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Abstract:

          The present study shows that a simple epidemiological model can reproduce the real data accurately. It demonstrates indisputably that the dynamics of the COVID-19 outbreak can be explained by the modified version of the compartmental epidemiological framework Susceptible-Infected-Recovered-Dead (SIRD) model. The parameters of this model can be standardized using prior knowledge. However, out of several time-series data available on several websites, only the number of dead individuals (D(t)) can be regarded as a more reliable representation of the course of the epidemic. Therefore it is wise to convert all the equations of the SIRD Model into a single one in terms of D(t). This modified SIRD model is now able to give reliable forecasts and conveys relevant information compared to more complex models.

Keywords:

COVID-19,Epidemic Disease,Modified SIRD Model,Parameter Estimation,

Refference:

I. Anastassopoulou et al. Data-based analysis, modelling and forecasting of the covid-19 out-break. PLOS ONE, 2020. doi:10.1371/journal.pone.0230405.

II. Asish Mitra, Covid-19 in India and SIR Model, J. Mech.Cont. & Math. Sci., 15, 1-8, 2020.

III. Castilho et al. Assessing the efficiency of different control strategies for the coronavirus (covid-19) epidemic. ArXiv e-prints, 2020, 2004.03539.

IV. Chen et al. A time-dependent sir model for covid-19 with undetectable infected persons. ArXiv e-prints, 2020, 2003.00122.

V. D. J. Daley and J. Gani. Epidemic Modelling: An Introduction. Cambridge University Press, 2001.

VI. Duccio Fanelli and Francesco Piazza. Analysis and forecast of covid-19 spreading in China, Italy and France. Chaos, Solitons and Fractals, 134:109761, 2020, 2003.06031. doi:10.1016/j.chaos.2020.109761.

VII. Goncalo Oliveira. Refined compartmental models, asymptomatic carriers and covid-19. ArXiv e-prints, 2020, 2004.14780. doi:10.1101/2020.04.14.20065128.

VIII. Herbert W. Hethcote. The mathematics of infectious diseases. SIAM Review, 42(4):599-653, 2000.

IX. https://data.humdata.org/dataset/novel-coronavirus-2019-ncov-cases.

X. Julie Blackwood and Lauren M. Childs. An introduction to compartmental modeling for the budding infectious disease modeler. Letters in Biomathematics, 5:1:195-221, 2018. doi:10.1080/23737867.2018.1509026.

XI. Keeling Matt J. and Pejman Rohani. Modeling Infectious Diseases in Humans and Animals. Princeton University Press, 2008.

XII. Lipsitch et al. Transmission dynamics and control of severe acute respiratory syndrome.Science, 300(5627):1966-1970, 2003. doi:10.1126/science.1086616.

XIII. Loli et al. Preliminary analysis of covid-19 spread in Italy with an adaptive SEIRD model. ArXiv e-prints, 2020, 2003.09909.
XIV. Md. Zaidur Rahman, Md. Abul Kalam Azad, Md. Nazmul Hasan, : MATHEMATICAL MODEL FOR THE SPREAD OF EPIDEMICS, J. Mech.Cont. & Math. Sci., Vol.-6, No.-2, January (2012) Pages 843-858.

XV. Michael Y Li. An Introduction to Mathematical Modeling of Infectious Diseases. Springer International Publishing, 2018.

XVI. Natalie M Linton et all. Incubation period and other epidemiological characteristics of 2019 novel coronavirus infections with right truncation: a statistical analysis of publicly available case data. Journal of clinical medicine, 9(2):538, 2020.

XVII. Prem et al. The effect of control strategies to reduce social mixing on outcomes of the covid-19 epidemic in Wuhan, China: a modelling study. The Lancet, 5:261-270, 2020. doi:10.1016/S2468-2667(20)30073-6.

XVIII. S. Gupta, R. Shankar Estimating the number of COVID-19 infections in Indian hot-spots using fatality data, arXiv:2004.04025 [q-bio.PE]

XIX. Solving applied mathematical problems with MATLAB / Dingyu Xue, Chapman & Hall/CRC.

XX. Villaverde. Estimating and simulating a SIRD model of covid-19 for many countries, states, and cities.
https://cepr.org/active/publications/discussion_papers/dp.php?dpno=14711, 2020.

XXI. W. O. Kermack and A. G. McKendrick. A contribution to the mathematical theory of epidemics. Proc. R. Soc. Lond. A, 115(772):700–721, 1927.

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Abstract:

In the current research, studied experimentally of a solar air collector was conducted using latent thermal storage (wax of paraffin), in which energy of solar is collected during the time day, and released after sunset. Experimental studies were conducted under the Climate of Iraq - Baghdad (longitude 44.4 degrees east and latitude 33.34 degrees north). At various rates of mass flow air 0.027 kg / s, 0.03255 kg / s, and 0.038 kg / s in winter 2020 and on clear days, measurements and experimental work were conducted. The experimental findings indicated that the speed of paraffin wax melting is reversely proportional to the rate of mass flow of air. In m=0.038kg/s, the maximum heat gain value occurs. An increase in the rate of air mass flow decreases heat storage time.

Keywords:

Air heater solar,Thermal storage,paraffin wax,Space heating,Phase Change Material (PCM).,

Refference:

I. A. E. Kabeel, A. Khalil, S. M. Shalaby, and M. E. Zayed, “Experimental investigation of thermal performance of flat and v-corrugated plate solar air heaters with and without PCM as thermal energy storage,” Energy Convers. Manag., vol. 113, pp. 264–272, 2016.

II. A. S. Mahmood, “Experimental Study on Double-Pass Solar Air Heater with and without using Phase Change Material,” J. Eng., vol. 25, no. 2, pp. 1–17, 2019.

III. Alaa A.Ghulam, Ihsan Y. Hussain, : PERFORMANCE ENHANCEMENTS OF PHASE CHANGE MATERIAL (PCM) CASCADE THERMAL ENERGY STORAGE SYSTEM BY USING METAL FOAM, J. Mech. Cont. & Math. Sci., Vol.-15, No.-5, May (2020) pp 159-173.

IV. Firas Ahmed Khalil, Najim Abed Jassim, : THERMAL PERFORMANCE OF A SOLAR-ASSISTED HEAT PUMP WITH A DOUBLE PASS SOLAR AIR COLLECTOR UNDER CLIMATE CONDITIONS OF IRAQ, J. Mech. Cont.& Math. Sci., Vol.-14, No.-6 November-December (2019) pp 426-449.
V. J. A. Duffie, W. A. Beckman, and N. Blair, Solar engineering of thermal processes, photovoltaics and wind. John Wiley & Sons, 2020.

