 44(3): 254–68p.
    7. Ebadi M, Habibagahi G, Hataf N. Effect of cement treatment on soil non-woven geotextile interface. Scientia Iranica. 2015; 22(1):69–80p.
    8. ASTM D5321. Standard Test Method for Determining the Shear Strength of Soil-Geosynthetic and Geosynthetic-Geosynthetic Interfaces by Direct Shear. ASTM International, West Conshohocken, PA; 2017.
    9. Wu W, Wick H, Ferstl F, et al. A tilt table device for testing geosynthetic interfaces in centrifuge. Geotextiles and Geomembranes. 2008; 26(1):31–38p.
    10. ASTM D422. Standard Test Method for Particle-Size Analysis of Soils. ASTM International, West Conshohocken, PA; 1998.
    11. ASTM D 5261. Standard Test Method for Measuring Mass per Unit Area of Geotextiles. ASTM International, West Conshohocken, PA; 1992.
    12. ASTM D 5199. Standard Test Method for Measuring the Nominal Thickness of Geosynthetics. ASTM International, West Conshohocken, PA; 2001.
    13. ASTM D 5035. Standard Breaking Force and Elongation of Textile Fabrics (Strip Method). ASTM International, West Conshohocken, PA; 2006.
    14. ASTM D 4632. Standard Test Method for Grab Breaking Load and Elongation of Geotextile. ASTM International, West Conshohocken, PA; 2008.
    15. ASTM D 6241. Standard Test Method for Static Puncture Strength of Geotextiles and Geotextile- Related Products Using a 50-mm Probe. ASTM International, West Conshohocken, PA; 2014.
    16. ASTM D 4757. Standard Practice for Placarding Solvent Vapor Degreasers. ASTM International, West Conshohocken, PA; 1998.
    17. ASTM D 4491. Standard Test Methods for Water Permeability of Geotextiles by Permittivity. ASTM International, West Conshohocken, PA; 1999.
    18. ASTM D 3080. Standard Test Method for Direct Shear Test of Soil. ASTM International, West Conshohocken, PA; 2004.
    19. ASTM D 5321. Standard Test Method for Determining the Shear Strength of Soil-Geosynthetic and Geosynthetic-Geosynthetic interfaces by direct Shear. ASTM International, West Conshohocken, PA; 2008.
    20. Ouria A, Mahmoudi A. Laboratory and numerical modeling of strip footing on geotextile-reinforced sand with cement-treated interface. Geotextiles and Geomembranes. 2018; 46(1): 29– 39p.
    21. Palmeira EM. Sixth Géotechnique symposium in print, discussion on ‘direct shear tests and reinforced sand. Géotech. 1988; 38(1):146–48.
    22. Takasumi DL, Green KR, Holtz RD. Soil-geosynthetic interface strength characteristics: A review of state-of-the-art testing procedures. Proc. Geosynthetics’91; 1991, Industrial Fabrics Association International, St. Paul, MN, 1991, 87–100p.

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    [if 424 not_equal=”Regular Issue”] Regular Issue[/if 424] Open Access Article

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    Editors Overview

    joge maintains an Editorial Board of practicing researchers from around the world, to ensure manuscripts are handled by editors who are experts in the field of study.

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      By  [foreach 286]n

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      Mahmud Sazzad, Rima Parvin

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    1. Professor, Lecturer,Department of Civil Engineering, Rajshahi University of Engineering & Technology, Department of Civil Engineering, Bangladeshi Army University of Science and Technology,,Bangladesh, Bangladesh
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    Abstract

    nSoil-geosynthetic interface is the weakest zone for shear failure. It is influenced by size, shape, density and water content of sand. It is also influenced by the properties of geosynthetic such as texture and structure. This paper explores the influence of the size of sand on the behavior of sand-geotextile interface. Three types of sands namely coarse, medium and fine sand and non-woven geotextile were used in this study. Several interface direct shear tests on these materials were performed using a direct shear box modified for interface testing. The test results depict that the peak interfacial friction angles between the sand particles and geosynthetic material (geotextile) depend on the relative size of sand particles. The interfacial friction angle for fine sand is higher than that of the coarse sand with the non-woven geotextile. Interfacial strength efficiency of fine sand is 19.45% greater than that of coarse sand and is 11.38% greater than that of medium sand for the same type of geosynthetic material. Interfacial friction angle between sand and non-woven geotextile is 0.70 to 0.90 times of sand to sand friction angle for dry condition.n

