scholarly journals Stress state of hinged supported thin-wall elastic structures

2021 ◽  
Vol 274 ◽  
pp. 03018
Author(s):  
Lilya Kharasova ◽  
Samat Timergaliev
Keyword(s):  
Boundary Conditions ◽  
Strain State ◽  
Holomorphic Functions ◽  
Integral Representations ◽  
Shell Structures ◽  
Normal Displacement ◽  
Nonlinear Operator Equation ◽  
Stress Strain ◽  
Stress Strain State ◽  
Generalized Displacements

The paper studies the stress-strain state of flat elastic isotropic thin-walled shell structures in the framework of the S. P. Timoshenko shear model with pivotally supported edges. The stress-strain state of shell structures is described by a system of five second-order nonlinear partial differential equations under given static boundary conditions with respect to generalized displacements. The system of equations under study is linear in terms of tangential displacements, rotation angles, and nonlinear in terms of normal displacement. To find a solution to the system that satisfies the given static boundary conditions, integral representations for generalized displacements containing arbitrary holomorphic functions are used. Finding holomorphic functions is one of the main and difficult points in the proposed study. The integral representations constructed in this way allow us to reduce the original problem to a single nonlinear operator equation with respect to the deflection, the solvability of which is established using the principle of compressed maps.

scholarly journals Strength of thin-walled elastic building structures

2021 ◽  
Vol 274 ◽  
pp. 03019
Author(s):  
Lilya Kharasova
Keyword(s):  
Boundary Conditions ◽  
Strain State ◽  
Holomorphic Functions ◽  
Integral Representations ◽  
Nonlinear Operator Equation ◽  
Equilibrium Equations ◽  
Stress Strain ◽  
Stress Strain State ◽  
Generalized Displacements ◽  
Thin Walled

The existence theorem is proved within the framework of the shear model by S.P. Timoshenko. The stress-strain state of elastic inhomogeneous isotropic shallow thin-walled shell constructions is studied. The stress-strain state of shell constructions is described by a system of the five equilibrium equations and by the five static boundary conditions with respect to generalized displacements. The aim of the work is to find generalized displacements from a system of equilibrium equations that satisfy given static boundary conditions. The research is based on integral representations for generalized displacements containing arbitrary holomorphic functions. Holomorphic functions are found so that the generalized displacements should satisfy five static boundary conditions. The integral representations constructed this way allow to obtain a nonlinear operator equation. The solvability of the nonlinear equation is established with the use of contraction mappings principle.

scholarly journals Influence of Boundary Conditions on the Stress-Strain State of a Corrugated Sheet Under Its Weight

2019 ◽  
Vol 661 ◽  
pp. 012029
Author(s):  
Alexey Beskopylny ◽  
Elena Kadomtseva ◽  
Grigory Strelnikov ◽  
Yaroslav Shabanov
Keyword(s):  
Boundary Conditions ◽  
Strain State ◽  
Stress Strain ◽  
Stress Strain State

Analytical model of the stress–strain state of multilayer composite plates under the influence of different load types with asymmetrical boundary conditions

2016 ◽  
Vol 54 (12) ◽  
pp. 1535-1548
Author(s):  
Olga Bitkina ◽  
Jang-Ho Lee ◽  
Ki-Weon Kang ◽  
Elena Darlington
Keyword(s):  
Boundary Conditions ◽  
Analytical Model ◽  
Strain State ◽  
Linear Partial Differential Equation ◽  
Composite Plates ◽  
Generalized Function ◽  
Entire Body ◽  
Multilayer Composite ◽  
Stress Strain ◽  
Stress Strain State

Composite structure design experience has demonstrated that use of the finite element method during the first stage of the design process is unfounded and that analytical methods to determine the stress–strain state are needed for more accurate calculations. Therefore, an analytical model of the stress–strain state of multilayer composite plates under the influence of temperature, technological, and power loads with different boundary conditions around four boundaries of a rectangular plate was developed. This model enables the solution of more than 240 different boundary value problems with a combination of the following boundary conditions: fixed, moving, hinged, and free edge. In the derivation of this mathematical analytic model, the Kirchhoff hypothesis was applied to the entire body of the anisotropic medium for the interconnected deflection and bending in the plate plane. The resulting equation is an octic linear partial differential equation to express the generalized function of movements.

scholarly journals Stress-strain state simulation of large-sized cable-stayed shell structures

2015 ◽  
Vol 71 ◽  
pp. 012070 ◽  
Author(s):  
S Ponomarev ◽  
A Zhukov ◽  
A Belkov ◽  
V Ponomarev ◽  
S Belov ◽  
...  
Keyword(s):  
Strain State ◽  
Shell Structures ◽  
Stress Strain ◽  
Stress Strain State

scholarly journals Visualization of the Stress-Strain State of Shell Structures Using Virtual and Augmented Reality Technologies

2020 ◽  
pp. paper13-1-paper13-12
Author(s):  
Alexey Semenov ◽  
Iurii Zgoda
Keyword(s):  
Mathematical Model ◽  
Thin Shell ◽  
Strain State ◽  
Interactive Visualization ◽  
Analysis Data ◽  
Shell Structures ◽  
Stress Strain ◽  
Heat Maps ◽  
Visualization Module ◽  
Stress Strain State

The paper describes a mathematical model of changes in the geometry of thin-shell structures for visualization of the analysis data on their stress-strain state (SSS). Based on this mathematical model, a visualization module for shell SSS visualization using VR and AR technologies was developed. The interactive visualization environment Unity 2019.3 and C# programming language were used. The interactive visualization module makes a 3D image of a shell structure and visualizes the SSS either through heat maps over the shell or through the changes in the shell geometry on the basis of the shell type, its geometric characteristics, and SSS analysis data (transferred to the visualization module by means of a JSON file). While working on the visualization module, the authors developed a system of components that makes it possible to visualize any 3D surface with coordinate axes (including numbers with a pitch determined automatically), visualize heat maps with a graduated scale, visualize a mesh over the graph to improve the perception of the surface deformations. The middle surface can also be deformed on the basis of SSS analysis data. This solution increases the efficiency of the work of specialists in civil engineering and architecture and can be used when training specialists in courses on thin-shell structures and procedural geometry.

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