engleski

Shear locking-free finite flement formulation for thick plate vibration analysis

The basic equations of the Mindlin thick plate theory are specified as starting point for the development of a new thick plate theory in which total deflection and rotations are split into pure bending deflection and shear deflection with bending angles of rotation, and in-plane shear angles. The equilibrium equations of the former displacement field are condensed into one partial differential equation for flexural vibrations. In the latter case two differential equations for in-plane shear vibrations are obtained and they are similar to the well-known membrane equations. Physical background of the derived equations is analysed in case of a simply supported square plate. Rectangular shear locking-free finite element for flexural vibrations is developed. For in-plane shear vibrations ordinary membrane finite elements can be used. Natural modes of plate layers in in-plane shear vibrations are the same as membrane modes, while natural frequencies have to be transformed. Application of the presented theory is illustrated in a case of simply supported and clamped square plate. Problems are solved analytically and by FEM. The obtained results, compared with the relevant ones available in literature, are discussed.

finite element method ; flexural vibrations ; Mindlin theory ; shear locking ; shear vibrations ; thick plate

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