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    Keywords: Size of sand, interfacial friction angle, sand-geotextile interface, direct shear test

    n[if 424 equals=”Regular Issue”][This article belongs to Journal of Geotechnical Engineering(joge)]

    n[/if 424][if 424 equals=”Special Issue”][This article belongs to Special Issue under section in Journal of Geotechnical Engineering(joge)] [/if 424]

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    References

    n[if 1104 equals=””]

    1. Yetimoglu T, Salbas O. A study on shear strength of sands reinforced with randomly distributed discrete fibers. Geotextiles and Geomembranes. 2003; 21(2):103–10p.
    2. Palmeira EM. Soil-geosynthetic interaction: Modelling and analysis. Geotextiles and Geomembranes. 2009; 27(5):368–90p.
    3. Lee KM, Manjunath VR. Soil-geotextile interface friction by direct shear tests. Canadian Geotechnical Journal. 2000; 37(1): 238-52p.
    4. Anubhav, Basudhar PK. Interface behavior of woven geotextile with rounded and angular particle sand. Journal of Materials in Civil Engineering. 2013; 25(12):1970–74p.
    5. Tuna SC, Altun S. Mechanical behaviour of sand-geotextile interface. Scientia Iranica, 2012; 19(4): 1044–51p.
    6. Vangla P, Gali ML. Effect of particle size of sand and surface asperities of reinforcement on their interface shear behaviour. Geotextiles and Geomembranes. 2016; 44(3): 254–68p.
    7. Ebadi M, Habibagahi G, Hataf N. Effect of cement treatment on soil non-woven geotextile interface. Scientia Iranica. 2015; 22(1):69–80p.
    8. ASTM D5321. Standard Test Method for Determining the Shear Strength of Soil-Geosynthetic and Geosynthetic-Geosynthetic Interfaces by Direct Shear. ASTM International, West Conshohocken, PA; 2017.
    9. Wu W, Wick H, Ferstl F, et al. A tilt table device for testing geosynthetic interfaces in centrifuge. Geotextiles and Geomembranes. 2008; 26(1):31–38p.
    10. ASTM D422. Standard Test Method for Particle-Size Analysis of Soils. ASTM International, West Conshohocken, PA; 1998.
    11. ASTM D 5261. Standard Test Method for Measuring Mass per Unit Area of Geotextiles. ASTM International, West Conshohocken, PA; 1992.
    12. ASTM D 5199. Standard Test Method for Measuring the Nominal Thickness of Geosynthetics. ASTM International, West Conshohocken, PA; 2001.
    13. ASTM D 5035. Standard Breaking Force and Elongation of Textile Fabrics (Strip Method). ASTM International, West Conshohocken, PA; 2006.
    14. ASTM D 4632. Standard Test Method for Grab Breaking Load and Elongation of Geotextile. ASTM International, West Conshohocken, PA; 2008.
    15. ASTM D 6241. Standard Test Method for Static Puncture Strength of Geotextiles and Geotextile- Related Products Using a 50-mm Probe. ASTM International, West Conshohocken, PA; 2014.
    16. ASTM D 4757. Standard Practice for Placarding Solvent Vapor Degreasers. ASTM International, West Conshohocken, PA; 1998.
    17. ASTM D 4491. Standard Test Methods for Water Permeability of Geotextiles by Permittivity. ASTM International, West Conshohocken, PA; 1999.
    18. ASTM D 3080. Standard Test Method for Direct Shear Test of Soil. ASTM International, West Conshohocken, PA; 2004.
    19. ASTM D 5321. Standard Test Method for Determining the Shear Strength of Soil-Geosynthetic and Geosynthetic-Geosynthetic interfaces by direct Shear. ASTM International, West Conshohocken, PA; 2008.
    20. Ouria A, Mahmoudi A. Laboratory and numerical modeling of strip footing on geotextile-reinforced sand with cement-treated interface. Geotextiles and Geomembranes. 2018; 46(1): 29– 39p.
    21. Palmeira EM. Sixth Géotechnique symposium in print, discussion on ‘direct shear tests and reinforced sand. Géotech. 1988; 38(1):146–48.
    22. Takasumi DL, Green KR, Holtz RD. Soil-geosynthetic interface strength characteristics: A review of state-of-the-art testing procedures. Proc. Geosynthetics’91; 1991, Industrial Fabrics Association International, St. Paul, MN, 1991, 87–100p.

