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Verma, Gaurav
- Theory of Elastic-Plastic Shells
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Authors
Affiliations
1 Department of Mathematics, Gobindgarh Public College, Alour, Khanna, IN
1 Department of Mathematics, Gobindgarh Public College, Alour, Khanna, IN
Source
Research Journal of Science and Technology, Vol 8, No 1 (2016), Pagination: 41-44Abstract
The Theory of Shells involves mainly the study of the structure and simplication of the problems occurring in the shells associated with the boundary/initial value problems. The purpose of this paper is to analysis the behaviour of shells under the effect of external forces. The external forces like pressure and temperature gradients play a major role in generating the stresses and displacements in shells due to elasticity. To analysis the behaviour of shells under given loading conditions, we have proper knowledge of the elastic-plastic theory of shells. The proper understanding of the principles and assumptions of shell theory is necessary to solve the various boundary/initial value problems related to the shells. Therefore, It is very important for engineers to obtain the solution of such problems for economical and safe designing of mechanical structures. There are various theoretical and numerical approaches based on finite element method, shear deformation theory, discrete convolution technique, direct method of calculus of variations useful in obtaining the numerical data for stresses and displacements in shells.Keywords
Shells, Elasticity, Thickness, Stress, Strain.
- Self Similarity in Fractals
Abstract Views :227 |
PDF Views:2
Authors
Affiliations
1 Department of Mathematics, Gobindgarh Public College, Khanna, Punjab, IN
1 Department of Mathematics, Gobindgarh Public College, Khanna, Punjab, IN
Source
Research Journal of Engineering and Technology, Vol 7, No 2 (2016), Pagination: 75-78Abstract
The purpose of the paper is to discuss the infinite similar behavior of fractal by discussing various natural and mathematical examples of the fractals. A fractal is a mathematical set that exhibits a repeating pattern that displays at every scale. It can be said that fractals are geometric shapes generally rough structures that can be divided into parts, each of which is diminished size copy of the original. The main characteristic of fractals is that they exhibit great complexity driven by simplicity.Keywords
Fractal, Similarity, Pattern, Set.- Effect of External Pressure on the Spherical Shell
Abstract Views :226 |
PDF Views:4
Authors
Affiliations
1 Department of Mathematics Gobindgarh Public College, Khanna, Ludhiana, Punjab, IN
1 Department of Mathematics Gobindgarh Public College, Khanna, Ludhiana, Punjab, IN
Source
Research Cell: An International Journal of Engineering Sciences, Vol 24, No 1 (2017), Pagination: 61-73Abstract
To grow the prosperity of different spherical shell structures under pressure situations, the present research deals with the examination of elastic - plastic stresses in a spherical shell under the effect of external pressure. The plan of the research has been obtained by using the Seth's transition speculation of elastic- plastic transitions. The transition hypothesis does not accept established suspicions like incompressibility and yield conditions. The radial and circumferential stresses have been computed for the spherical shell for compressible and additionally incompressible materials. It has been watched that the spherical shell made of incompressible material requires high pressure to begin initial yielding in the shell when contrasted with spherical shell made of compressible material. The outcomes inferred are demonstrated graphically.Keywords
Elastic-Plastic, Pressure, Spherical Shell, Stresses.Full Text
References
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- Cong, P. H., Duc, N. D., Anh, V. T., 2104, “Nonlinear axisymmetric response of FGM shallow spherical shells on elastic foundations under uniform external pressure and temperature”, European Journal of Mechanics - A/Solids, Volume 45, pp. 80-89.
- Łukasiewicz, S.A., 1976, "Introduction of concentrated loads in plates and shells, Progress in Aerospace Sciences, Volume 17, Pages 109-146.
- Viola, E., Rossetti, L., Tornabene, N. F., 2016, “Generalized stress–strain recovery formulation applied to functionally graded spherical shells and panels under static loading”,Composite Structures, Volume 156, 15, pp. 145-164.
- Thakur, P., 2011, "Elastic-plastic transition stresses in rotating cylinder by finite deformation under steady- state temperature, Thermal Science International Scientific Journal", 15(2), pp.537-543.
- Thakur, P., 2010, “Creep transition stresses in a thin rotating disc with shaft by finite deformation under steady state temperature”, Thermal Science, Vol. 14, No. 2, 2010, pp. 425-436..
- Thakur, P., Singh, S.B., Sawhney S., 2016, "Elastic–Plastic Infinitesimal Deformation in a Solid Disk under Heat Effect by Using Seth Theory", Int. J. Appl. Computional Math, Springer, doi: 10.1007/s40819-015-0116-9.
