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New $$B$$-spline finite element approach for geometrical design and mechanical analysis. (English) Zbl 0912.73058
The main idea of this paper is to integrate a mechanically based geometrical design concept with the mechanical analysis module in a uniform $$B$$-spline finite element (BSFE) environment. We formulate the BSFE method and verify its validity and adequacy for linear elastic rod and plate models. In particular, we demonstrate the feasibility of applying $$B$$-spline functions as base functions of the finite element method for design and analysis.

##### MSC:
 74S05 Finite element methods applied to problems in solid mechanics 74K99 Thin bodies, structures
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