VI. K. Bin Sopian, M. Sohif, and M. Alghoul, “Output air temperature prediction in a solar air heater integrated with phase change material,” Eur. J. Sci. Res., vol. 27, no. 3, pp. 334–341, 2009.

VII. K. I. Abaas, “The Effect of Using a Paraffin Wax-Aluminum Chip Compound As Thermal Storage Materials in a Solar Air Heater,” Al-Rafidain Univ. Coll. Sci., no. 34, pp. 259–284, 2014.

VIII. M. Sajawal, T. Rehman, H. M. Ali, U. Sajjad, A. Raza, and M. S. Bhatti, “Experimental thermal performance analysis of finned tube-phase change material based double pass solar air heater,” Case Stud. Therm. Eng., vol. 15, p. 100543, 2019.

IX. O. Ojike and W. I. Okonkwo, “Study of a passive solar air heater using palm oil and paraffin as storage media,” Case Stud. Therm. Eng., vol. 14, p. 100454, 2019.

X. P. Charvat, L. Klimes, and O. Pech, “Experimental and numerical study into solar air collectors with integrated latent heat thermal storage,” Cent. Eur. Towar. Sustain. Build. Low-tech high-tech Mater. Technol. Sustain. Build., pp. 1–4, 2013.

XI. S. Bouadila, S. Kooli, M. Lazaar, S. Skouri, and A. Farhat, “Performance of a new solar air heater with packed-bed latent storage energy for nocturnal use,” Appl. Energy, vol. 110, pp. 267–275, 2013.

XII. S. M. Salih, J. M. Jalil, and S. E. Najim, “Experimental and numerical analysis of double-pass solar air heater utilizing multiple capsules PCM,” Renew. Energy, vol. 143, pp. 1053–1066, 2019.

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Abstract:

With the advances in the field of computing, robust CFD models have evolved in the last two decades. Initially, one and two-dimensional models were used but these days, three-dimensional models are used frequently that produce more accurate results. However, the solution of 3D models is expensive not only in terms of computational costs but is time-consuming. In this work, a two-dimensional CFD model that is based on shallow water equations coupled with an erosion model is presented. The equations are solved using finite volume formulation and high-resolution shock capturing methods. This study is an attempt to cover accuracy issues with 2D models by incorporating high-resolution shock capturing methods as compared to 3D models, the solution of which is based on conventional schemes. The model is initially used to simulate dam-break problems over fixed and mobile beds to assess the model stability and hydraulic performance in terms of simulating the flow and bed morphology. The assessment has shown the model to be stable throughout the simulation and the produced results have shown the hydro-dynamic capability of the model. The model is then applied to simulate flow over an erodible sediment bed in a channel with spur dykes on its flood plain. The simulated results are compared with experimental results and numerical results of a 3D model. The comparison has shown a close agreement both with experimental and numerical 3D model results that show that the model could be applied to study bed morphology confidently.

Keywords:

CFD,High Resolution,Shock Capturing,Mobile Beds,

Refference:

I. A. Canestrelli, M. Dumbser, A. Siviglia, and E. F. Toro, “Well-balanced high-order centered schemes on unstructured meshes for shallow water equations with fixed and mobile bed,” Adv. Water Resour., vol. 33, no. 3, pp. 291–303, 2010.
II. B. van Leer, “Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov’s method,” J. Comput. Phys., vol. 32, no. 1, pp. 101–136, 1979.
III. C. F. Scott and F. A. Khan, “Two-Dimensional Dam Break Hydraulics Over an Erodible Bed,” Annual Conference on Hydraulic Engineering, Dresden, 2010.
IV. C. Juez, J. Murillo, and P. García-Navarro, “A 2D weakly-coupled and efficient numerical model for transient shallow flow and movable bed,” Advances in Water Resources, vol. 71, pp. 93–109, 2014.
V. D. Santillán, L. Cueto-Felgueroso, A. Sordo-Ward, and L. Garrote, “Influence of Erodible Beds on Shallow Water Hydrodynamics during Flood Events,” Water, vol. 12, no. 12, p. 3340, 2020.
VI. E. Elawady, M. Michiue, and O. Hinokidani, “Experimental Study of Flow Behavior Around Submerged Spur-Dike On Rigid Bed,” Proc. Hydraul. Eng., vol. 44, pp. 539–544, 2000.
VII. E. F. Toro, “Shock-capturing methods for free-surface shallow flows,” 2001.
VIII. F. Bahmanpouri, M. Daliri, A. Khoshkonesh, M. Montazeri Namin, and M. Buccino, “Bed compaction effect on dam break flow over erodible bed; experimental and numerical modeling,” J. Hydrol., 2020.
IX. G. Kesserwani, A. Shamkhalchian, and M. J. Zadeh, “Fully Coupled Discontinuous Galerkin Modeling of Dam-Break Flows over Movable Bed with Sediment Transport,” J. Hydraul. Eng., vol. 140, no. 4, 2014.
X. H. Hu, J. Zhang, and T. Li, “Dam-Break Flows: Comparison between Flow-3D, MIKE 3 FM, and Analytical Solutions with Experimental Data,” Appl. Sci., vol. 8, no. 12, Dec. 2018.
XI. H. Nakagawa, H. Zhang, and Y. Muto, “Modeling of sediment transport in alluvial rivers with spur dykes,” in Ninth International Symposium on River Sedimentation, Yichang, China, pp. 18–21, 2004.
XII. J. H. Almedeij and P. Diplas, “Bedload Transport in Gravel-Bed Streams with Unimodal Sediment,” J. Hydraul. Eng., vol. 129, no. 11, pp. 896–904, 2003.
XIII. J. Xia, B. Lin, R. A. Falconer, and G. Wang, “Modelling dam-break flows over mobile beds using a 2D coupled approach,” Adv. Water Resour., vol. 33, no. 2, pp. 171–183, 2010.
XIV. M. Ghodsian and M. Vaghefi, “Experimental study on scour and flow field in a scour hole around a T-shape spur dike in a 90° bend,” Int. J. Sediment Res., vol. 24, no. 2, pp. 145–158, 2009.
XV. M. J. Creed, I.-G. Apostolidou, P. H. Taylor, and A. G. L. Borthwick, “A finite volume shock-capturing solver of the fully coupled shallow water-sediment equations,” Int. J. Numer. Methods Fluids, vol. 84, no. 9, pp. 509–542, 2017.
XVI. M. Vaghefi, S. Solati, and C. Abdi Chooplou, “The effect of upstream T-shaped spur dike on reducing the amount of scouring around downstream bridge pier located at a 180° sharp bend,” Int. J. River Basin Manag., 2020.
XVII. P. Batten, C. Lambert, and D. M. Causon, “Positively conservative high-resolution convection schemes for unstructured elements,” Int. J. Numer. Methods Eng., 1996.
XVIII. R. A. Kuhnle, C. V. Alonso, and F. D. Shields, “Local Scour Associated with Angled Spur Dikes,” J. Hydraul. Eng., vol. 128, no. 12, pp. 1087–1093, 2002.
XIX. S. Zhang and J. G. Duan, “1D finite volume model of unsteady flow over mobile bed,” J. Hydrol., vol. 405, no. 1–2, pp. 57–68, 2011.
XX. Sepehr Mortazavi Farsani, Najaf Hedayat, Nelia sadeghi Khoveigani, : Numerical Simulation of the effect of simple and T-shaped dikes on turbulent flow field and sediment scour/deposition around diversion intakes, J. Mech. Cont.& Math. Sci., Vol.-14, No.-4, July-August (2019) pp 197-215
XXI. T. Uchida and S. Fukuoka, “Quasi-3D two-phase model for dam-break flow over movable bed based on a non-hydrostatic depth-integrated model with a dynamic rough wall law,” Adv. Water Resour., vol. 129, pp. 311–327, 2019.
XXII. Uzair Ali, Syed Shujaat Ali, : SIMULATION OF RIVER HYDRAULIC MODEL FOR FLOOD FORECASTING THROUGH DIMENSIONAL APPROACH, J. Mech. Cont.& Math. Sci., Vol.-15, No.-1, January (2020) pp 275-282
XXIII. W. Wu and S. S. Wang, “One-Dimensional Modeling of Dam-Break Flow over Movable Beds,” J. Hydraul. Eng., vol. 133, no. 1, pp. 48–58, 2007.
XXIV. X. Liu, A. Mohammadian, and J. Á. Infante Sedano, “A numerical model for three-dimensional shallow water flows with sharp gradients over mobile topography,” Comput. Fluids, vol. 154, pp. 1–11, 2017.
XXV. X. Zhang, P. Wang, and C. Yang, “Experimental study on flow turbulence distribution around a spur dike with different structure,” in Procedia Engineering, vol. 28, pp. 772–775, 2012.
XXVI. Y. Jia and S. S. Y. Wang, “Numerical Model for Channel Flow and Morphological Change Studies,” J. Hydraul. Eng., vol. 125, no. 9, pp. 924–933, Sep. 1999.
XXVII. Y. Muto, K. Kitamura, A. Khaleduzzaman, and H. Nakagawa, “Flow and bed topography around impermeable spur dykes.,” Adv. River Eng. JSCE, vol. 9, 2003.
XXVIII. Z. Cao, “Equilibrium near-bed concentration of suspended sediment,” J. Hydraul. Eng., vol. 125, pp. 1270-1278, 1999.
XXIX. Z. Cao, G. Pender, S. Wallis, and P. Carling, “Computational Dam-Break Hydraulics over Erodible Sediment Bed,” J. Hydraul. Eng., vol. 130, no. 7, pp. 689–703, 2004.

