Numerical modeling of bending of micropolar plates

Abstract

In this paper we present the Finite Element modeling of the bending of micropolar elastic plates. Based on our recently published enhanced mathematical model for Cosserat plate bending, we present the micropolar plate field equations as an elliptic system of nine differential equations in terms of the kinematic variables. The system includes an optimal value of the splitting parameter, which is the minimizer of the micropolar plate stress energy. We present the efficient algorithm for the estimation of the optimal value of this parameter and discuss the approximations of stress and couple stress components. The numerical algorithm also includes the method for finding the unique solution of the micropolar plate field equations corresponding to the optimal value of the splitting parameter.

We provide the results of the numerical modeling for the plates made of polyurethane foam used in

structural insulated panels. The comparison of the numerical values of the vertical deflection for the

square plate made of dense polyurethane foam with the analytical solution of the three-dimensional

micropolar elasticity confirms the high order of approximation of the three-dimensional (exact) solution.

The size effect of micropolar plate theory predicts that plates made of smaller thickness will be more

rigid than would be expected on the basis of the Reissner plate theory. We present the numerical results

for plates of different shapes, including shapes with rectangular holes, under different loads.

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