-
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
.
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
- Andreev V.I., Potekhin I.A. O ravnoprochnykh i ravnonapryazhennykh konstruktsiyakh [About Equal Strength and Equal Stress Structures]. Sb. tr. Voronezh. gos. arkh.-stroit. un-t. [Collection of Works. Voronezh State University of Architecture and Civil Engineering]. 2007, pp. 84—90.
- 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.
- 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.
- 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.
- Yazyev B.M. Nelineynaya polzuchest’ nepreryvno neodnorodnykh tsilindrov [Non-linear Creeping of Continuously Heterogeneous Cylinders]. Moscow, 1990, 171 p.
- 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.
- 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.
- Potekhin I.A. Sposob optimizatsii konstruktsiy na osnove resheniya obratnykh zadach teorii uprugosti neodnorodnykh tel [Method of Optimization of Structures on the Basis of Solution to Inverse Problems of the Theory of Elasticity of Heterogeneous Bodies]. Moscow, 2009, 144 p.
- Andreev V.I., Potekhin I.A. Iteratsionnyy metod postroeniya modeli ravnoprochnogo tsilindra [Iterative Method for Development of a Model of an Equally Strong Cylinder]. Stroitel’naya mekhanika inzhenernykh konstruktsiy i sooruzheniy [Structural Mechanics of Engineering Constructions and Structures]. 2008, no. 1, pp. 45—49.
- Andreev V.I., Potekhin I.A. Modelirovanie ravnoprochnogo tsilindra na osnove iteratsionnogo podkhoda [Modeling of an Equally Strong Cylinder on the Basis of Iterative Approach]. International Journal for Computational Civil and Structural Engineering. 2008, vol. 4, no. 1, pp. 79—84.
- Zhenhai Guo, Xudong Shi. Experiment and Calculation of Reinforced Concrete at Elevated Temperatures. Butterworth-Heinemann, 2011, 226 p.
- 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.
- 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.
- Aleksandrov A.V., Potapov V.D., Derzhavin B.P.; Aleksandrov A.V., editor. Soprotivlenie materialov [Resistance of Materials]. Moscow, Vyssh. Shk. Publ., 2003, 560 p.
-
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
.
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
- Andreev V.I., Malashkin Yu.N. Raschet tolstostennoy truby iz nelineyno-uprugogo materiala [Calculation of Thick-Walled Pipe of a Nonlinear-Elastic Material]. Stroitel’naya mekhanika i raschet sooruzheniy [Structural Mechanics and Calculation of Structures]. 1983, no. 6, pp. 70—72. (In Russian)
- Birger I.A. Nekotorye obshchie metody resheniya zadach teorii plastichnosti [Some Common Methods for Solving the Problems of the Theory of Plasticity]. Prikladnaya matematika i mekhanika [Applied Mathematics and Mechanics]. 1951, vol. 15, no. 6, pp. 765—770. (In Russian)
- Novozhilov I.V. Ob utochnenii predel’nykh modeley mekhaniki [On a Refinement of Limit Models of Mechanics]. Nelineynaya mekhanika [Nonlinear Mechanics]. Moscow, Fizmatlit Publ., 2001, 432 p. (In Russian)
- 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.
- Stupishin L.U., Nikitin K.E. Determining the Frequency of Free Oscillations Geometrically Nonlinear Shell Using the Mixed Finite Element Method. Applied Mechanics and Materials. 2014, vols. 580—583, pp. 3017—3020. DOI: http://dx.doi.org/10.4028/www.scientific.net/AMM.580-583.3017.
- 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)
- Kolchin G.B. Raschet elementov konstruktsiy iz uprugikh neodnorodnykh materialov [Calculation of Structural Elements Made of Inhomogeneous Elastic Materials]. Kishinev, Kartya Moldovenyaske Publ., 1971, 172 p. (In Russian)
- Kolchin G.B. Ploskie zadachi teorii uprugosti neodnorodnykh tel [Plane Problems of Elasticity Theory of Inhomogeneous Bodies]. Kishinev, Shtiintsa Publ., 1977, 119 p. (In Russian)
- Ol’shak V., Rykhlevsky Ya., Urbanovskiy V. Teoriya plastichnosti neodnorodnykh tel [Theory of Plasticity of Heterogeneous Bodies]. Translated from English. Moscow Mir, 1964. 156 s. (In Russian)
- Rostovtsev N.A. K teorii uprugosti neodnorodnykh tel [To the Theory of Elasticity of Inhomogeneous Bodies]. Prikladnaya matematika i mekhanika [Applied Mathematics and Mechanics]. 1964, vol. 28, no. 4, pp. 601—611. (In Russian)
- Nowinski J. Axisymmetric Problem of the Steady-State Thermal-Dependent Properties. Applied Scientific Research. 1964, vol. 12, no. 4—5, pp. 349—377. DOI: http://dx.doi.org/10.1007/BF03185007.