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Abstract:

The technique to evade jerk from a dynamical system is to reduce the rate of acceleration or deceleration. It is an important issue for our real life. In motion control systems the term “jerk” is the main topic. The jerk equation containing velocity times acceleration-squared describes the characteristics of chaotic behaviour in many nonlinear phenomena, cosmological analysis, kinematical physics, pendulum analysis etc. Thus, the mentioned equation is important in its own right. An extended iteration method, based on Haque’s approach has been applied to find the analytical solution of the oscillator. The recently various method has been developed for finding analytical solutions of the nonlinear equation but; modified extended iteration method based on Haque’s approach is faster and straight forward than others.

Keywords:

Jerk equation,Nonlinear oscillator,Extended iteration technique,Truncated Fourier series,

Refference:

I. Alam, M.S., Razzak M.A., Hosen M.A. and Parvez M.R., “The rapidly convergent solutions of strongly nonlinear oscillators” Spring. Plu., vol. 5, pp. 1258-1273, 2016.
II. Belendez A., Hernandez A., Belendez T., Fernandez E., Alvarez M.L. and Neipp C., “Application of He’s Homotopy perturbation method to Duffing-harmonic oscillator” Int. J. Nonlinear Sci. and Numer. Simul., vol. 8(1), pp. 79-88, 2007.
III. Gottlieb, H.P.W., “Question #38. What is the simplest jerk function that gives chaos?” American Journal of Physics, vol. 64, pp. 525, 1996.
IV. Gottlieb, H.P.W., “Harmonic balance approach to periodic solutions of nonlinear jerk equation” J. Sound Vib., vol. 271, pp. 671-683, 2004.
V. Gottlieb, H.P.W., “Harmonic balance approach to limit cycle for nonlinear jerk equation” J. Sound Vib., vol. 297, pp. 243-250, 2006.
VI. Hu, H., “Perturbation method for periodic solutions of nonlinear jerk equations” Phys. Lett. A, vol. 372, pp. 4205-4209, 2008.
VII. Hu, H., Zheng, M.Y. and Guo, Y.J., “Iteration calculations of periodic solutions to nonlinear jerk equations” Acta Mech., vol. 209, pp. 269-274, 2010.
VIII. Haque, B.M.I., Alam, M.S. and Majedur Rahmam, M., “Modified solutions of some oscillators by iteration procedure” J. Egyptian Math. Soci., vol. 21, pp. 68-73, 2013.
IX. Haque, B.M.I., A “New Approach of Iteration Method for Solving Some Nonlinear Jerk Equations” Global Journal of Science Frontier Research Mathematics and Decision Sciences, vol. 13, pp. 87-98, 2013.
X. Haque, B.M.I., “A New Approach of Mickens’ Extended Iteration Method for Solving Some Nonlinear Jerk Equations” British journal of Mathematics & Computer Science, vol. 4, pp. 3146-3162, 2014.
XI. Haque, B.M.I., Bayezid Bostami M., Ayub Hossain M.M., Hossain M.R. and Rahman M.M., “Mickens Iteration Like Method for Approximate Solution of the Inverse Cubic Nonlinear Oscillator” British journal of Mathematics & Computer Science, vol. 13, pp. 1-9, 2015.
XII. Haque, B.M.I., Ayub Hossain M.M., Bayezid Bostami M. and Hossain M.R., “Analytical Approximate Solutions to the Nonlinear Singular Oscillator: An Iteration Procedure” British journal of Mathematics & Computer Science, vol. 14, pp. 1-7, 2016.
XIII. Haque, B.M.I., Asifuzzaman M. and Kamrul Hasam M., “Improvement of analytical solution to the inverse truly nonlinear oscillator by extended iterative method” Communications in Computer and Information Science, vol. 655, pp. 412-421, 2017.

