Axisymmetric bending of a heated circular plate on an elastic base with account of its deformability over its thickness

1985 ◽  
Vol 48 (6) ◽  
pp. 735-739
Author(s):  
M. D. Martynenko ◽  
E. A. Svirskii
Keyword(s):  
Circular Plate ◽  
Elastic Base ◽  
Axisymmetric Bending

scholarly journals NUMERICAL ANALYSIS OF CIRCULAR PLATES ON AN ELASTIC BASE WITH VARIABLE BED COEFFICIENT

2020 ◽  
pp. 66-75
Author(s):  
Yu.S. Krutii ◽  
◽  
M.G. Surianinov ◽  
M.M. Soroka ◽  
G.S. Karnauhova ◽  
...  
Keyword(s):  
Finite Element ◽  
Differential Equations ◽  
Circular Plate ◽  
Elastic Foundation ◽  
Elastic Base ◽  
Variable Coefficients ◽  
Transverse Load ◽  
Decimal Point ◽  
Round Plate ◽  
Significant Digit

Abstract. The paper presents the results of a study of the stress-strain state of a circular plate of constant cylindrical stiffness, which lies on a variable elastic foundation and is under the influence of a continuously distributed transverse load. Twelve variants of calculation are considered ‒ six for a steel round plate and six more ‒ for a concrete round plate under two conditions of fixing and three different laws of variation of the bed coefficient. To solve the problem, the finite element method implemented in the LIRA-SAPR software package is used. It is noted that in the case when the bedding coefficient is a variable value depending on the coordinate in which the foundation settlement is determined, the analytical approach leads to the need to solve the corresponding differential equations with variable coefficients. Therefore, calculations of circular and annular plates lying on a variable elastic foundation by means of analytical solutions of differential equations are extremely rare in scientific periodicals and are of a private nature. An effective method for the analytical solution of differential equations with variable coefficients for a number of problems in mechanics was proposed by one of the authors of the article, however, the application of the method to the calculation of a circular plate on an elastic foundation with a variable bed coefficient requires verification, therefore, here we consider the features of the finite element analysis of such a plate under different boundary conditions and different laws of variation of the bed coefficient. In all versions, the results completely coincide with the known results of bending of slabs that do not have an elastic base and in the case when this base exists and its resistance is constant. The discrepancy here is very insignificant ‒ in the third significant digit after the decimal point for deflection when hinged and in the second for moments. In case of rigid clamping, the deflections and moments also differ from the corresponding values of the known solutions in the second significant digit after the decimal point.

scholarly journals Axisymmetric bending analysis of functionally graded one-dimensional hexagonal piezoelectric quasi-crystal circular plate

2020 ◽  
Vol 476 (2241) ◽  
pp. 20200301
Author(s):  
Yang Li ◽  
Yuan Li ◽  
Qinghua Qin ◽  
Lianzhi Yang ◽  
Liangliang Zhang ◽  
...  
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
State Space ◽  
Circular Plate ◽  
Hankel Transform ◽  
Functionally Graded ◽  
The State ◽  
One Dimensional ◽  
Present Solution ◽  
Axisymmetric Bending

Within a framework of the state space method, an axisymmetric solution for functionally graded one-dimensional hexagonal piezoelectric quasi-crystal circular plate is presented in this paper. Applying the finite Hankel transform onto the state space vector, an ordinary differential equation with constant coefficients is obtained for the circular plate provided that the free boundary terms are zero and an exponential function distribution of material properties is assumed. The ordinary differential equation is then used to obtain the stress, displacement and electric components in the physical domain of the elastic simply supported circular plate through the use of the propagator matrix method and the inverse Hankel transform. The numerical studies are carried out to show the validity of the present solution and reveal the influence of material inhomogeneity on the axisymmetric bending of the circular plate with different layers and loadings, which provides guidance for the design and manufacture of functionally graded one-dimensional hexagonal piezoelectric quasi-crystal circular plate.

Nonlinear axisymmetric bending analysis of strain gradient thin circular plate

2021 ◽  
Vol 89 ◽  
pp. 363-380
Author(s):  
Anqing Li ◽  
Xue Ji ◽  
Shasha Zhou ◽  
Li Wang ◽  
Jun Chen ◽  
...  
Keyword(s):  
Circular Plate ◽  
Strain Gradient ◽  
Bending Analysis ◽  
Thin Circular Plate ◽  
Axisymmetric Bending

Axisymmetric bending of a circular plate with stiff edge on a soft FGM layer

2016 ◽  
Vol 59 (2) ◽  
pp. 227-241 ◽  
Author(s):  
Sergey S. Volkov ◽  
Alexander N. Litvinenko ◽  
Sergey M. Aizikovich ◽  
Yun-Che Wang ◽  
Andrey S. Vasiliev
Keyword(s):  
Circular Plate ◽  
Axisymmetric Bending ◽  
Fgm Layer

scholarly journals Stable and unstable bifurcation in the von Kármán problem for a circular plate

2005 ◽  
Vol 2005 (8) ◽  
pp. 889-899 ◽  
Author(s):  
Andrei Borisovich ◽  
Joanna Janczewska
Keyword(s):  
Circular Plate ◽  
Elastic Plate ◽  
Analytical Methods ◽  
Compressive Force ◽  
Elastic Base ◽  
Solution Set ◽  
Simply Supported ◽  
Bifurcation Points ◽  
Von Karman ◽  
Von Kármán

In this work, we study bifurcation in the von Kármán equations for a thin circular elastic plate which lies on the elastic base and is simply supported and subjected to a compressive force along the boundary. Applying analytical methods, we prove the existence of stable and unstable simple bifurcation points in the solution set of these equations.

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