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    Volume 8
    Issue 3
    Received September 21, 2021
    Accepted October 9, 2021
    Published November 30, 2021

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    Thermal Analysis of Isotropic and Orthotropic Plate by Trigonometric Shear Deformation Theory

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    By [foreach 286]u00a0

    u00a0Rajal Shivraj Phulari, Mohammed Ishtiyaque, Swami S.K.,

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    nJanuary 9, 2023 at 4:44 am

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    nAbstract

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    In the present study, a sinusoidal shear and normal deformation theory taking into account effects of transverse shear as well as transverse normal is used to develop the analytical solution for the bidirectional bending analysis of isotropic, transversely isotropic, laminated composite and sandwich rectangular plates. Governing equations and boundary conditions of the theory are obtained using the principle of virtual work. The Navier solution for simply supported laminated composite plates have to develop. Results obtained for displacements and stresses of simply supported rectangular plates have to compare with those of other refined theories and exact elasticity solution wherever applicable. The Navier-type exact solutions for static bending analysis are have to for sinusoidally and uniformly distributed loads. The accuracy of the present theory is ascertained by comparing it with various available results in the literature.

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    Volume :u00a0u00a08 | Issue :u00a0u00a02 | Received :u00a0u00a0June 15, 2021 | Accepted :u00a0u00a0July 5, 2021 | Published :u00a0u00a0August 30, 2021n[if 424 equals=”Regular Issue”][This article belongs to Journal of Geotechnical Engineering(joge)] [/if 424][if 424 equals=”Special Issue”][This article belongs to Special Issue Thermal Analysis of Isotropic and Orthotropic Plate by Trigonometric Shear Deformation Theory under section in Journal of Geotechnical Engineering(joge)] [/if 424]
    Keywords Trigonometric shear deformation theory, transverse in-plane stress, transverse displacement, trigonometric function

