Dynamic finite element formulations for moderately thick plate vibrations based on the modified Mindlin theory

2017 ◽  
Vol 136 ◽  
pp. 100-113 ◽  
Author(s):  
Ivo Senjanović ◽  
Marko Tomić ◽  
Neven Hadžić ◽  
Nikola Vladimir
Keyword(s):  
Finite Element ◽  
Thick Plate ◽  
Plate Vibrations ◽  
Dynamic Finite Element ◽  
Moderately Thick Plate ◽  
Finite Element Formulations

An advanced theory of moderately thick plate vibrations

2013 ◽  
Vol 332 (7) ◽  
pp. 1868-1880 ◽  
Author(s):  
Ivo Senjanović ◽  
Nikola Vladimir ◽  
Marko Tomić
Keyword(s):  
Thick Plate ◽  
Plate Vibrations ◽  
Moderately Thick Plate

scholarly journals A higher order triangular plate finite element using Airy functions

2020 ◽  
Vol 12 (11) ◽  
pp. 168781402097190
Author(s):  
Mohammed Himeur ◽  
Hamza Guenfoud ◽  
Mohamed Guenfoud
Keyword(s):  
Finite Element ◽  
Transverse Shear ◽  
Thick Plate ◽  
Plate Theory ◽  
Thin Plates ◽  
Airy Functions ◽  
Triangular Finite Element ◽  
Patch Tests ◽  
Moderately Thick Plate ◽  
Transverse Shear Locking

The present paper describes the formulation of a new moderately thick plate bending triangular finite element based on Mindlin–Reissner plate theory. It is called a Great Triangular Moderately Thick Plate Finite Element, or GTMTPFE. The formulation is based on the strain approach, on solution of Airy’s function and on the analytical integration in the construction of the stiffness matrix. The strengths associated with this approach consist of: • automatic verification of equilibrium conditions and kinematic compatibility conditions, • the enrichment of the degrees of the interpolation polynomials of displacements, strains and constraints (refinement p), • the consideration distortions sections related to Poisson effects, • the treatment of blocking phenomena related to transverse shear. In general, this approach results in a competitive, robust and efficient new moderately thick plate finite element. This is visible, on the one hand, through its stability against patch tests (constant twists, state of constants moments, transverse shear locking phenomenon, isotropy test). This is visible, through its good response to the patch tests to which it is subjected (constant torsions, state of constant moments, phenomenon of blocking in transverse shears, isotropy test). As has excellent convergence to the reference solution. Thus, it exhibits better performance behavior than other existing plate elements in the literature, particularly for moderately thick plates and for thin plates (L/h ratio greater than 4).

Conforming shear-locking-free four-node rectangular finite element of moderately thick plate

2016 ◽  
Vol 25 (5-6) ◽  
pp. 141-152
Author(s):  
Ivo Senjanović ◽  
Marko Tomić ◽  
Smiljko Rudan ◽  
Neven Hadžić
Keyword(s):  
Finite Element ◽  
Thick Plate ◽  
Plate Theory ◽  
Shear Stiffness ◽  
Mindlin Plate ◽  
Shear Locking ◽  
Shape Functions ◽  
Beam Shape ◽  
Stiffness Matrices ◽  
Moderately Thick Plate

AbstractAn outline of the modified Mindlin plate theory, which deals with bending deflection as a single variable, is presented. Shear deflection and cross-section rotation angles are functions of bending deflection. A new four-node rectangular finite element of moderately thick plate is formulated by utilizing the modified Mindlin theory. Shape functions of total (bending+shear) deflections are defined as a product of the Timshenko beam shape functions in the plate longitudinal and transversal direction. The bending and shear stiffness matrices, and translational and rotary mass matrices are specified. In this way conforming and shear-locking-free finite element is obtained. Numerical examples of plate vibration analysis, performed for various combinations of boundary conditions, show high level of accuracy and monotonic convergence of natural frequencies to analytical values. The new finite element is superior to some sophisticated finite elements incorporated in commercial software.

Affordable structural optimization for large-size dynamic finite element models

1997 ◽  
Author(s):  
Francois Hemez ◽  
Emmanuel Pagnacco ◽  
Francois Hemez ◽  
Emmanuel Pagnacco
Keyword(s):  
Finite Element ◽  
Structural Optimization ◽  
Finite Element Models ◽  
Dynamic Finite Element ◽  
Large Size
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