scholarly journals Investigation of the thermally stressed state of shallow shells on a rigid base with a sliding contact layers using analytic solutions of equations оf elasticity theory

Author(s):  
Alexander Marchuk ◽  
◽  
Sergii Levkivskiy ◽  
Elena Gavrilenko ◽  
◽  
...  

Modern calculations of layered plates and shells in a three-dimensional formulation are based on a technique where the distribution of the desired functions over the thickness of a structure is sought by the method of discrete orthogonalization. In this article, based on the approaches developed by the authors, the thermally stressed state of layered composite shallow shells with a rigidly fixed lower surface is analyzed. The distribution of the desired functions over the thickness of the structure is found based on the exact analytical solution of the system of differential equations. An approach to the study of the thermal stress state of shallow composite shells is considered, and an analytical model is constructed for calculating the thermal stress state of shallow shells on a rigid base with a sliding contact of the layers. Currently, this is a very urgent task when calculating the pavement of bridges. A feature of this approach is the assignment of the desired functions to the outer surfaces of the layers, which allows one to break the layer into sublayers, reducing the approximation error to almost zero. Using the model in question, an analysis of flat layered composite shells on a rigid base with a sliding contact of the layers under the influence of temperature loading was carried out. To build a spatial model, a load option is selected with temperature loads (according to the sine law) and boundary conditions (Navier), which lead to the distribution of the desired functions in terms of a plate with trigonometric harmonics of the Fourier series. A polynomial approximation of the desired functions by thickness is involved. Using the model in question, an analysis of flat layered composite shells on a rigid base with a sliding contact of the layers under the influence of temperature loading was carried out. The considered example showed that the proposed model provides sufficient accuracy in the calculations of layered shallow shells when considering each layer within one sublayer. The proposed approach can be used as a reference method for testing applied approaches in calculating various stress states of layered flat composite shells.

Author(s):  
Alexander Marchuk ◽  
◽  
Sergii Levkivskiy ◽  
Elena Gavrilenko ◽  
◽  
...  

Modern calculations of layered plates and shells in a three-dimensional formulation are based on a technique where the distribution of the desired functions over the thickness of a structure is sought by the method of discrete orthogonalization. In this article, based on the approaches developed by the authors, the thermally stressed state of layered composite shallow shells with a rigidly fixed lower surface is analyzed. The distribution of the desired functions over the thickness of the structure is found based on the exact analytical solution of the system of differential equations. An approach to studying the thermally stressed state of layered composite shells is also considered, and a spatial model for calculating the thermally stressed state of shallow shells on a rigid basis is constructed. Currently, this is a very urgent task when calculating the pavement of bridges. A feature of this approach is the assignment of the desired functions to the outer surfaces of the layers, which allows one to break the layer into sublayers, reducing the approximation error to almost zero. To build a spatial model, a load option is selected with temperature loads (according to the sine law) and boundary conditions (Navier), which lead to the distribution of the desired functions in terms of a plate with trigonometric harmonics of the Fourier series. A polynomial approximation of the desired functions by thickness is involved. Using the model under consideration, an analysis of flat layered composite shells on a rigid basis under the influence of temperature load was carried out. The considered example showed that the proposed model provides sufficient accuracy in the calculations of layered shallow shells when considering each layer within one sublayer. When dividing each layer into 32, 64, 128 sublayers, almost the same result was obtained. The proposed approach can be used as a reference method for testing applied approaches in calculating the stress states of layered shallow composite shells.


1986 ◽  
Vol 18 (1) ◽  
pp. 87-92
Author(s):  
A. S. Tsybenko ◽  
B. A. Kuranov ◽  
A. D. Chepurnoi ◽  
V. A. Shaposhnikov ◽  
N. G. Krishchuk

Vestnik MGSU ◽  
2020 ◽  
pp. 380-398
Author(s):  
Nikolay A. Aniskin ◽  
Nguyen Trong Chuc

Introduction. The concreting of solid structures, such as concrete dams, bridge constructions, foundations of buildings and structures, is accompanied by exothermic heating, caused by cement hydration. Heat, emitted by mass concrete blocks, slowly leaves constructions. A substantial temperature difference frequently arises between the solid concrete centre and its surface. If this temperature difference reaches a critical value, thermal cracking occurs, which destroys structural continuity. Temperature problems and those associated with thermal stress state should be resolved to pre-assess and prevent potential cracking. This problem has enjoyed the attention of specialists, and it has been the subject of numerous research projects. Materials and methods. The overview is based on the information about implemented research projects focused on the thermal cracking of mass concrete dams and its prevention. Computer modeling techniques were applied to develop a mathematical model capable of projecting and assessing the potential cracking of mass concrete. Results. The co-authors have compiled an overview of advanced approaches to the assessment of potential thermal crack formation, contemporary problem-solving methods and selected research findings obtained using the finite element method. The co-authors offer a thermal behaviour/thermal stress state projection methodology for solid concrete, as well as a thermal crack formation assessment methodology. Conclusions. The thermal cracking problem has not been solved yet. The proposed methodology and a projection-oriented numerical model can be used as a reference by civil engineers in the process of designing and constructing concrete gravity dams. It may help to reduce cracking probability caused by heat evolution in cement.


1986 ◽  
Vol 18 (5) ◽  
pp. 692-698
Author(s):  
Ya. S. Podstrigach ◽  
Yu. A. Chernukha ◽  
N. I. Voitovich

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