# The Morley plate element in the frame of a generalized, frequency-dependent hybrid finite element formulation

## Palavras-chave:

Morley plate element, Hybrid finite element, Generalized modal analysis## Resumo

The Morley plate element is the simplest triangular finite element for homogeneous, isotropic material,

and represents constant bending curvature/moment exactly, as the flexural counterpart of the membrane, constant

strain/stress finite element. It has six degrees of freedom: three corner-node transversal displacements and three

edge rotations. We propose a slightly modified, improved Morley element based on a frequency-dependent hybrid

finite element formulation to be used in the frame of a generalized modal analysis for stiffness and mass matrices

given as frequency power series. The domain stress solution satisfies the homogeneous elastodynamic equilibrium

equations for moderately thick plates, as we resort to the concept of mean transversal shear distortion proposed

in a previous conference contribution (PANACM/CILAMCE 2021). We show that the formulation for just one

mass matrix corresponds to a plain displacement formulation, as proposed in the literature for the thin-plate, static

problem (although introducing some due corrections). Some numerical tests with one and two mass matrices show

that the model can be seamlessly applied to both moderately-thick and thin plate problems – thus without the

shear-locking inconvenience – and in spite of its shape-function simplicity ensures good, asymptotic convergence

for natural frequencies. As we have a similar generalized modal development for the membrane triangle, this leads

to the simplest – and consistently – conceivable shell element.