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Advances in Applied Mechanics, Vol. 12 by Chia-Shung Yih

By Chia-Shung Yih

This hugely acclaimed sequence offers survey articles at the current kingdom and destiny path of study in very important branches of utilized mechanics

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More detailed discussions of the interpolation functions over triangular elements can be found in the article by Felippa and Clough (1970). The linear interpolation over an area which is decomposed into triangular elements can also be depicted by Fig. 12. e. it is equal to unity at the node i and slopes linearly toward the opposite edges of the triangles around this node. The function +i(x, y) remains zero outside the area immediate to this node. The linear interpolation obviously cannot create a smooth surface.

Triangular elements using quadratic interpolation. Isoparametric transformations can also be used to construct the interpolation formulas of triangular elements with curved sides. More detailed discussions of the interpolation functions over triangular elements can be found in the article by Felippa and Clough (1970). The linear interpolation over an area which is decomposed into triangular elements can also be depicted by Fig. 12. e. it is equal to unity at the node i and slopes linearly toward the opposite edges of the triangles around this node.

Along each edge of the triangle. , is linear along each edge. The resulting strain energy by the hybrid stress model should be bounded by that of the other two models if the element sizes are the same. Figure 4 consists of plots of the ratios of the calculated central deflections and the exact value versus the number of elements per half span. In the present case the central deflection is a measure of the strain energy in the plate and the results are shown to follow our prediction that the hybrid model solutions are bounded by those of the other two models.

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