XIV. Haque, B.M.I., Selim Reza A.K.M. and Mominur Rahman M., “On the Analytical Approximation of the Nonlinear Cubic Oscillator by an Iteration Method” Journal of Advances in Mathematics and Computer Science, vol. 33, pp. 1-9, 2019.
XV. Haque, B.M.I. and Ayub Hossain M.M., “A Modified Solution of the Nonlinear Singular Oscillator by Extended Iteration Procedure” Journal of Advances in Mathematics and Computer Science, vol. 34, pp. 1-9, 2019.
XVI. Haque B M I, Zaidur Rahman M and Iqbal Hossain M, “Periodic solution of the nonlinear jerk oscillator containing velocity times acceleration-squared: an iteration approach”, J. Mech. Cont.& Math. Sci., Vol.-15, No.-6, June (2020) pp 493-433.
XVII. Leung, A.Y.T. and Guo, Z., “Residue harmonic balance approach to limit cycles of nonlinear jerk equations” Int. J. Nonlinear Mech., vol. 46, pp. 898-906, 2011.
XVIII. Ma, X., Wei, L. and Guo, Z., “He’s homotopy perturbation method to periodic solutions of nonlinear jerk equations” J. Sound Vib., vol. 314, pp. 217-227, 2008.
XIX. Mickens, R.E., “Comments on the method of harmonic balance” J. Sound Vib., vol. 94, pp. 456-460, 1984.
XX. Mickens, R.E., “Iteration Procedure for determining approximate solutions to nonlinear oscillator equation” J. Sound Vib., vol. 116, pp. 185-188, 1987.
XXI. Nayfeh, A.H., “Perturbation Method” John Wiley & Sons, New York, 1973.
XXII. Ramos, J.I. and Garcia-Lopez, “A Volterra integral formulation for determining the periodic solutions of some autonomous, nonlinear, third-order ordinary differential equations” Appl. Math. Comput., vol. 216, pp. 2635-2644, 2010.
XXIII. Wu, B.S., Lim, C.W. and Sun, W.P., “Improved harmonic balance approach to periodic solutions of nonlinear jerk equations” Phys. Lett. A, vol. 354, pp. 95-100, 2006.
XXIV. Zheng, M.Y., Zhang, B.J., Zhang, N., Shao, X.X. and Sun, G.Y., “Comparison of two iteration procedures for a class of nonlinear jerk equations” Acta Mech. vol. 224, pp. 231-239, 2013.

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Abstract:

In the paper, we develop the Adomian Decomposition Method for the fractional-order nonlinear Time Regularized Long Wave Equation (TRLW) equation. Caputo fractional derivatives are used to define fractional derivatives. We know that nonlinear physical phenomena can be explained with the help of nonlinear evolution equations. Therefore solving TRLW is very helpful to obtain the solution of many physical theories. In this paper, we will solve the time-fractional TRLW equation which may help researchers with their work. We solve some examples numerically, which will show the efficiency and convenience of the Adomian Decomposition Method.

Keywords:

Time Regularized Long Wave equation,Fractional derivative,Adomian Decomposition Method,Convergence,Mathematica,

Refference:

I. Adomian G., “A Review of Decomposition method in applied mathematics”,J. Math. Anal. Appl., 135, (1988), 501-544.
II. Adomian G., “Solving Frontier Problems of Physics: The Decomposition Method”,Kluwer, Boston, 1994.
III. Adomian G., “The diffusion-Brusselator equation”, Comput. Math. Appl., 29 , (1995), 1-3.
IV. Adomian G., ”Solution of coupled nonlinear partial differential equations by decomposition”, Comput. Math. Appl., 31(6), (1996), 117-120.
V. Biazar J., Babolian E., “Solution of the system of ordinary differential equationsby Adomian Decomposition Method”, Appl.Math.Comput.147 (3), (2004), 713-719.
VI. Bratsos A., Ehrhardt M.,.Famelis I .,“A discrete Adomian Decomposition Method for discrete nonlinear Schrondinger equations”, Appl. Math. Comput., 197,(2008), 190-205.
VII. Daftardar-Gejji V., Jafari H., “Adomian Decomposition: a tool for solving a system of fractional differential equations”, J. Math. Anal. Appl., 301, (2005) , 508-518.
VIII. Daftardar-Gejji V. and Bhalekar S., “Solving multi-term linear and non-linear diffusion-wave equations of fractional order by Adomian Decomposition Method”, Appl. Math. Comput., (202),(2008), 113-120.
IX. Dhaigude D. B., Birajdar G. A,. Nikam V. R., “Adomian decomposition method for fractional Benjamin-Bona-Mahony-Burger’s equation”, int. of appl. math, and mech 8 (12), (2012), 42-51.
X. Jafari H., “Solving a system of nonlinear fractional differential equations using Adomian Decomposition”, Journal of computational and Applied Mathematics 196, (2006).644-651.
XI. Jafari H., Daftardar-Gejji V., “Solving Linear and nonlinear fractional diffusion and wave equations by Adomian Decomposition Method”.Appl. Math. Comput., 180,(2006), 488-497.
XII. Kazi sazzad Hossain., Ali Akbar and Md., “Abul Kalam Azad, Closed form wave solutions of two nonlinear evolution equations”, Cogent Physics,4:1396948, (2017)
XIII. Kulkarni S., Jogdand S., Takale K. C., “Error Analysis of solution of time fractional convection diffusion equation”, JETIR, 6 (3), (2019).
XIV. Li C., And Wang Y., “Numerical algorithm based on Adomian Decomposition Method for fractional differential equations”, Comput. Math. Appl., 57 ,(2009), 1672-1681.
XV. M. Hafiz Uddin, M. Ali Akbar, Md. Ashrafuzzaman Khan, Md. Abdul Haque, : Families of exact traveling wave solutions to the space time fractional modified KdV equation and the fractional Kolmogorov-Petrovskii-Piskunovequation, J. Mech.Cont. & Math. Sci., Vol.-13, No.-1, March – April (2018) Pages 17-33.
XVI. Md. Tarikul Islam, M. Ali Akbar, Md. Abul Kalam Azad, : The exact traveling wave solutions to the nonlinear space-time fractional modified Benjamin-Bona-Mahony equation, J. Mech.Cont. & Math. Sci., Vol.-13, No.-2, May-June (2018) Pages 56-71
XVII. Mittal R. C., and Nigam R., “Solution of fractional integro-differential equations by Adomian Decomposition Method”, Int. J. Appl. Math. Mech., 4 (2), (2008), 8794.
XVIII. Momani S. and Al-Khaled K., “Numerical solutions for system of fractional differential equations by the Decomposition Method”. Appl. Math. Comput. Simul., 70,(2005), 1351-1365.
XIX. Miller K. S., Ross B.,” An Introduction to the Fractional Calculus and Fractional Differential Equations”, New York, (1993).
XX. Momani S., Odibat Z., “ Analytical solutions of a time fractional Navier-Stokes Equation by Adomian decomposition method”, Appl. Math. Comput. 177, 2 , (2006), 488 – 494.
XXI. Oldham K. B., Spanier J., “The fractional calculus, Academic Press”, New York, (1974).
XXII. Podlubny I., “Fractional Differential equations”, Academic Press, San Diago 1999.
XXIII. Rayhanul Islam S. M., Khan K., “Exact solution of unsteady Korteweg-deVries and time regularized long wave equations”, Springer-Plus,4 ; 124 (2015).
XXIV. Sontakke B. R., Sangvikar V. V., “Approximate Solution for Time-Space Fractional Soil Moisture Diffusion Equation and its Applications”, International Journal of Scientific and Technology Research, 5(5)(2016),197-202.
XXV. Sontakke B. R and Shelke A. S., “ Approximate Scheme for Time Fractional Diffusion Equation and Its Applications”, Global Journal of Pure and Applied Mathematics. 13(8) (2017), 4333-4345.
XXVI. Sontakke B. R., and Pandit R.B., “Convergence Analysis and Approximate Solution of fractional differential Equations”, Journal of Mathematics,7(2),(2019),338344.
XXVII. Sontakke B. R, Adomian Decomposition Method for Solving Highly Nonlinear Fractional Partial Differential Equations IOSR Journal of Engineering, 9 (3)( 2019), 39-44.
XXVIII. Saha Ray S., New Approach for General Convergence of the ADM, World Applied Sciences Journal, 32 (11), (2014) 2264-2268.
XXIX. Wazwaz A. M., A reliable modification of Adomian’s Decomposition Method. Appl. Math. Comput., 102,(1999), 77-86.
XXX. Wazwaz A. M., The decomposition method applied to systems of partial differential equations and to the reaction-diffusion Brusselator model. Appl. Math. Comput., 110,(2009), 251-264.
XXXI. Wyss W., and Schneider W.R., Fractional Diffusion and wave equations, J. Math. Phys. 30, (1989).
XXXII. Yang Q., Turner I., Liu F, Analytical and Numerical Solutions for the time and Space-Symmetric Fractional Diffusion Equation, ANZIAM J., 50 (CTA 2008) , (2009) ,pp. C800-C814.
XXXIII. Zahram Emad H. , Khater Mostafa M. A., Exact Travelling Wave Solutions for the system of shallow water wave equations and Modified Liouville equation using extended Jacobian elliptic function expansion method, American Journal of computational Mathematics, 4, (2014), 455-463.

