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 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

Analysis of Stress–Strain State in a Steel Pipe Strengthened With a Composite Wrap

2014 ◽  
Vol 136 (5) ◽  
Author(s):  
Oleg V. Trifonov ◽  
Vladimir P. Cherniy
Keyword(s):  
Internal Pressure ◽  
Analytical Model ◽  
Strain State ◽  
Steel Pipe ◽  
Stress Strain ◽  
Stress Strain State ◽  
Element Simulation ◽  
Load Carrying ◽  
Scale Test ◽  
Buried Gas Pipeline

In this paper, strengthening of a steel pipe with a composite wrap is analyzed. An analytical model taking into account joint reaction of the pipe and the wrap, two-dimensional stress state and plastic strains in the pipe wall is developed. Verification of the model is performed by comparison of the numerical results to the full-scale test results for a strengthened pipe under the action of internal pressure. The developed model is applied to the analysis of a buried gas pipeline subjected to the internal pressure and temperature loading. The results obtained with the analytical model are compared to the results of a finite-element simulation. A good agreement is established. The effect of wrap thickness on the stress–strain state and load-carrying capacity of the strengthened pipe is studied.

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.

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