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    References

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    1. Hosseini-Hashemi Sh, Rokni Damavandi Taher H, Akhavan H, Omidi M. Free vibration of functionally graded rectangular plates using first-order shear deformation plate theory. Appl Math Modell. 2010;34(5):1276–91. doi: 10.1016/j.apm.2009.08.008.
    2. Thai CH, Tran LV, Tran DT, Nguyen-Thoi T, Nguyen-Xuan H. Analysis of laminated composite plates using higher-order shear deformation plate theory and node-based smoothed discrete shear gap method. Appl Math Modell. 2012;36(11):5657–77. doi: 10.1016/j.apm.2012.01.003.
    3. Shi G. A new simple third-order shear deformation theory of plates. Int J Solids Struct. 2007;44(13):4399–417. doi: 10.1016/j.ijsolstr.2006.11.031.
    4. Matsunaga H. A comparison between 2-D single-layer and 3-D layerwise theories for computing interlaminar stresses of laminated composite and sandwich plates subjected to thermal loadings. Compos Struct. 2004;64(2):161–77. doi: 10.1016/j.compstruct.2003.08.001.
    5. Loredo A, Castel A. Two multilayered plate models with transverse shear warping functions issued from three dimensional elasticity equations. Compos Struct. 2014;117:382–95. doi: 10.1016/j.compstruct.2014.07.001.
    6. Loredo A. A multilayered plate theory with transverse shear and normal warping functions. Compos Struct. 2016;156:361–74. doi: 10.1016/j.compstruct.2015.08.084.
    7. Adhikari B, Singh BN. An efficient higher order non-polynomial quasi-3-D theory for dynamic responses of laminated composite plates. Compos Struct. 2018;189:386–97. doi: 10.1016/j.compstruct.2017.10.044.
    8. Sayyad AS. A new shear and normal deformation theory for isotropic, transversely isotropic, laminated composite and sandwich plates. Published online; February 12 2014.
    9. Ghugal YM, Shimpi RP. A review of refined shear deformation theories of isotropic and anisotropic laminated plates. J Reinf Plast Compos. 2002;21(9):775–813. doi: 10.1177/073168402128988481.
    10. Bessaim A, Houari MS, Tounsi A, Mahmoud S, Bedia EAA. A new higher-order shear and normal deformation theory for the static and free vibration analysis of sandwich plates with functionally graded isotropic face sheets. J Sandwich Struct Mater. September 2013;15(6):1–33.
    11. Sireesha P. Bending response of laminated composite plates using finite element method. Int J Eng Technol Manag Appl Sci. May 2015;3;Special Issue.
    12. Ghugal YM, Kulkarni SK. Flexural analysis of cross-ply laminated plates subjected to nonlinear thermal and mechanical loadings. Published online: 4 December 2012. Acta Mech 224. 2013;2012:675–90.
    13. Kotlyar R. Effect of band warping and wafer orientation on NMOS mobility under arbitrary applied stress. Published online; December 12 2007. p. 95–8.
    14. Jadhav P. Stability analysis of thick piezoelectric metal based FGM plate using first order and higher order shear deformation theory. Published online; October 21 2014.
    15. Kant T, Swaminathan K. Analytical solutions for the static analysis of laminated composite and sandwich plates based on a higher order refined theory. Compos Struct. 2002;56(4):329–44. doi: 10.1016/S0263–8223(02)00017-X.
    16. Hongxing LJH. Free vibration analyses of axially loaded laminated composite beams based on higher-order shear deformation theory. Published online; December 10 2010.
    17. Sayyad AS, Ghugal YM, Shinde PN. Stress analysis of laminated composite and soft core sandwich beams using a simple higher order shear deformation theory. J Serb Soc Comp Mech/Vol. 9/No. 2015/pp;1(1):15–35. doi: 10.5937/jsscm1501015S.
    18. Sayyad AS. A new shear and normal deformation theory for isotropic, transversely isotropic, laminated composite and sandwich plates. Published online; February 12 2014.
    19. Sayyad AS, Ghugal YM. On the free vibration analysis of laminated composite and sandwich plates: a review of recent literature with some numerical results. Compos Struct. 2015;129:177–201. doi: 10.1016/j.compstruct.2015.04.007.
    20. Adim B. A simple higher order shear deformation theory for mechanical behavior of laminated composite plates. Published online; May 6 2016.
    21. Chien HT. A generalized layerwise higher-order shear deformation theory for laminated composite and sandwich plates based on isogeometric analysis. Published online; January 6 2016.
    22. Goswami S. A New Rectangular Finite Element Formulation Based on Higher Order Displacement Theory for Thick and Thin Composite and Sandwich Plates. World Journal of Published Online June 2013.
    23. Aydogdu M. A new shear deformation theory for laminated composite plates. Compos Struct. 2009;89(1):94–101. doi: 10.1016/j.compstruct.2008.07.008.
    24. Mantari JL, Oktem AS, Guedes Soares C. A new trigonometric shear deformation theory for isotropic, laminated composite and sandwich plates. Int J Solids Struct. 2012;49(1):43–53. doi: 10.1016/j.ijsolstr.2011.09.008.
    25. Wu Z, Chen R, Chen W. Refined laminated composite plate element based on global–local higher-order shear deformation theory. Compos Struct. 2005;70(2):135–52. doi: 10.1016/j.compstruct.2004.08.019.
    26. Milan B. The derivation of the equations of moderately thick plates by the method of successive approximations. Published online; July 15 2009.
    27. Mohammad A. A new modified higher-order shear deformation theory for nonlinear analysis of macro- and nano-annular sector plates using the extended Kantorovich method in conjunction with SAPM; June 17 2017.
    28. Carrera E. Theories and finite elements for multilayered, anisotropic, composite plates and shells. Arch Comput Meth Eng. 2002;9(2):87–140. doi: 10.1007/BF02736649.
    29. Ferreira AJM, Batra RC, Roque CMC, Qian LF, Martins PALS. Static analysis of functionally graded plates using third-order shear deformation theory and a meshless method. Compos Struct. 2005;69(4):449–57. doi: 10.1016/j.compstruct.2004.08.003.
    30. Arafa E-H. Free vibration response of laminated composite plate shear walls. September 2017;13(9):28–38.
    31. Maiti DK. Bending and Buckling Analyses of Composite Laminates with and without Presence of Damage and its Passive Control with Optimized Piezoelectric Patch Location. 2016 June; Spl Issue:329–40.
    32. Sreehari VM. Bending and Buckling Analyses of Composite Laminates with and without Presence of Damage and its Passive Control. Jun 2 Spl Issue 2017 p.p. 329–40.
    33. Kadbhane SC. Damping evaluation of conventional and composite plates using different structures-A review. Int J Res Emerg Sci Technol. 2016;3(1).
    34. Kulkarni SK. Thermal flexural analysis of cross-ply laminated plates Latin American Journal. 2014;10:1001–23.
    35. Kharate NK. Damping evaluation of conventional and composite plates. Int J Res Emerg Sci Technol. 2017;3(1).
    36. Ghugal YM, Kulkarni SK. Thermal flexural analysis of cross-ply laminated plates using trigonometric shear deformation theory. Lat Am j solids struct. 2013;10(5):1001–23. doi: 10.1590/S1679–78252013000500008.

