Non-parametric design of free-form shells with curved boundaries and specified reaction forces.

• Shape design method specifying thrust and horizontal projected stress distribution. • Graph surface with curved boundary parametrized using Bernstein polynomial. • Finite difference approximation of differential equilibrium equation for self weight. • FE-analysys to confirm stress distribution after slight contraction on plane. A shape design method is proposed for free-form shells specifying the distribution of horizontal reaction forces along the boundary as well as the stresses projected to the horizontal plane. The shell supports the self-weight with only in-plane stresses without out-of-plane shear and bending. A parametric form is presented to model the shape of the shell with curved boundary on a plane. The vertical coordinate of the shell surface is defined as a graph surface with respect to the horizontal coordinates that is expressed by Bernstein polynomials of normalized parameters. It is demonstrated in the numerical examples that various shapes can be generated by specifying the horizontal reaction forces that are not necessarily continuous. A static finite element analysis is carried out to show that the stresses are sufficiently close to the specified values even considering the deformation under self-weight. [ABSTRACT FROM AUTHOR]