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Abstract:

While solving the fractional order differential equation the requirement of the higher-order derivative is obvious therefore, this paper gives a definite expression for constructing the operational matrices of derivative which is the direct method to find the derivative of higher-order according to the requirement of the total differential equation. The proposed work expands the Chebyshev polynomial of type four up to six degrees that could help get the accuracy for the numerical solution of a given differential equation. Previously Chebyshev polynomial of the third type has been used by cutting the domain from [-1, 1] to [0, 1]. This study also generates the integrational operational matrix for solving the integral equation as well as an integrodifferential equation by using the Chebyshev polynomial of type four and expand it up to six order and generate the matrix by cutting the domain from [-1, 1] to [0, 1].  This is the first attempt to generate an integrational operational matrix that has never been highlight nor generate by any researcher.  Another contribution of this paper is the generation of categorical expressions for the product of two Chebyshev vectors that will help in solving the differential equation of several kinds.

Keywords:

Operational matrix of derivative,Operational matrix of integration,Operational matrix of the product of Shifted Chebyshev polynomials of type four,

Refference:

I. A. Tatarczak, “An Extension of the Chebyshev’s polynomials”, Complex analysis operational theory, vol.10, pp: 1519-1533, 2016.
II. Azim Rivaz, Samane Jahan ara, “Two dimension Chebyshev polynomial for solving two dimensional integro differential equation”, Can kaya university journal of science, vol.12, 2015.
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Abstract:

The research aims to understand the design parameters of steam ejector nozzle on the performance of flash evaporation induced by the effect of a steam jet passing through it. The research concentrates on studying the effect of ejector nozzle outlet diameter on induced flow from preheated water in a specified evaporator using a subsonic ejector. The thermal energy extracted from the condensed steam mixture in the condenser is used to heat the water in the evaporator. The experimental tests investigate the effect of nozzle geometry on the induced evaporation process by changing nozzle outlet diameter while keeping the pressure of evaporator, condenser and primary steam constant. The experimental results proved that both primary and secondary steam mass flow rates increase versus nozzle outlet diameter, while the entrainment ratio of secondary to primary steam flow rates decreases due to the restricted increase of the secondary steam mass flow rate. The mathematical model prepared to simulate the behaviour of the subsonic ejector is validated using the comparison between experimental and theoretical results. The mathematical model showed that maximum entrainment of 0.57 is obtained at a primary steam pressure of 2 bars when the nozzle outlet diameter is fixed at 1.5 mm, while minimum entrainment ratio of 0.17 is estimated at 1.5 bar pressure related to primary steam when the nozzle outlet diameter is fixed at 2.5mm. The authors recommend defining nozzle geometrical parameters according to the operating conditions of the experimental test rig to enhance ejector efficiency.

Keywords:

Flash evaporation,Induced flow,Nozzle,Subsonic,Ejector,

Refference:

I. A. Ezzat et al., Investigation of steam jet flash evaporation with solar thermal collectors in water desalination systems, Thermal science and engineering progress, 20 (2020) 100720.
II. Antonio, et al., Thermodynamic modeling of an ejector with compressible flow by one dimensional approach, Entropy 14 (4) (2012) 599–614.
III. kavous Ariafar . Effect of Nozzle Geometry on a Model Thermo compressor Performance – a Numerical Evaluation. Journal ISME 2012
IV. Lam Ratna Raju, Ch. Pavan Satyanarayana, Neelamsetty Vijaya Kavya, : AN APPROACH FOR OPTIMISING THE FLOW RATE CONDITIONS OF A DIVERGENT NOZZLE UNDER DIFFERENT ANGULAR CONDITIONS, J. Mech. Cont.& Math. Sci., Vol.-15, No.-7, July (2020) pp 608-625.
V. M. Dennis. Solar Cooling Using Variable Geometry Ejectors, 2009, Croll Reynold Steam Ejectors, 2018, https://croll.com/vacuum-systems/applications/
VI. Mehran Ahmadi , Poovanna Thimmaiah ,Majid Bahrami ,Khaled Sedraoui, Hani H. Sait and Ned Djilali . Experimental and numerical investigation of a solar eductorassisted low-pressure water desalination system. Journal Science Bulletin 2016.
VII. N.M.K. Sarath Kumar, A. Vamsi Krishna, G. Shyam Mahesh, K. Bharath Kumar, M. Venkataiah, : CFD ANALYSIS OF RB211 AND CFM56 CHEVRON NOZZLES, J. Mech. Cont.& Math. Sci., Vol.-15, No.-7, July (2020) pp 405-415.