- Olszak W., Urbanovski W., Rychlewski J. Sprężysto-plastyczny gruboscienny walec niejednorodny pod działaniem parcia wewnetrznego i siły podłużnej. Arch. mech. stos. 1955, vol. VII, no. 3, pp. 315—336.
- Olszak W., Urbanowski W. Sprężysto-plastyczna gruboscienna powłoka kulista z materiału niejednorodnego poddana działaniu cisnienia wewnetrznego i zewnetrznego. Rozprawy inżynierskie. 1956, vol. IV, no. 1, pp. 23—41.
- Andreev V.I. Ravnovesie tolstostennogo shara iz nelineynogo neodnorodnogo materiala [Equilibrium of a Thick-Walled Sphere Made of Nonlinear Inhomogeneous Material]. Stroitel’naya mekhanika i raschet sooruzheniy [Structural Mechanics and Calculation of Structures]. 1983, no. 2, pp. 24—27. (In Russian)
- 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)
- 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)
- 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)
- 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.
- Lukash P.A. Osnovy nelineynoy stroitel’noy mekhaniki [Fundamentals of Nonlinear Structural Mechanics]. Moscow, Stroyizdat Publ., 1978, 208 p. (In Russian)
- Andreev V.I. Equilibrium of a Thick-Walled Sphere of Inhomogeneous Nonlinear-Elastic Material. Applied Mechanics and Materials. 2013, vols. 423—426, pp. 1670—1674. DOI: http://dx.doi.org/10.4028/www.scientific.net/AMM.423-426.1670.
-
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
.
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
- Ekel’chik V.S., Klyunin O.S. Novyy podkhod k sozdaniyu oblegchennykh metallo-plastikovykh ballonov vysokogo davleniya dlya szhatykh gazov [New Approach to the Creation of Lightweight Reinforced-Plastic High Pressure Cylinders for Compressed Gases]. Voprosy materialovedeniya [Problems of Materials Science]. 2003, no. 2 (34), pp. 26—31. (In Russian)
- Turusov R.A., Memaryanfard H. Diskretnaya model’ v analize ostatochnykh napryazheniy odnonapravlennykh namotochnykh tsilindrov iz armirovannogo plastika v protsesse okhlazhdeniya [Discrete Model in the Analysis of Residual Stresses in Unidirectional Winding Cylinders Made of Fiber-Reinforced Plastic]. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2015, no. 1, pp. 27—35. (In Russian)
- Turusov R.A., Korotkov V.N., Rogozinskiy A.K., Kuperman A.M., Sulyaeva Z.P. Tekhnologicheskaya monolitnost’ obolochek iz polimernykh kompozitnykh materialov [Monolithic Technology of the Shells of Polymer Composite Materials]. Mekhanika kompozitnykh materialov [Mechanics of Composite Materials]. 1987, no. 6, pp. 1072—1076. (In Russian)
- Turusov R.A., Korotkov V.N., Rogozinskiy A.K. Temperaturnye napryazheniya v tsilindre iz kompozitnogo materiala v protsesse ego okhlazhdeniya i khraneniya [Thermal Stresses in a Cylinder Made of a Composite Material in the Process of Cooling and Storage]. Mekhanika kompozitnykh materialov [Mechanics of Composite Materials]. 1983, no. 2, pp. 290—295. (In Russian)
- Korotkov V.N., Dubovitskiy A.Ya., Turusov R.A., Rozenberg B.A. Teoriya optimizatsii rezhima okhlazhdeniya tolstostennykh izdeliy iz kompozitnykh materialov [Optimization Theory of Cooling Regime of Thick-Walled Products Made of Composite Materials]. Mekhanika kompozitnykh materialov [Mechanics of Composite Materials]. 1982, no. 6, pp. 1051—1055. (In Russian)
- Bolotin V.V., Blagonadezhin V.L., Varushkin E.M., Perevozchikov V.G. Ostatochnye napryazheniya v namotochnykh elementakh konstruktsiy iz armirovannykh plastikov [Residual Stresses in Winding Elements of Constructions Made of Reinforced Plastics]. Moscow, Izdatel’stvo TsNII informatsii Publ., 1977. (In Russian)
- Bolotin V.V., Vorontsov A.N. Formation of Residual Stresses in Components Made out of Laminated and Fibrous Composites during the Hardening Process. Mechanics of Composites. September 1976, vol. 12, no. 5, pp. 701—705. DOI: http://dx.doi.org/10.1007/BF00856324.
