A kind of bivariate spline space over rectangular partition and pure bending of thin plate
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The mechanical background of the bivariate spline space of degree 2 and smoothness 1 on rectangular partition is presented constructively. Making use of mechanical analysis method, by acting couples along the interior edges with suitable evaluations, the deflection surface is divided into piecewise form, therefore, the relation between a class of bivariate splines on rectangular partition and the pure bending of thin plate is established. In addition, the interpretation of smoothing cofactor and conformality condition from the mechanical point of view is given. Furthermore, by introducing twisting moments, the mechanical background of any spline belong to the above space is set up.
Key wordssmoothing cofactor conformality condition pure bending of thin plate
Chinese Library ClassificationO241 O343
2000 Mathematics Subject Classification65D07 74K20
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