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DESIGNING AND DETAILING OF BUILDING SYSTEMS. MECHANICS IN CIVIL ENGINEERING

Calculation of the three-layer shallow shell taking into account the creep of the middle layer

Vestnik MGSU 7/2015
  • 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 .
  • 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 .
  • 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 .
  • Litvinov Stepan Viktorovch - Rostov State University of Civil Engineering (RSUCE) , Rostov State University of Civil Engineering (RSUCE), 162 Sotsialisticheskaya str., Rostov-on-Don, 344022, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 17-24

The equations of the finite element method for calculation of sandwich shells taking into account creep were obtained. The shell is represented as a set of flat triangular elements. The thickness of the carrier layers is supposed to be small compared to the total thickness of the shell. It is assumed that the outer layers perceive normal stresses, and the average layer perceives the shear forces. In the derivation of governing equations we used variational Lagrange principle. According to this principle, the true moves of all the possible ones satisfying the boundary conditions, are the ones that give a minimum of the total energy. Total energy is the sum of the strain energy and the work of external forces. The problem is reduced to a system of linear algebraic equations. On the right side of this system there is the vector of the sum of the external nodal forces and the contribution of creep strains to the load vector. The calculations were performed in mathematical package Matlab. As the law for description of the relationship between stress and creep strain, we used linear creep theory of heredity. If the core of creep is exponential, the creep law can be written in differential form. This allows the calculation by step method using a linear approximation of the time derivative. The model problem has been solved for a spherical shell hinged along the contour. The relationship between the curvature of shell and the growth of deflections was analyzed. It was found out that for the shells of large curvature the creep has no appreciable effect on the deflections.

DOI: 10.22227/1997-0935.2015.7.17-24

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