- Seth, B. R., 1962, “Transition theory of elastic- plastic deformation, creep and relaxation”, Nature, 195, pp. 896 -897, doi:10.1038/195896a..
- Seth, B. R., 1966, “Measure concept in Mechanics”, International Journal of Non-linear Mechanics, Vol. 1, Issue 1, pp. 35- 40.
- Sokolnikoff , I. S., 1946, “The Mathematical Theory of Elasticity”, MCGRAW Hill.
- Thakur, P., Singh, S. B., 2015, "Elastic-plastic transitional stresses distribution and displacement for transversely isotropic circular disc with inclusion subject to mechanical load", Kragujevac Journal of Science 37, 25-36.
- Thakur, P., Singh, S. B., 2016, “Steady thermal stresses in solid disk under heat generation subjected to variable density", Kragujevac J. Sci. 38, 2016, 5-14.
- Thakur, P., Singh, S. B., 2015, "Mechanical Load in a circular rotating Disk With Shaft For Different Materials Under Steady-State Temperature", Scientific Technical Review, Military Technical Institute Ratka Resanovića, Belgrade, Serbia 65, 2015 36-42.
- Verma, G., Rana, P., Pathania, D.S., and Thakur, P., 2017. “Creep transition in the rotating spherical shell under the effect of density variable by Seth’s transition theory”, AIP Conference proceeding,1802, 020020
- Verma, G., Gupta, S., 2014, “Elastic-plastic Transition In Shells under internal pressure”, Int. J. of emerging technology and advanced engineering., Vol. 4, issue8, pp. 126-129.
- Verma, G., Gupta, S., 2015, “Creep transition of spherical shell under internal pressure”, Theoretical and applied Science, 24, 201-207.
- Verma, G., Pathania, D.S., and Thakur, P., 2017, "Elastic-plastic stress analysis in a Spherical shell under internal pressure and steady state temperature", Structural Integrity and Life, Serbia, Vol. 17(1), pp. 39-43.
- Verma, G., Pathania, D.S., and Thakur, P., 2017, "Elastic-plastic transition on raotating spherical shells in dependence of compressibility", Kragujevac J. Sci. 39, 2017, 5-16.
- Preparation of Nanosized Bioapatite by Cryogenic Grinding from Sintered Scales of Silver Carp Hypophthalmichthys Molitrix (Cuvier and Valenciennes)
Abstract Views :339 |
PDF Views:113
Authors
Affiliations
1 Department of Zoology, Panjab University, Chandigarh - 160014, IN
2 Dr S. S. Bhatnagar University Institute of Chemical Engineering and Technology, Panjab University, Chandigarh - 160014, IN
1 Department of Zoology, Panjab University, Chandigarh - 160014, IN
2 Dr S. S. Bhatnagar University Institute of Chemical Engineering and Technology, Panjab University, Chandigarh - 160014, IN
Source
Current Science, Vol 115, No 5 (2018), Pagination: 977-982Abstract
The present study is based on the processing of bioapatite (BAp) of sintered fish scales, i.e. heat treated fish scales at 900°C, by the cryogenic grinding technique. It shows that BAp formed by cryogenic grinding of sintered fish scales became purer and nanosized. Earlier studies had reported that nanosized bioapatite increases the resorbability and bioactivity for tissue replacement and regeneration like bones and dental tissues of human beings. Energy dispersive X-ray spectroscopy of sintered fish scale BAp confirmed the presence of tetracalcium phosphate with Ca/P ratio of 1.97. Field emission scanning electron microscopy and dynamic light scattering (DLS) showed microsized particles. The sintered fish scales when cryoground showed the formation of nanosized particles as revealed by transmission electron microscopy and DLS. The Fourier transform infrared spectroscopy results of sintered and cryoground BAp had similar functional groups, but cryoground BAp showed greater purity.Keywords
Bioapatite, Biogenic Source, Cryogenic Grinding, Fish Scales, Sintering.Full Text
References
- Supova, M. and Suchy, T., Bio-nanoceramics and bio-nanocomposites. In Handbook of Nanoceramic and Nanocomposite Coatings and Materials (eds Makhlouf, A. and Scharnweber, D.), Elsevier, Butterworth-Heinemann, Amsterdam, The Netherlands, 2015, pp. 29–58.
- Scalera, F., Influence of the calcinations temperature on morphological and mechanical properties of highly porous hydroxyapatite scaffolds. Ceram. Int., 2013, 39, 4839–4846.
- Mondal, S., Mondal, B., Dey, A. and Mukhopadhyay, S. S., Studies on processing and characterization of hydroxyapatite biomaterials from different biowastes. J. Miner. Mater. Character. Eng., 2012, 11, 55–67.