- Afanas’ev Yu.A., Ekel’chik B.C., Kostritskiy S.N. Temperaturnye napryazheniya v tolstostennykh ortotropnykh tsilindrakh iz armirovannykh polimernykh materialov pri neodnorodnom okhlazhdenii [Temperature Stresses in Thick-Walled Orthotropic Cylinders Made of Reinforced Polymer Materials in Case of Inhomogeneous Cooling]. Mekhanika kompozitnykh materialov [Mechanics of Composite Materials]. 1980, no. 4, pp. 651—660. (In Russian)
- Hyer M.W., Rousseau C.Q. Thermally-Induced Stresses and Deformations in Angle-Ply Composite Tubes. Journal of Composite Materials. 1987, vol. 21, no. 5, pp. 454—480. DOI: http://dx.doi.org/10.1177/002199838702100504.
- Jerome T. Tzeng. Prediction and Experimental Verification of Residual Stresses in Thermoplastic Composites. Journal of Thermoplastic Composite Materials. April 1995, vol. 8, no. 2, pp. 163—179. DOI: http://dx.doi.org/10.1177/089270579500800202.
- Tzeng T., Chien L.S. A Thermal Viscoelastic Analysis for Thick-Walled Composite Cylinders. Journal of Composite Materials March. 1995, vol. 29, no. 4, pp. 525—548.
- Wisnom M.R., Stringer L.G., Hayman R.J., Hinton M.J. Curing Stresses in Thick Polymer Composite Components. Part I: Analysis. 12th International Conference on Composite Materials, Paris, July 1999. Woodhead Publishing Ltd, 1999, p. 859. Available at: http://iccm-central.org/Proceedings/ICCM12proceedings/site/papers/pap859.pdf.
- Li C., Wisnom M.R., Stringer L.G., Hayman R., Hinton M.J. Effect of Mandrel Contact on Residual Stresses During Cure of Filament Wound Tubes. 8th International Conference on Fibre Reinforced Composites, 13—15 September 2000, Newcastle-upon-Tyne, UK. 2000, pp. 105—112.
- Gorbatkina Yu.A. Adhesive Strength of Fibre-Polymer Systems. New York, London, Ellis Horwood, 1992, 264 p.
- Turusov R.A. Adgezionnaya mekhanika [Adhesion Mechanics]. Moscow, MGSU Publ., 2015, 230 p. (In Russian)
- Babich V.F. Issledovanie vliyaniya temperatury na mekhanicheskie kharakteristiki zhestkikh setchatykh polimerov : avtoreferat dissertatsii … kandidata tekhnicheskikh nauk [Study of Temperature Influence on the Mechanical Properties of Rigid Cross-Linked Polymers : Abstract of the Dissertation of Candidate of Technical Sciences]. Moscow, 1966, 12 p. (In Russian)
- Gurevich G.I. Deformiruemost’ sred i rasprostranenie seysmicheskikh voln [Deformability of Media and Propagation of Seismic Waves]. Moscow, Nauka Publ., 1974, 482 p. (In Russian)
- Nemat-Nasser S., Hori M. Micromechanics: Overall Properties of Heterogeneous Materials. Amsterdam, Elsevier Science Publishers, 1993.
- Aboudi J. Mechanics of Composite Materials, a Unified Micromechanical Approach. Amsterdam, Elsevier Science Publishers, 1991.
- Zihui Xia, Yunfa Zhang, Fernand Ellyin. A Unified Periodical Boundary Conditions for Representative Volume Elements of Composites and Applications. International Journal of Solids and Structure. April 2003, vol. 40, issue 8, pp. 1907—1921. DOI: http://dx.doi.org/10.1016/S0020-7683(03)00024-6.
- Zheng-Ming Huang, Li-min Xin. Stress Concentration Factors of Matrix in a Compo-Site. Subjected to Transverse Loads. ICCM 2014, July 28—30. Cambridge, 3 p. Available at: http://www.sci-en-tech.com/ICCM2014/PDFs/321-979-1-PB.pdf.