Читать книгу Rethinking Prototyping - Группа авторов - Страница 63

We present a general scheme to solve grid patterns for elastic grid shells according to material properties and geometric constraints. Our form-finding scheme is based on the dynamic relaxation method with six DOF per node and the Euler-Bernoulli beam theory.

We can build the pre-stress of bending moments and torsions directly into structures by assigning specific initial orientations of beam-ends. This method enables us to begin the structural simulation from a strained state such that the tricky pre-stressing process of bending-active structures is prevented.

Using the projection method and the constraint force method, we can apply geometric constraints to grids. The projection method can generate grid patterns that exactly fit the geometric constraints, while the constraint force method produces grid patterns that are close to the target geometry and have less strain energy compared with the results derived from the projection method.

The profile stiffness plays as an active role in the form-finding process in our scheme. The real stiffness facilitates the form-finding of a grid pattern in accordance with the pre-determined grid lengths. The fictitious stiffness enables the grids to have a larger range of strained lengths, which facilitates the reduction of bending stresses and can be utilised to generate smoothly curved grid patterns with various grid lengths.