DESIGNING AND DETAILING OF BUILDING SYSTEMS. MECHANICS IN CIVIL ENGINEERING

DEVELOPMENT OF A MODEL OF AN EQUAL STRESS CYLINDER BASED ON MOHR’S STRENGTH THEORY

Vestnik MGSU 5/2013
  • Chepurnenko Anton Sergeevich - Don State Technical University (DGTU) Candidate of Engineering Science, teaching assistant of the strength of materials department, Don State Technical University (DGTU), 162 Sotsialisticheskaya str., Rostov-on-Don, 344022; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Andreev Vladimir Igorevich - Moscow State University of Civil Engineering (National Research University) (MGSU) Doctor of Technical Sciences, Professor, corresponding member of Russian Academy of Architecture and Construction Sciences, chair, Department of Strength of Materials, Moscow State University of Civil Engineering (National Research University) (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Yazyev Batyr Meretovich - Rostov State University of Civil Engineering (RSUCE) Doctor of Technical Sciences, Professor, Chair, Depart- ment of Strength of Materials; +7 (863) 201-91-09, Rostov State University of Civil Engineering (RSUCE), 162 Sotsialisticheskaya St., Rostov-on-Don, 344022, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 56-61

The authors have employed analytical methods to identify the nature of dependence of the elastic modulus distribution over the thickness of a cylinder, loaded by internal pressure p , if the equivalent stress is the same in all points, according to Mohr’s theory of strength. The problem in which dependence of an elastic modulus is to be identified along the radius, and the stress value is available, is called the inverse prob- lem. The idea of the method is that if a certain area of a body has the value of its elastic modulus lower than the one in the homogeneous material, stresses in this area are also reduced. The problem is solved for the case of plane strain and plane stress in the elastic formulation. It is proven that assurance of artificial heterogeneity reduces the maximal equivalent stress. Therefore, we have taken two variants of shells: one having inner radius a = 1 m and outer radius b = 2 m, the other one having inner radius a = 1 m and outer radius b = 0.52 m. The value of the maximal equivalent stress calculated using Mohr’s theory reduces almost two-fold in the first case and 1.5-fold in the second case. Moreover, the use of non-uniform thick-walled cylinders can significantly reduce their thickness with the value of the internal pressure being the same. In our case, the shell thickness reduces from 1 m to 0.52 m, which is almost 2 times. We also proven that the first, second and third strength theories in the case of an axisymmetric problem are the special cases of Mohr’s strength theory. This result coincides with well-known analytical and numerical solutions.

DOI: 10.22227/1997-0935.2013.5.56-61

References
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  2. Andreev V.I. Nekotorye zadachi i metody mekhaniki neodnorodnykh tel [Some Problems and Methods of Mechanics of Heterogeneous Bodies]. Moscow, ASV Pub., 2002, 288 p.
  3. Andreev V.I. Uprugoe i uprugo-plasticheskoe ravnovesie tolstostennykh tsilindricheskikh i sfericheskikh nepreryvno-neodnorodnykh tel [Elastic and Elastoplastic Equilibrium of Thickwalled Cylindrical and Spherical Continuously Heterogeneous Bodies]. Moscow, 1986, 427 p.
  4. Andreev V.I. Optimization of Thick-walled Shells Based on Solutions of Inverse Problems of the Elastic Theory for Inhomogeneous Bodies. Computer Aided Optimum Design in Engineering XII (OPTI XII). WIT Press. 2012, pp. 189—201.
  5. Yazyev B.M. Nelineynaya polzuchest’ nepreryvno neodnorodnykh tsilindrov [Non-linear Creeping of Continuously Heterogeneous Cylinders]. Moscow, 1990, 171 p.
  6. Andreev V.I., Potekhin I.A. O sposobe sozdaniya optimal’nykh stroitel’nykh konstruktsiy na osnove resheniya obratnykh zadach teorii uprugosti neodnorodnykh tel [Method of Development of Optimal Structural Units on the Basis of Solutions to Inverse Problems of Theory of Elasticity of Heterogeneous Bodies]. Vestnik stroit. nauk. [Herald of Civil Engineering Sciences]. 2007, no. 11, pp. 48—52.
  7. Andreev V.I., Potekhin I.A. Postroenie modeli ravnonapryazhennogo tsilindra na osnove vtoroy i chetvertoy teorii prochnosti [Development of a Model of an Equal Stress Cylinder on the Basis of the Second and Fourth Theories of Strength]. Teoreticheskie osnovy stroitel’stva. Tr. XVI Slovatsk.-ross.-pol’sk. sem. [Theoretical Fundamentals of Construction. Works of the 16th Slovak-Russian-Polish Seminar]. Moscow, 2007, pp. 29—34.
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  11. Zhenhai Guo, Xudong Shi. Experiment and Calculation of Reinforced Concrete at Elevated Temperatures. Butterworth-Heinemann, 2011, 226 p.
  12. Bin Yang, Jinhua Huang, Chunjiao Lin, Xinkun Wen. Temperature Effects and Calculation Method of Closure Temperatures for Concrete-filled Steel Tube Arch Rib of Dumbbellshape Section. The Open Civil Engineering Journal. 2011, no. 5, pp. 179—189. Available at: http://www.benthamscience.com/open/tociej/articles/V005/179TOCIEJ.pdf.
  13. Litvinov C.B., Yazyev S.B., Yazyeva S.B. Ploskaya deformatsiya neodnorodnykh mnogosloynykh tsilindrov s uchetom nelineynoy polzuchesti [Plane Deformation of Heterogeneous Multilayered Cylinders with Account for Nonlinear Creeping]. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2010, no. 1, pp. 128—132.
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Analytical solution of physically nonlinear problem for an inhomogeneous thick-walled cylindrical shell

