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DESIGNING AND DETAILING OF BUILDING SYSTEMS. MECHANICS IN CIVIL ENGINEERING

Generalized equations of finite difference method in the problems of dynamic load calculation for thin bending plates

Вестник МГСУ 9/2014
  • Gabbasov Radek Fatykhovich - Moscow State University of Civil Engineering (MGSU) Doctor of Technical Sciences, Professor, Department of Structural Mechanics, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; +7 (495) 287-49-14; Этот e-mail адрес защищен от спам-ботов, для его просмотра у Вас должен быть включен Javascript .
  • Hoang Tuan Anh - Moscow State University of Civil Engineering (MGSU) postgraduate student, Department of Structural Mechanics, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; +7 (495) 287-49-14; Этот e-mail адрес защищен от спам-ботов, для его просмотра у Вас должен быть включен Javascript .
  • Shikunov Maksim Alekseevich - Moscow State University of Civil Engineering (MGSU) postgraduate student, Department of Structural Mechanics, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; +7 (495) 287-49-14; Этот e-mail адрес защищен от спам-ботов, для его просмотра у Вас должен быть включен Javascript .

Страницы 32-38

Bending plate is widely used in the construction of large-span structures. Its advantage is light weight, industrial production, low cost and easy installation. Implementing the algorithm for calculating bending plates in engineering practice is an important issue of the construction science. The generalized equations of finite difference method is a new trend in the calculation of building construction. FDM with generalized equation provides additional options for an engineer along with other methods (FEM). In the article the algorithm for dynamic calculation of thin bending plates basing on FDM was developed. The computer programs for dynamic calculation were created on the basis of the algorithm. The authors come to the conclusion that the more simple equations of FDM can be used in case of solving the impulse load problems in dynamic load calculation of thin bending plate.

DOI: 10.22227/1997-0935.2014.9.32-38

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Calculation of plates with variable rigidity on elastic basis by finite difference method

Вестник МГСУ 12/2014
  • 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; Этот e-mail адрес защищен от спам-ботов, для его просмотра у Вас должен быть включен Javascript .
  • Barmenkova Elena Vyacheslavovna - Moscow State University of Civil Engineering (MGSU) Candidate of Technical Science, Associate Professor, Department of the Strength of materials, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; Этот e-mail адрес защищен от спам-ботов, для его просмотра у Вас должен быть включен Javascript .
  • Matveeva Alena Vladimirovna - Moscow State University of Civil Engineering (MGSU) postgraduate student, Department of the Strength of materials, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; Этот e-mail адрес защищен от спам-ботов, для его просмотра у Вас должен быть включен Javascript .

Страницы 31-39

The article describes the calculation of plates on the elastic basis, both two-layer and single-layer. The calculation is based on the solution of the differential equation of bending plate by finite difference method. The calculation results are compared with the numerical solution in the program complex. The percentage of differences of values depending on the method of division or method of solving is shown. We considered a problem when a foundation plate and a construction are plates, which are deformed together, that, in fact, corresponds to the problem of bending a two-layer plate on elastic basis. In case of a two-layer plate in order to find the solution of the problem we need to solve the equation of bending of plates that are structurally similar to the traditional, but still give different results. In solving finite difference operators derivatives are substituted into differential equation which must be in accordance with each grid point, as well as at the border. If we consider the problem in the conventional formulation, only the lower layer is bended in the plate; the analysis of the plate, which takes into account the weight of its own layers, both layers are deformed together. Also when considering a two-layer plate, the neutral layer is deposed away from the upper layer, consequently, the whole foundation plate may be in the condition of stretching. When comparing the results of analytical and numerical calculations of the values obtained in general there are little discrepancies. Thus, there is the possibility of holding combined calculation of the “structure-foundation-base system” by finite difference method using a two-layer model of a plate on elastic basis.

DOI: 10.22227/1997-0935.2014.12.31-39

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Dynamic load calculation of a bending plate of average thickness using general equations of finite differences method

Вестник МГСУ 10/2014
  • Gabbasov Radek Fatykhovich - Moscow State University of Civil Engineering (MGSU) Doctor of Technical Sciences, Professor, Department of Structural Mechanics, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; +7 (495) 287-49-14; Этот e-mail адрес защищен от спам-ботов, для его просмотра у Вас должен быть включен Javascript .
  • Hoang Tuan Anh - Moscow State University of Civil Engineering (MGSU) postgraduate student, Department of Structural Mechanics, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; +7 (495) 287-49-14; Этот e-mail адрес защищен от спам-ботов, для его просмотра у Вас должен быть включен Javascript .

Страницы 16-23

The theory of plates and shells is the most important application of the theory of elasticity. Rectangular slabs of average thickness are quite widely in construction, engineering and other fields of modern technology. Calculation of such structures cannot be conducted on the basis of the classical theory of bending of thin plates. In order to obtain a reliable picture of stress-strain state of a plate with average thickness, it is necessary to use different versions of improved theories. The aim of this work is the use generalized equations of the finite difference method (FDM) to calculate the dynamic loads of the plates average with thickness basing on the Reissner theory. On the basis of the developed algorithms computer programs have been worked out for calculating the dynamic load of bending plates of average thickness. The algorithm of calculating the dynamic load of bending plates of average thickness according to generalized equations of FDM can be recommended for practical use in frames of studying process.

DOI: 10.22227/1997-0935.2014.10.16-23

Библиографический список
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Axisymmetric bending of a round elastic plate in case of creep

Вестник МГСУ 5/2014
  • 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; Этот e-mail адрес защищен от спам-ботов, для его просмотра у Вас должен быть включен Javascript .
  • 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; Этот e-mail адрес защищен от спам-ботов, для его просмотра у Вас должен быть включен Javascript .
  • 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; Этот e-mail адрес защищен от спам-ботов, для его просмотра у Вас должен быть включен Javascript .

Страницы 16-24

In the article the problem of bending of circular axially loaded flexible plate during creep was solved. The solution is reduced to a system of two nonlinear differential equations. These equations are suitable for arbitrary dependencies between tensions and creep deformations. The system was solved by the method of successive approximations in conjunction with the finite difference method. Calculations were performed with the help of software package Matlab. We considered round rigidly clamped along the contour plate, which was loaded by the load uniformly distributed over the area. Polymer EDB-10 was taken as a material, which obeys the Maxwell-Gurevich physical law. Creep strains at each point of time were found using linear approximation. In order to verify the correctness of the program, we compared the elastic solution with the result of Professor A. Volmir. He solved this problem by the method of Bubnov-Galerkin only taking into account the geometric nonlinearity. Our results are in good agreement with the solution of. A. Volmir.It is revealed that the calculation excluding geometric nonlinearity gives high values of deflections. The analysis of the equations for t→∞ showed that in linear geometric theory stresses across the thickness of the plate at the end of the creep change linearly. Also the formula for long cylindrical rigidity was obtained. This formula allows us to find the deflection at the end of the creep process, if we know the elastic solution. It is shown that long cylindrical rigidity depends not only on the long elastic modulus v , but also on short elastic modulus v and Poisson's ratio v . It was also found out that in case of high loads stress distribution across the thickness is nonlinear.

DOI: 10.22227/1997-0935.2014.5.16-24

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