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    [if 424 not_equal=”Regular Issue”] Regular Issue[/if 424] Open Access Article

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    Editors Overview

    joge maintains an Editorial Board of practicing researchers from around the world, to ensure manuscripts are handled by editors who are experts in the field of study.

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      By  [foreach 286]n

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      Rajal Shivraj Phulari, Mohammed Ishtiyaque, Swami S.K.

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    1. Student,Department of Civil Engineering, Marathwada Institute of Technology,Maharashtra,India
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    Abstract

    nIn the present study, a sinusoidal shear and normal deformation theory taking into account effects of transverse shear as well as transverse normal is used to develop the analytical solution for the bidirectional bending analysis of isotropic, transversely isotropic, laminated composite and sandwich rectangular plates. Governing equations and boundary conditions of the theory are obtained using the principle of virtual work. The Navier solution for simply supported laminated composite plates have to develop. Results obtained for displacements and stresses of simply supported rectangular plates have to compare with those of other refined theories and exact elasticity solution wherever applicable. The Navier-type exact solutions for static bending analysis are have to for sinusoidally and uniformly distributed loads. The accuracy of the present theory is ascertained by comparing it with various available results in the literature.n

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    Keywords: Trigonometric shear deformation theory, transverse in-plane stress, transverse displacement, trigonometric function

    n[if 424 equals=”Regular Issue”][This article belongs to Journal of Geotechnical Engineering(joge)]

    n[/if 424][if 424 equals=”Special Issue”][This article belongs to Special Issue under section in Journal of Geotechnical Engineering(joge)] [/if 424]

