scholarly journals Phenomenological invariants and their application to geometrically nonlinear formulation of triangular finite elements of shear deformable shells

2009 ◽  
Vol 46 (5) ◽  
pp. 1019-1032 ◽  
Author(s):  
V.V. Kuznetsov ◽  
S.V. Levyakov
Keyword(s):  
Finite Elements ◽  
Geometrically Nonlinear ◽  
Nonlinear Formulation ◽  
Triangular Finite Elements ◽  
Shear Deformable

scholarly journals Calculation of plates in a geometrically nonlinear setting with the use of generalized equations of finite difference method

2018 ◽  
Vol 196 ◽  
pp. 01024 ◽  
Author(s):  
Natalia Uvarova ◽  
Radek Gabbasov
Keyword(s):  
Differential Equations ◽  
Numerical Method ◽  
Geometrically Nonlinear ◽  
Generalized Equations ◽  
Nonlinear Formulation ◽  
First Derivative ◽  
Equation Solving ◽  
Flexible Plates ◽  
Minimum Number ◽  
The Right

The article proposes a numerical method and an algorithm for analysis rectangular flexible plates in a geometrically nonlinear formulation. The generalized equations of the method of finite differences (MD) are used to solve the problem within the integrable region taking into account the discontinuities of the desired function, its first derivative and the right part of the original differential equation. Solving differential equations of the problem, composed with respect to the desired functions of deflection and stress are reduced to the 4th differential equations of the second order, which are solved numerically. As an example, a square plate loaded with a uniformly distributed load is considered. The results of the calculation with a minimum number of partitions are compared with the known analytical solution of A. S. Volmir [1] and indicate the possibility of using the numerical method for solving problems in a nonlinear formulation.

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