Vestnik MGSU 11/2015
  • Andreev Vladimir Igorevich - Moscow State University of Civil Engineering (National Research University) (MGSU) Doctor of Technical Sciences, Professor, corresponding member of Russian Academy of Architecture and Construction Sciences, chair, Department of Strength of Materials, Moscow State University of Civil Engineering (National Research University) (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Polyakova Lyudmila Sergeevna - Moscow State University of Civil Engineering (National Research University) (MGSU) Master student, Department of Strength of Materials, Moscow State University of Civil Engineering (National Research University) (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 38-45

Among the classical works devoted to Solid Mechanics a significant place is occupied by the studies taking into account the physical and geometric nonlinearity. Also there is enough of works, which concern linear problems taking into account the inhomogeneity of the material. At the same time there are very few publications, which take into account both effects (non-linearity and inhomogeneity). This is due to the lack of experimental data on the influence of various factors on the parameters defining the non-linear behavior of the materials. Thus it is of great importance to study the influence of inhomogeneity when solving the problems of structures made of physically nonlinear materials. This article provides a solution to one of the problems of the nonlinear theory of elasticity taking into account the inhomogeneity. The problem is solved in an axisymmetric formulation, i.e. all the parameters of the nonlinear relationship between the intensities of stresses and strains are functions of the radius. The article considers an example - the stress distribution in the inhomogeneous soil massif with a cylindrical cavity.

DOI: 10.22227/1997-0935.2015.11.38-45

References
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  4. Stupishin L.U., Nikitin K.E. Numerical Research Methodology of Free Oscillations of Geometrically Nonlinear Shell Using the Mixed Finite Element Method. Advanced Materials Research. 2014, vol. 988, pp. 338—341. DOI: http://dx.doi.org/10.4028/www.scientific.net/AMR.988.338.
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  6. Grigorenko Ya.M., Vasilenko A.T., Pankratova N.D. Nesimmetrichnaya deformatsiya tolstostennykh neodnorodnykh sfericheskikh obolochek [Asymmetrical Non-Uniform Deformation of the Thick-Walled Spherical Shells]. Doklady AN USSR [Reports of the Ukrainian Academy of Sciences ]. Series A, 1981, no. 6, pp. 42—45. (In Russian)
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  15. Andreev V.I. Nekotorye zadachi i metody mekhaniki neodnorodnykh tel [Some Problems and Methods of Inhomogeneous Bodies Mechanics]. Moscow, ASV Publ., 2002, 288 p. (In Russian)
  16. Vasilenko A.T., Grigorenko Ya.M., Pankratova N.D. Napryazhennoe sostoyanie tolstostennykh neodnorodnykh sfericheskikh obolochek pri nesimmetrichnykh nagruzkakh [The Stress State of Thick-Walled Non-Uniform Spherical Shells]. Prikladnaya mekhanika [Applied Mechanics]. 1982, vol. XVIII, no. 4, pp. 22—28. (In Russian)
  17. Grigorenko Ya.M., Vasilenko A.T., Pankratova N.D. O reshenii zadach statiki sloistykh obolochek v trekhmernoy postanovke [On the Solution of Statics Problems of Layered Shells in Three-Dimensional Statement]. Vychislitel’naya i prikladnaya matematika [Computational and Applied Mathematics]. 1981, no. 43, pp. 123—132. (In Russian)
  18. Andreev V.I. About the Unloading in Elastoplastic Inhomogeneous Bodies. Applied Mechanics and Materials. 2013, vols. 353—356, pp. 1267—1270. DOI: http://dx.doi.org/10.4028/www.scientific.net/AMM.353-356.1267.
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NUMERICAL AND EXPERIMENTAL STUDIES OF MONOLITHIC CHARACTER OF THICK-WALLED ANISOTROPIC SHELL

Vestnik MGSU 7/2016
  • Memarianfard Mahsa - K.N. Toosi University of Technology Associate Professor, Department of Engineering Ecology, K.N. Toosi University of Technology, 470 Mirdamad Ave. West, 19697, Tehran, Iran; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Turusov Robert Alekseevich - Moscow State University of Civil Engineering (National Research University) (MGSU) Doctor of Physical and Mathematical Sciences, Professor, Department of Strength of Materials, Moscow State University of Civil Engineering (National Research University) (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Memarianfard Memaryanfard - Moscow State University of Civil Engineering (National Research University) (MGSU) postgraduate student, Department of Strength of Materials, Moscow State University of Civil Engineering (National Research University) (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 36-45

This paper presents t experimental and numerical studies of cracking in the thick-walled filament-wound cylindrical shells made of fiber reinforced plastic during the manufacturing process (specifically, in the process of curing and cooling). The experiments have shown that, when the cylinder is cooled by optimum cooling regime, at the end of the cooling process the obtained cylinder is monolithic and without ring cracking. In this regard, the residual thermal stresses in thick-walled cylinder in the cooling process is calculated using finite element method with account for transient heat conduction and the temperature dependence of the mechanical properties of the material and the viscoelastic behavior of the polymer. The calculations are conducted for cooling in standard and optimum regimes. The results showed that the maximum radial stress in the most dangerous initial area is several times less when the cylinder is cooled down in the optimum regime than when it is cooled in the standard regime.

DOI: 10.22227/1997-0935.2016.7.36-45

References
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