IJNAOE
A new finite element formulation for vibration analysis of thick plates

https://doi.org/10.1515/ijnaoe-2015-0023Get rights and content
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ABSTRACT

A new procedure for determining properties of thick plate finite elements, based on the modified Mindlin theory for moderately thick plate, is presented. Bending deflection is used as a potential function for the definition of total (bending and shear) deflection and angles of cross-section rotations. As a result of the introduced interdependence among displacements, the shear locking problem, present and solved in known finite element formulations, is avoided. Natural vibration analysis of rectangular plate, utilizing the proposed four-node quadrilateral finite element, shows higher accuracy than the sophisticated finite elements incorporated in some commercial software. In addition, the relation between thick and thin finite element properties is established, and compared with those in relevant literature.

Keywords

Mindlin plate theory
Finite element formulation
Thick-thin plate relation
Vibration analysis
Shear locking

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