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The analyst can proceed to simulate the beam using a variety of elements:  one- dimensional beam elements, plane strain triangles, plane strain quadrilaterals, plane stress triangles, plane stress quadrilaterals, and three-dimensional brick elements (using what the analyst believes to be sufficiently relaxed end constraints, as per the previous example). The results for maximum transverse deflection are reported in Fig. 4.12. All results are reported in dimensionless form, normalized by a the characteristic deflection defined in the text in Example 4.2Problem Specification Section earlier.

According to these results, and still believing that Euler-Bernoulli beam theory is correct, the analyst would see that the maximum converged transverse deflection predicted by plane stress conditions  underestimates the deflection predicted by Euler-Bernoulli beam theory by nearly  50%; by comparison, the maximum converged transverse deflection predicted by plane strain conditions overestimate the prediction of Euler-Bernoulli theory by 40%. The analyst also realizes that the converged results from the three-dimensional brick elements appear to be in agreement with the con- verged plane stress results, but that a coarse mesh instance of the plane strain model seems to agree well with the expected Euler-Bernoulli beam theory. How does the analyst sort out these mixed messages?

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