Integration of geometric design and mechanical analysis using B-spline functions on surface

B-spline finite element method which integrates geometric design and mechanical analysis of shell structures is presented. To link geometric design and analysis modules completely, the non-periodic cubic B-spline functions are used for the description of geometry and for the displacement interpolation function in the formulation of an isoparametric B-spline finite element. Non-periodic B-spline functions satisfy Kronecker delta properties at the boundaries of domain intervals and allow the handling of the boundary conditions in a conventional finite element formulation. In addition, in this interpolation, interior supports such as nodes can be introduced in a conventional finite element formulation. In the formulation of the mechanical analysis of shells, a general tensor-based shell element with geometrically exact surface representation is employed. In addition, assumed natural strain fields are proposed to alleviate the locking problems. Various numerical examples are provided to assess the performance of the present B-spline finite element