VIII. Natthawut Ruangtrakoon, Tongchana Thongtip, Satha Aphornratana, Thanarath Sriveerakul.CFD simulation on the effect of primary nozzle geometries for a steam ejector in refrigeration cycle. International Journal of Thermal Sciences 2012.
IX. R. Kelso, Applied aerodynamics: compressible flow, PowerPoint Presentation (2018).
X. Seyedali Sabzpoushan, Masoud Darband I and Gerry E. Schneider. Numerical Investigation on the Effects of Operating Conditions on the Performance of a Steam Jet-Ejector. Journal international Conference of Fluid Flow.
XI. S. Han, et al., One-dimensional numerical study of compressible flow ejector, AIAA
XII. J. 40 (7) (2002) 1469–1473.
XIII. S. Liu, et al., Thermodynamic analysis of steam ejector refrigeration cycle, Int. Refrigeration Air Conditioning Conf. (2014) 2306–2307.
XIV. Szabolcs Varga, Armando C. Oliveira, Xiaoli Ma and Siddig A. Omer. Comparison of CFD and experimental performance results of a variable area ratio steam ejector. International Journal of Low-Carbon Technologies • June 2011
XV. Szabolcs Vargaa, Armando C. Oliveiraa and Bogdan Diaconua. Numerical assessment of steam ejector efficiencies using CFD. International journal of refrigeration, 2009.
XVI. Vineet V. Chandra and M.R. Ahmed. Experimental and computational studies on a steam jet refrigeration system with constant area and variable area ejectors. Journal of Elsevier, 2013.

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Abstract:

This article is presented a modified quadrature iterated methods of Boole rule and Weddle rule for solving non-linear equations which arise in applied sciences and engineering. The proposed methods are converged quadratically and the idea of developed research comes from Boole rule and Weddle rule. Few examples are demonstrated to justify the proposed method as the assessment of the newton raphson method, steffensen method, trapezoidal method, and quadrature method. Numerical results and graphical representations of modified quadrature iterated methods are examined with C++ and EXCEL. The observation from numerical results that the proposed modified quadrature iterated methods are performance good and well executed as the comparison of existing methods for solving non-linear equations.

Keywords:

Boole Rule and Weddle Rule,convergence criteria,existing methods,graph,results,

Refference:

I. Akram, A. and Q. U. Ann, Newton Raphson Method, International Journal of Scientific & Engineering Research, Vol. 6. 456-462, 2015.
II. Khatri, A., A. A. Shaikh and K. A. Abro, Closed Newton Cotes Quadrature Rules with Derivatives, ,, Vol.9, No.5, 2019.
III. Liu, Z. and H. Zhang, Steffensen-Type Method of super third-order convergence for solving nonlinear equations, Journal of Applied Mathematics and Physics, vol 2, 581-586, 2014.
IV. Memon Kashif, Muhammad Mujtaba Shaikh, Muhammad Saleem Chandio, Abdul Wasim Shaikh, : A NEW AND EFFICIENT SIMPSON’S 1/3-TYPE QUADRATURE RULE FOR RIEMANN-STIELTJES INTEGRAL, J. Mech. Cont. & Math. Sci., Vol.-15, No.-11, November (2020) pp 132-148
V. Perhiyar, M. A., S. F. Shah and A. A. Shaikh, Modified Trapezoidal Rule Based Different Averages for Numerical Integration, Mathematical Theory and Modeling, Vol.9, No.9, 2019.
VI. Qureshi, U. K., A New Accelerated Third-Order Two-Step Iterative Method for Solving Nonlinear Equations, Mathematical Theory and Modeling, Vol: 8(5), 2018.
VII. Qureshi, U. K., I. A. Bozdar, A. Pirzada and M. B. Arain, Quadrature Rule Based Iterative Method for the Solution of Non-Linear Equations, Proceedings of the Pakistan Academy of Sciences, Pakistan Academy of Sciences A. Physical and Computational Sciences, vol: 56 (1): 39–43, 2019.
VIII. Qureshi, U. K., Z. A. Kalhoro, A. A. Shaikh and A. R. Nagraj, Trapezoidal Second Order Iterated Method for Solving Nonlinear Problems, University of Sindh Journal of Information and Communication Technology (USJICT), Vol: 2(2), 2018.
IX. Shaikh, M. M., M. S. Chandio and A. S. Soomro, A Modified Four-point Closed Mid-point Derivative Based Quadrature Rule for Numerical Integration, Sindh University Research Journal, SURJ (Science Series), 48(2), 2016.
X. Umar Sehrish , Muhammad Mujtaba Shaikh , Abdul Wasim Shaikh, : A NEW QUADRATURE-BASED ITERATIVE METHOD FOR SCALAR NONLINEAR EQUATIONS, J. Mech. Cont.& Math. Sci., Vol.-15, No.-10, October (2020) pp 79-93.
XI. Weerakoon, S. and T. G. I. Fernando, 2000, A Variant of Newton’ s Method with Accelerated Third-Order Convergence, Applied Mathematics Letters, vol 13 87-93.
XII. Zafar, F., Saira S. and C. O. E. Burg, New Derivative Based Open Newton-Cotes Quadrature Rules, Hindawi Publishing Corporation Abstract and Applied Analysis Volume 2014.
XIII. Zhao, W. and L. Hongxing, Midpoint Derivative-Based Closed Newton-Cotes Quadrature, Hindawi Publishing Corporation Abstract and Applied Analysis Volume 2013.

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Abstract:

Growth of photovoltaic systems that require more and more productive alternatives, not only in micro-fabrication techniques but also in methods of energy extraction. In recent years, a large number of Maximum Power Point Tracking algorithms with various complexities over decades the ability to efficiently locate the global maximum under partial shading was followed by evolved. Partial Shading Conditions (PSC) play a major role in determining the energy and power productivity of a solar photovoltaic (SPV) system. Under PSC, the SPV panels receive varying levels of solar irradiance, resulting in a decrease in the power generation of the SPV system, and these losses in SPV panels can be minimized by adjusting the configuration of the array/module panels. The panels can be designed to increase production energy and power quality in several different configurations, such as Series(S), Parallel (P), Series-Parallel (SP), Complete Cross Tied (TCT), Bridge Linked (BL) and Honeycomb (HC). This work is aimed at presenting all the configurations already presented in the literature and referencing and evaluating the findings of PSC on SPV systems. In this paper, there are four 4-4 array configurations of solar photovoltaic panels to be addressed. Parallel series (SP), complete cross-linked (TCT), the bridge linked (BL) and honeycomb are four configurations (HC). To decide on the effect of shadow with 10 shading patterns, four simulated models were carried out. For the above-mentioned configuration, the simulated results indicate a power against voltage (PV) curve of 4 to 4 SPV array under PSC. This thesis will be a reference point for useful and important knowledge for researchers in the field of solar panels.

