A Mindlin–Reissner Variational Principle to Analyze the Behavior of Moderately Thick Plates

1989 ◽  
Vol 42 (11S) ◽  
pp. S32-S38
Author(s):  
Roberto S. Carnicer ◽  
Stefano Alliney
Keyword(s):  
Finite Element ◽  
Variational Principle ◽  
Plate Theory ◽  
Mindlin Plate ◽  
General Boundary Conditions ◽  
Thick Plates ◽  
Numerical Examples ◽  
Simple Support ◽  
Mindlin Plate Theory ◽  
Moderately Thick Plates

In the present work a method to solve the plate behavior under the assumption of the Mindlin plate theory is analyzed by means of finite element techniques, avoiding the tendency of the thin element to lock when the thickness of the plates becomes very small. A different formulation is developed from the Mindlin–Reissner principle for general boundary conditions. Numerical examples to evaluate the noninfluence of locking on clamped and simple support plates are calculated.

Sharp Corner Functions for Mindlin Plates

2005 ◽  
Vol 72 (1) ◽  
pp. 1-9 ◽  
Author(s):  
O. G. McGee ◽  
J. W. Kim ◽  
A. W. Leissa
Keyword(s):  
Plate Theory ◽  
Thin Plates ◽  
Mode Shapes ◽  
Mindlin Plate ◽  
Transverse Displacement ◽  
Thick Plates ◽  
Thin Plate Theory ◽  
Mindlin Plate Theory ◽  
Moderately Thick Plates ◽  
Sharp Corners

Transverse displacement and rotation eigenfunctions for the bending of moderately thick plates are derived for the Mindlin plate theory so as to satisfy exactly the differential equations of equilibrium and the boundary conditions along two intersecting straight edges. These eigenfunctions are in some ways similar to those derived by Max Williams for thin plates a half century ago. The eigenfunctions are called “corner functions,” for they represent the state of stress currently in sharp corners, demonstrating the singularities that arise there for larger angles. The corner functions, together with others, may be used with energy approaches to obtain accurate results for global behavior of moderately thick plates, such as static deflections, free vibration frequencies, buckling loads, and mode shapes. Comparisons of Mindlin corner functions with those of thin-plate theory are made in this work, and remarkable differences are found.

scholarly journals Finite Element Modelling of a Composite Shell with Shear Connectors

Symmetry ◽  
2019 ◽  
Vol 11 (4) ◽  
pp. 527 ◽  
Author(s):  
Nguyen ◽  
Canh ◽  
Thanh ◽  
Ke ◽  
Phan ◽  
...  
Keyword(s):  
Finite Element ◽  
Composite Shell ◽  
Plate Theory ◽  
Dynamic Responses ◽  
Mindlin Plate ◽  
Physical Parameters ◽  
Working Process ◽  
Shear Connectors ◽  
Layer Composite ◽  
Mindlin Plate Theory

A three-layer composite shell with shear connectors is made of three shell layers with one another connected by stubs at the contact surfaces. These layers can have similar or different geometrical and physical properties with the assumption that they always contact and have relative movement in the working process. Due to these characteristics, they are used widely in many engineering applications, such as ship manufacturing and production, aerospace technologies, transportation, and so on. However, there are not many studies on these types of structures. This paper is based on the first-order shear deformation Mindlin plate theory and finite element method (FEM) to establish the oscillator equations of the shell structure under dynamic load. The authors construct the calculation program in the MATLAB environment and verify the accuracy of the established program. Based on this approach, we study the effects of some of the geometrical and physical parameters on the dynamic responses of the shell.

A Two Dimensional Finite Element Model for Prestress Effects on Magnetoelectric Laminated Composites

2020 ◽  
Author(s):  
Sudersan Sridhar ◽  
Arockiarajan Arunachalakasi
Keyword(s):  
Finite Element ◽  
Plate Theory ◽  
Element Model ◽  
Mindlin Plate ◽  
Shear Stresses ◽  
Compressive Stresses ◽  
Dimensional Finite Element ◽  
Finite Element Procedure ◽  
Magnetic Loading ◽  
Mindlin Plate Theory

Abstract Magnetoelectric (ME) composites are viable candidates for use in numerous applications owing to their multifunctional capabilities. These composites develop voltages across the piezo-electric phase under external magnetic fields. Numerous models available in literature consider the magnetostriction under pure magnetic loading. However, fabrication of ME composites results in development of compressive stresses on the magnetostrictive layer, which leads to a poor ME response and hence an initial effective tensile prestress to the magnetostrictive phase is required to either compensate or enhance the ME coupling. In this work, the ME response of an unsymmetric laminate is predicted using a finite element procedure based on Mindlin plate theory, giving due consideration the magnetostrictive nonlinearity, the direction of the applied field and the effect of the stress state on the magnetostrictive response. The model predicts that initial shear stresses, positive or negative, provide the best enhancement to the ME coupling.

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