scholarly journals FINITE ELEMENTS FOR THE ANALYSIS OF REISSNE-RMINDLIN PLATES WITH JOINT INTERPOLATION OF DISPLACEMENTS AND ROTATIONS (JIDR)

2021 ◽  
Vol 17 (3) ◽  
pp. 48-62
Author(s):  
Viktor Karpilovsky
Keyword(s):  
Finite Elements ◽  
Numerical Experiments ◽  
Simultaneous Approximation ◽  
Approximation Of Functions ◽  
Design Models ◽  
Locking Effect

This paper proposes a method for creating finite elements with simultaneous approximation of functions corresponding to displacements and rotations. New triangular and quadrangular finite elements have been created, which can have additional nodes on the sides. No locking effect is observed for all the created elements. All created elements retain the existing symmetry of the design models. The results of numerical experiments are presented.

The Finite Elements for Design of Frame of Thin-Walled Beams

2014 ◽  
Vol 578-579 ◽  
pp. 858-863 ◽  
Author(s):  
Vladimir Lalin ◽  
Vladimir Rybakov ◽  
Alexander Sergey
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Linear Approximation ◽  
Torsional Angle ◽  
Warping Function ◽  
Approximation Of Functions ◽  
Development Cycle ◽  
Independent Functions ◽  
Thin Walled ◽  
Mutually Independent

Recent years there have been observed a wide application of a metalware in industrial and civil engineering. Special place in the building industry is belonged to light steel thin-walled constructions having a lot of technological advantages. In the article the first development cycle of a numerical method creating is considered – creating of the stiffness matrixes of thin-walled finite elements of various types using the semisheared theory (by V.I.Slivker) – depending on a way of approximation of functions of deformations (torsion and warping): 1. Linear approximation of torsional functions with a 2-central finite element having 4 transitions; 2. Quadratic approximation of torsional functions and linear approximation of warping function with a 3-central finite element having 5 transitions; 3. Cubical approximation of functions of torsional and warping functions with a 3-central finite element having 6 transitions. Thus deformation functions (torsional angle and warping) are approximated as mutually independent functions.

scholarly journals Error estimates for the unilateral buckling load of a plate involving the membrane efforts consistency error

2008 ◽  
pp. 1003-1038
Author(s):  
Mekki Ayadi
Keyword(s):  
Finite Elements ◽  
Error Estimate ◽  
Critical Load ◽  
Error Estimates ◽  
Thin Plate ◽  
Numerical Experiments ◽  
Mesh Size ◽  
Buckling Load ◽  
Plate Model ◽  
Consistency Error

The paper deals with error estimates for the unilateral buckling critical load of a thin plate in presence of an obstacle. The error on the membrane efforts tensor is taken into account. First, using the Mindlin’s plate model together with a finite elements scheme of degree one, an error estimate, depending on the mesh size h, is established. In order to validate this theoretical error estimate, some numerical experiments are presented. Second, using the Kirchhoff-Love’s plate model, an abstract error estimate is achieved. Its drawback is that it contains a hard term to evaluate.

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