Keywords:

Photo-voltaic cells,Power Enhancement,Partial Shading,series-parallel (SP),total cross-tied (TCT),total cross-tied (TCT),honeycomb (HC),

Refference:

I. Patel H and Agarwal V 2008 Matlab-based modeling to study the effects of partial shading on PV array characteristics. IEEE Transact. on Energy Convers. 23(1) doi: 10.1109/TEC.2007.914308
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IV. Bidram A, Davoudi A D, and Balog R S 2012 Control and circuit techniques to mitigate partial shading effects in photovoltaic arrays. IEEE Journal of Photovoltaics 2(4) doi: 10.1109/JPHOTOV.2012.2202879
V. Karatepe, E Syafaruddin and Hiyama T 2010 Simple and high-efficiency photovoltaic system under non- uniform operating conditions. IET Renewable Power Generation 4(4) 354 doi:10.1049/iet- rpg.2009.0150
VI. D.P.Kothari,K.C.SingalandRakeshRanjan,“RenewableEnergySourcesandEmerging Technologies”, Prentice-Hall of India, New Delhi,3rd edition 2021
VII. D.P.KothariandI.J.Nagrath,”ModernPowerSystemAnalysis,”TataMcGrawHill,New Delhi,1980, fifth edition 2021
VIII. Teo J C, Rodney H G, Vigna V R V, Mok H and Tan C 2018 Impact of partial shading on the p- v characteristics and the maximum power of a photovoltaic string. Energies 11 1860 doi: 10.3390/en11071860
IX. Young-Hyok, J Jung D Kim J_G Kim J H Lee T W and Won C Y 2011 A real maximum power point tracking method for mismatching compensation in PV array under partially shaded conditions.
X. IEEE Transactions on Power Electronics 26(4) doi: 10.1109/TPEL.2010.2089537
XI. Maki A and Valkealahti S 2012 Power losses in long string and parallel-connected short strings of series- connected silicon-based photovoltaic modules due to partial shading conditions. IEEE Transactions on Energy Conversion 27(1) doi: 10.1109/TEC.2011.2175928
XII. Markvart T 2016 From steam engine to solar cells: can thermodynamics guide the development of future generations of photovoltaics? WIREs Energy and Environment doi: 10.1002/wene.204
XIII. Amit Kumar, Rupendra Kumar Pachauri, Yogesh K. Chauhan Experimental Analysis of Proposed SP-TCT, TCT- BL and CT-HC Configurations under Partial shading Conditions
XIV. Seyedmahmoudian M Mekhilef S Rahmani R Yusof R and Shojaei A A 2014 Maximum power point tracking of partial shaded photovoltaic array using an evolutionary algorithm: A particle swarm optimization technique. J. of Renewable and Sustainable Energy 6(2) doi: 10.1063/1.4868025
XV. Pavlovic T and Ban Z 2013 An improvement of incremental conductance MPPT algorithm for PV systems based on the Nelder–Mead optimization. IEEE 6
XVI. Patel Hiren and Vivek Agarwal, “MATLAB-based modelling to study the effects of partial shading on PV array characteristics,” IEEE Transactions on Energy Conversion, vol. 23, no. 1 , pp. 302-310, 2008.
XVII. R. Ramaprabha and B. L. Mathur, “A comprehensive review and analysis of solar photovoltaic array configurations under partial shaded conditions,” International Journal of Photo energy, vol. 2012, 2012.
XVIII. Wang Yaw-Juen and Po-Chun Hsu, “An investigation on partial shading of PV modules with different connection configurations of PV cells,” Energy, vol. 36.5, pp. 3069-3078, 2011.
XIX. Wilson K. Rahul, Y. Srinivasa Rao, : EFFECTS OF PARTIAL SHADING ON DIFFERENT STRUCTURES OF SOLAR PHOTOVOLTAIC ARRAYS, J. Mech. Cont.& Math. Sci., Vol.-14, No.-6 November-December (2019) pp 845-854

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Abstract:

This research paper aims at a detailed study of the seismic performance of reinforced concrete Beam-Column Joint (BCJ) under quasi-static cyclic loading. Firstly, the numerical simulations of the previously experimented specimen have been performed by Finite Element Method (FEM) using ABAQUS 6.14. Secondly, the parametric study has been conducted for the validated model by the introduction of Fiber Reinforced Polymer (FRP) bars in the form of Carbon Fiber Reinforced Polymer (CFRP) and Glass Fiber Reinforced Polymer (GFRP). An investigation has also been carried out to study the effect of T-304 Stainless Steel Wire Mesh (SSWM) on the strengthening of the finite element numerical model. Ten different numerical models were evaluated which included two sets, the first set includes five models having a control model and the models in which the steel reinforcement was partially or full replaced by CFRP and GFRP bars, the next set contains further five models in which stainless-steel wire mesh was wrapped around the core concrete in the aforementioned models. The results show the evidence for GFRP bars to be used in seismic designing, as have shown an almost 100% increase in deflection with the requisite amount of energy dissipation and ultimate strength capacities. Furthermore, the crack initiation was delayed by 30-40% in terms of deflection when stainless-steel wire mesh was used which controls the damage in the critical zone of BCJ. The prime factors in controlling the crack pattern, energy dissipation, ultimate strength and deflection capacity of beam-column joint were the position of FRP bars, reinforcement ratio, dimensions of beam-column joints and the available economy.

