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Non-conforming finite element solution of the plate bending problem with application to visual surface reconstruction

Abstract:

The finite element solution of the classic plate bending problem is studied using the noncon- forming elements of Adini [1] and Specht [18]. A brief discussion of the theoretical implications of nonconformity is presented in each case. Detailed computation of the corresponding basis functions and stiffness matrix is included in the appendices. Of the three types of boundary conditions, computations are performed on the clamped and free plate problems. Specifically, a known analytical solution to the clamped plate is used to verify predicted convergence rates for both elements. In addition, the application of the free plate to the problem of visual surface reconstruction is studied using synthetic data. Finally, excellent results are obtained applying the Specht triangular element to a real set of depth data for an areal view of land and water near St Mary lake. Some interesting comments with regards to conditioning and solution of the finite element equations are also included.

Authors: David Moulton, Raymond J. Spiteri

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