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    References

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    1. Hosseini-Hashemi Sh, Rokni Damavandi Taher H, Akhavan H, Omidi M. Free vibration of functionally graded rectangular plates using first-order shear deformation plate theory. Appl Math Modell. 2010;34(5):1276–91. doi: 10.1016/j.apm.2009.08.008.
    2. Thai CH, Tran LV, Tran DT, Nguyen-Thoi T, Nguyen-Xuan H. Analysis of laminated composite plates using higher-order shear deformation plate theory and node-based smoothed discrete shear gap method. Appl Math Modell. 2012;36(11):5657–77. doi: 10.1016/j.apm.2012.01.003.
    3. Shi G. A new simple third-order shear deformation theory of plates. Int J Solids Struct. 2007;44(13):4399–417. doi: 10.1016/j.ijsolstr.2006.11.031.
    4. Matsunaga H. A comparison between 2-D single-layer and 3-D layerwise theories for computing interlaminar stresses of laminated composite and sandwich plates subjected to thermal loadings. Compos Struct. 2004;64(2):161–77. doi: 10.1016/j.compstruct.2003.08.001.
    5. Loredo A, Castel A. Two multilayered plate models with transverse shear warping functions issued from three dimensional elasticity equations. Compos Struct. 2014;117:382–95. doi: 10.1016/j.compstruct.2014.07.001.
    6. Loredo A. A multilayered plate theory with transverse shear and normal warping functions. Compos Struct. 2016;156:361–74. doi: 10.1016/j.compstruct.2015.08.084.
    7. Adhikari B, Singh BN. An efficient higher order non-polynomial quasi-3-D theory for dynamic responses of laminated composite plates. Compos Struct. 2018;189:386–97. doi: 10.1016/j.compstruct.2017.10.044.
    8. Sayyad AS. A new shear and normal deformation theory for isotropic, transversely isotropic, laminated composite and sandwich plates. Published online; February 12 2014.
    9. Ghugal YM, Shimpi RP. A review of refined shear deformation theories of isotropic and anisotropic laminated plates. J Reinf Plast Compos. 2002;21(9):775–813. doi: 10.1177/073168402128988481.
    10. Bessaim A, Houari MS, Tounsi A, Mahmoud S, Bedia EAA. A new higher-order shear and normal deformation theory for the static and free vibration analysis of sandwich plates with functionally graded isotropic face sheets. J Sandwich Struct Mater. September 2013;15(6):1–33.
    11. Sireesha P. Bending response of laminated composite plates using finite element method. Int J Eng Technol Manag Appl Sci. May 2015;3;Special Issue.
    12. Ghugal YM, Kulkarni SK. Flexural analysis of cross-ply laminated plates subjected to nonlinear thermal and mechanical loadings. Published online: 4 December 2012. Acta Mech 224. 2013;2012:675–90.
    13. Kotlyar R. Effect of band warping and wafer orientation on NMOS mobility under arbitrary applied stress. Published online; December 12 2007. p. 95–8.
    14. Jadhav P. Stability analysis of thick piezoelectric metal based FGM plate using first order and higher order shear deformation theory. Published online; October 21 2014.
    15. Kant T, Swaminathan K. Analytical solutions for the static analysis of laminated composite and sandwich plates based on a higher order refined theory. Compos Struct. 2002;56(4):329–44. doi: 10.1016/S0263–8223(02)00017-X.
    16. Hongxing LJH. Free vibration analyses of axially loaded laminated composite beams based on higher-order shear deformation theory. Published online; December 10 2010.
    17. Sayyad AS, Ghugal YM, Shinde PN. Stress analysis of laminated composite and soft core sandwich beams using a simple higher order shear deformation theory. J Serb Soc Comp Mech/Vol. 9/No. 2015/pp;1(1):15–35. doi: 10.5937/jsscm1501015S.