Keywords:

CFRP bars,GFRP bars,wire mesh,beam-column joint,

Refference:

I. A. M. Ibrahim, M. Fahmy & and Z. Wu (2016) 3D finite element modeling of bond-controlled behavior of steel and basalt FRP-reinforced concrete square bridge columns under lateral loading. Composite Structures, 143, 33–52.
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III. Amir Mirmiran, Wenqing Yuan (2000) Nonlinear finite element modeling of concrete confined by fiber composites. Finite Elements in Analysis and Design 35, 79-96.
IV. Ayesha Siddika et. al (2019) Flexural performance of wire mesh and geotextile-strengthened reinforced concrete beam. SN Applied Sciences
V. Dassault Systems Simulia Corporation, (2010) User’s Manual 6.10-EF, Dassault Systems Simulia Corporation, Providence, RI, USA.
VI. De Normalisation CE (2004) Eurocode 2 Design of concrete structures, part 1–1.
VII. Genikomsou AS, P. M. ( (2015)) Finite element analysis of punching shear of concrete slabs using damaged plasticity model in ABAQUS. Eng Struct, 98, 38-48.
VIII. Hawileh, R. W. Nawaz & J. A. Abdalla (2018) Flexural behavior of reinforced concrete beams externally strengthened with Hardwire Steel-Fiber sheets. Construction and Building Materials, 172, 562-573.
IX. Huang, J. Wang & W. Liu (2017) Mechanical properties and reinforced mechanism of the stainless steel wire mesh–reinforced Al-matrix composite plate fabricated by twin-roll casting. 9, 1687814017716639.
X. Kara, Ilker Fatih Ashour, Ashraf F, Dundar & Cengiz (2013) Deflection of concrete structures reinforced with FRP bars. Composites Part B: Engineering, 44, 375-384.
XI. Karabinis, T. C. Rousakis & G. E. Manolitsi (2008) 3D Finite-Element Analysis of Substandard RC Columns Strengthened by Fiber-Reinforced Polymer Sheets. Journal of Composites for Construction, 12, 531-540.
XII. Kazemi, J. Li, S. Lahouti Harehdasht, N. Yousefieh, S. Jahandari & M. Saberian (2020) Non-linear behaviour of concrete beams reinforced with GFRP and CFRP bars grouted in sleeves. Structures, 23, 87-102.
XIII. Kmiecik & M. Kami´nski (2011) Modelling of reinforced concrete structures and composite structures with concrete strength degradation taken into consideration. Archives of Civil and Mechanical Engineering, vol. 11, pp. 623–636.
XIV. M. A. Najafgholipour, S. M. Dehghan, A. Dooshabi & A. Niroomandi (2017) Finite element analysis of reinforced concrete beam-column connections with governing joint shear failure mode. Latin American Journal of Solids and Structures,, 14, 1200–1225.
XV. M. Elchalakani, A. Karrech, M. Dong, M. S. Mohamed Ali & and B. Yang (2018) Experiments and finite element analysis of GFRP reinforced geopolymer concrete rectangular columns subjected to concentric and eccentric axial loading, . ” Structures, 14, 273–289.
XVI. M. Fiaz Tahir (2015) Response of Seismically Detailed Beam Column Joints Repaired with CFRP Under Cyclic Loading. Arabian Journal for Science and Engineering, 41, 1355-1362.
XVII. Manaha, P. Suprobo & E. Wahyuni (2019) Retrofitting of square reinforced concrete column by welded wire mesh jacketing with consentric axial load. IOP Conference Series: Materials Science and Engineering, 508, 012042.
XVIII. Mohamed Mady, Amr El-Ragaby & a. E. El-Salakawy (2011) Seismic Behavior of Beam-Column Joints Reinforced with GFRP Bars and Stirrups. Journal of Composites For Construction ASCE 15, 875-886.
XIX. Muhammad Masood Rafi , A. N., Faris Ali, Didier Talamona (2008) Aspects of behaviour of CFRP reinforced concrete beams in bending. Construction and Building Materials, 22, 277–285.
XX. Nayal & H. A. Rasheed (2006) Tension Stiffening Model for Concrete Beams Reinforced with Steel and FRP Bars. Journal of Materials in Civil Engineering, 18, 831–841.
XXI. Ozbakkaloglu, A. Gholampour & J. C. Lim (2016) Damage-Plasticity Model for FRP-Confined Normal-Strength and High-Strength Concrete. Journal of Composites for Construction, 20.
XXII. Piscesa, B, M. Attard & A. K. Samani (2017) Three-dimensional Finite Element Analysis of Circular Reinforced Concrete Column Confined with FRP using Plasticity Model. Procedia Engineering, 171, 847-856.
XXIII. Raafat El-Hacha & M. Gaafar (2011) Flexural strengthening of reinforced concrete beams using prestressed near-surface-mounted CFRP. PCI Journal fall
XXIV. Raza, Ali Khan, Qaiser uz Zaman & Afaq Ahmad (2019) Numerical Investigation of Load-Carrying Capacity of GFRP-Reinforced Rectangular Concrete Members Using CDP Model in ABAQUS. Advances in Civil Engineering, 2019, 1745341.
XXV. Rousakis, A. I. Karabinis, P. D. Kiousis & R. Tepfers (2008) Analytical modelling of plastic behaviour of uniformly FRP confined concrete members. Composites Part B: Engineering, 39, 1104-1113.
XXVI. S.M. Mourad & M. J. Shannag (2012) Repair and strengthening of reinforced concrete square columns using ferrocement jackets. Cement & Concrete Composites, 34 288–294.
XXVII. Shahzad Khan, Samiullah Qazi, Ali Siddique, Muhammad Rizwan, Muhammad Saqib, : SEISMIC RETROFITTING OF REINFORCED CONCRETE SHEAR WALL USING CARBON FIBER REINFORCED POLYMERS (CFRP), J. Mech. Cont.& Math. Sci., Vol.-15, No.-12, December (2020) pp 67-78.
XXVIII. Tahir, Q. Khan, F. Shabbir, N. Ijaz & A. Malik (2017) Performance of RC Columns Confined with Welded Wire Mesh Around External and Internal Concrete Cores. University of Engineering and Technology Taxila. Technical Journal, 22, 8.
XXIX. Usama Ali, Naveed Ahmad, Yaseen Mahmood, Hamza Mustafa, Mehre Munir, : A comparison of Seismic Behavior of Reinforced Concrete Special Moment Resisting Beam-Column Joints vs. Weak Beam Column Joints Using Seismostruct, J. Mech. Cont.& Math. Sci., Vol.-14, No.- 3, May-June (2019) pp 289-314.
XXX. Varinder Kumar & P. V. Patel (2016) Strengthening of axially loaded circular concrete columns using stainless steel wire mesh (SSWM) – Experimental investigations. Construction and Building Materials 124 186–198.
XXXI. W. X.M. Liu & Z. Chen (2014) Parameters calibration and verification of concrete damage plasticity model of ABAQUS. Industrial Construction, vol. 44, 167–213.
XXXII. Zhang, K. & Q. Sun (2018) The use of Wire Mesh-Polyurethane Cement (WM-PUC) composite to strengthen RC T-beams under flexure. Journal of Building Engineering, 15, 122-136.
XXXIII. Zike Wang & X.-L. Z. e. al (2017) Durability study on interlaminar shear behaviour of basalt-, glass- and carbon-fibre reinforced polymer (B/G/CFRP) bars in seawater sea sand concrete environment. Construction and Building Materials, 156, 985–1004.

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