PLATE DEFORMATION

In this section we consider the deformation of a cantilever plate due to uniaxial loading and pure bending. The deformation of the cantilever plate is simple enough so that the MOSES results can be easily compared to the analytical solutions.

We considered three plate models. In all three models the main dimensions of the cantilever plate remained the same. However, the refinement of the sections being considered was changed. This example not only illustrates how the plate element is used, but it also demonstrates how accuracy is increased with additional refinement of the finite element mesh.

The three plate models that were considered are:

1. a plate modeled using a single element,
2. a plate refined along the $y$-axis, and
3. a plate refined along both the $y$-axis and the $x$-axis.

For all three cases, there was an axial force in the negative $x$-direction, a shear load in the negative $z$-direction and a shear load in the negative $y$-direction. These three cases are shown below in Figure 5. The dimensions of the plate are such that it has a length $l=$ 10 ft, a width $w=$ 4 ft, and a thickness $t=$ 1 in.

The equations that govern the deformation of the plate are:

$$ \begin{aligned} \delta_x &= \frac{f\,l}{EA} \\ \delta_y &= \frac{P\,l^3}{3EI_{yy}} \\ \delta_z &= \frac{P\,l^3}{3EI_{zz}} \end{aligned} \tag*{(9)} $$

where

$$ \begin{aligned} A &= wt \\ I_{yy} &= \frac{tw^3}{12} \\ I_{zz} &= \frac{wt^3}{12} \end{aligned} \tag*{(10)} $$

The comparison of MOSES values to the hand-calculated values is shown in the table below. A key observation is the significant improvement in the predicted value of $\delta_y$ as the mesh is refined. This highlights that a single low-order plate element is insufficient to capture global bending behavior due to membrane stresses.

Plate Deformation with Different MOSES Models

Figure 5: Plate Refinement Models