    18. Sayyad AS. A new shear and normal deformation theory for isotropic, transversely isotropic, laminated composite and sandwich plates. Published online; February 12 2014.
    19. Sayyad AS, Ghugal YM. On the free vibration analysis of laminated composite and sandwich plates: a review of recent literature with some numerical results. Compos Struct. 2015;129:177–201. doi: 10.1016/j.compstruct.2015.04.007.
    20. Adim B. A simple higher order shear deformation theory for mechanical behavior of laminated composite plates. Published online; May 6 2016.
    21. Chien HT. A generalized layerwise higher-order shear deformation theory for laminated composite and sandwich plates based on isogeometric analysis. Published online; January 6 2016.
    22. Goswami S. A New Rectangular Finite Element Formulation Based on Higher Order Displacement Theory for Thick and Thin Composite and Sandwich Plates. World Journal of Published Online June 2013.
    23. Aydogdu M. A new shear deformation theory for laminated composite plates. Compos Struct. 2009;89(1):94–101. doi: 10.1016/j.compstruct.2008.07.008.
    24. Mantari JL, Oktem AS, Guedes Soares C. A new trigonometric shear deformation theory for isotropic, laminated composite and sandwich plates. Int J Solids Struct. 2012;49(1):43–53. doi: 10.1016/j.ijsolstr.2011.09.008.
    25. Wu Z, Chen R, Chen W. Refined laminated composite plate element based on global–local higher-order shear deformation theory. Compos Struct. 2005;70(2):135–52. doi: 10.1016/j.compstruct.2004.08.019.
    26. Milan B. The derivation of the equations of moderately thick plates by the method of successive approximations. Published online; July 15 2009.
    27. Mohammad A. A new modified higher-order shear deformation theory for nonlinear analysis of macro- and nano-annular sector plates using the extended Kantorovich method in conjunction with SAPM; June 17 2017.
    28. Carrera E. Theories and finite elements for multilayered, anisotropic, composite plates and shells. Arch Comput Meth Eng. 2002;9(2):87–140. doi: 10.1007/BF02736649.
    29. Ferreira AJM, Batra RC, Roque CMC, Qian LF, Martins PALS. Static analysis of functionally graded plates using third-order shear deformation theory and a meshless method. Compos Struct. 2005;69(4):449–57. doi: 10.1016/j.compstruct.2004.08.003.
    30. Arafa E-H. Free vibration response of laminated composite plate shear walls. September 2017;13(9):28–38.
    31. Maiti DK. Bending and Buckling Analyses of Composite Laminates with and without Presence of Damage and its Passive Control with Optimized Piezoelectric Patch Location. 2016 June; Spl Issue:329–40.
    32. Sreehari VM. Bending and Buckling Analyses of Composite Laminates with and without Presence of Damage and its Passive Control. Jun 2 Spl Issue 2017 p.p. 329–40.
    33. Kadbhane SC. Damping evaluation of conventional and composite plates using different structures-A review. Int J Res Emerg Sci Technol. 2016;3(1).
    34. Kulkarni SK. Thermal flexural analysis of cross-ply laminated plates Latin American Journal. 2014;10:1001–23.
    35. Kharate NK. Damping evaluation of conventional and composite plates. Int J Res Emerg Sci Technol. 2017;3(1).
    36. Ghugal YM, Kulkarni SK. Thermal flexural analysis of cross-ply laminated plates using trigonometric shear deformation theory. Lat Am j solids struct. 2013;10(5):1001–23. doi: 10.1590/S1679–78252013000500008.

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    [if 344 not_equal=””]ISSN: 2394-1987[/if 344]

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    Volume 8
    Issue 2
    Received June 15, 2021
    Accepted July 5, 2021
    Published August 30, 2021

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