Finite Element Multidisciplinary Analysis, Second Edition

4.9: Numerical Examples

4.9 Numerical Examples

Two example problems are presented herein that verify the solution convergence characteristics.

Example 4.2: Simply Supported Plate

A simply supported plate with unit uniformly distributed loading is shown in Fig. 4.23 ( E = 10 7, ? = 0.3, thickness t = 0.1). Table 4.2 depicts the pattern of solution convergence as a function of mesh size.


Figure 4.23: Simply supported plate.

Table 4.2: Solution convergence of the plate problem

Mesh size

Center deflection

4 4

0.04287

8 8

0.04447

16 16

0.04469

32 32

0.04467

Exact value

0.04540

Example 4.3: Cylindrical Shell

Figure 4.24 depicts a cantilever cylindrical shell under unit uniform loading ( E = 29.5 10 6, ? = 0.3, t = 0.1, A = B = 10, R = 2.0). Table 4.3 presents the solution results.


Figure 4.24: Cantilever cylindrical shell.

Table 4.3: Solution convergence for the cantilever cylindrical shell

Mesh size

Maximum tip deflection

8 8

0.24157 10 ?1

16 16

0.24283 10 ?1

32 32

0.24319 10 ?1

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