Abstract
Recent studies on the control of smart material partial differential equation systems point toward a need for considering higher-ordered polynomial splines in the formulation of bases for approximate solutions obtained via the Galerkin finite element method. However, basis modifications are not well documented in the literature, nor are they well understood by researchers who are often utilizing software packages in their basis and control designs. In this study, solutions are generated using modified bases with quintic and biquintic B-splines for three clamped structures: an ordinary differential equation cantilevered beam, a partial differential equation cantilevered beam, and an isotropic clamped plate. Convergent solutions are obtained and verified for all three models.
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