- Iwamoto, T., Hieda, Y. and Kogai, Y., Effect of hydroxyapatite surface morphology on cell adhesion. Mater. Sci. Eng. C, 2016, 69, 1263–1267.
- Raynaud, S., Champion, E., Bernache-Assollant, D. and Laval, J. P., Determination of calcium/phosphorus atomic ratio of calcium phosphate apatites using X-ray diffractometry. J. Am. Ceram. Soc., 2001, 84, 359–366.
- Habraken, W., Habibovic, P., Epple, M. and Bohner, M. Calcium phosphates in biomedical applications: materials for the future? Mater. Today, 2016, 19, 69–87.
- Moseke, C. and Gbureck, U., Tetracalcium phosphate: Synthesis, properties and biomedical applications. Acta Biomater., 2010, 6, 3815–3823.
- Huang, J., Lin, Y. W., Fu, X. W., Best, S. M., Brooks, R. A., Rushton, N. and Bonfield, W., Development of nano-sized hydroxyapatite reinforced composites for tissue engineering scaffolds. J. Mater. Sci.: Mater. Med., 2007, 18, 2151–2157.
- Posner, A. S., Crystal chemistry of bone mineral. Physiol. Rev., 1969, 49, 760–787.
- Eppell, J. S., Tong, W., Katz, L. Z., Kuhn, L. and Glimcher, J. M., Shape and size of isolated bone mineralites measured using atomic force microscopy. J. Orthop. Res., 2001, 19, 1027–1034.
- Varma, H. K. and Babu, S., Synthesis of calcium phosphate bioceramics by citrate gel pyrolysis method. Ceram. Int., 2005, 31, 109–114.
- Kai, D., Fan, H., Li, D., Zhu. X. and Zhang, X., Preparation of tetracalcium phosphate and the effect on the properties of calcium phosphate cement. Mater. Res. Forum, 2009, 610–613, 1356.
- Panda, N. N., Pramanik, K. and Sukla, L. B., Extraction and characterization of biocompatible hydroxyapatite from freshwater fish scales for tissue engineering scaffold. Bioprocess Biosyst. Eng., 2014, 37, 433.
- Measures in Mathematics
Abstract Views :188 |
PDF Views:0
Authors
Affiliations
1 Gobindgarh Public College, Khanna, Ludhiana -141001, IN
1 Gobindgarh Public College, Khanna, Ludhiana -141001, IN
Source
Research Journal of Engineering and Technology, Vol 8, No 3 (2017), Pagination: 230-232Abstract
The current paper presents the concept of measures in mathematics. The terms "measure," "measurable," etc. have very precise technical definitions that can make them appear difficult to understand. Measures are important not only because of their intrinsic geometrical and probabilistic significance, but because they allow us to define integrals. In this paper, we discuss brief theory of measures and their properties. The paper also includes the various important list of examples of the measure that are used in various fields of mathematics. We have used standard definitions and notations from set theory.Keywords
Measure, Set, Lebsegue.References
- Bogachev V. I., Measure Theory, Vol. I. and II, Springer-Verlag, Heidelberg, 2007.
- Cohn D. L., Measure Theory, Birkhauser, Boston, 1980.
- Evans L.C. and Gariepy R. F., Measure Theory and Fine Properties of Functions, CRC Press, Boca Raton, 1992.
- Taylor M. E., Measure Theory and Integration, American Mathematical Society, Providence, 2006.
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- Bear H. S., A Primer of Lebesgue Integration, San Diego: Academic Press, ISBN 978-0120839711, 2001.
- Bogachev V. I., Measure theory, Berlin: Springer, ISBN 9783540345138, 2006.
- Czyz J., Paradoxes of Measures and Dimensions Originating in Felix Hausdorff's Ideas. Singapore: World Scientific, 1994.
- Jech T. J., Set Theory, 2nd ed. Berlin: Springer-Verlag, p. 295, 1997.
- Wheeler R. L. and ZygmundZ, Measure and Integral, Marcel Dekker, 1977.
- Seth B. R., Generalized strain measure with applications to physical problems, Rep. 1966.
- Countering Future COVID-19 like Pandemics: Strategies and Thoughts
Abstract Views :381 |
PDF Views:0
Authors
Affiliations
1 Carmel Convent School, Sector 9B, Chandigarh, IN
2 Centre for Nanoscience and Nanotechnology (UIEAST), Panjab University, Chandigarh, IN
1 Carmel Convent School, Sector 9B, Chandigarh, IN
2 Centre for Nanoscience and Nanotechnology (UIEAST), Panjab University, Chandigarh, IN