Читать книгу Rethinking Prototyping - Группа авторов - Страница 60

In this example, we apply the weighted stiffness in the form-finding stage to the above grid structure to see its effect on the grid patterns: A factor of 10E4 is applied to the bending and torsional stiffness to enable the beam element to have a larger range of the strained length. This fictitious stiffness setting is only used in the form-finding stage. Once the form is found, the material stiffness is recovered and the strained lengths of the found form are taken as the new unstrained grid lengths.

The comparison of the strain energy between the two forms, which are found with the real stiffness setting and the fictitious stiffness setting, is showed in Tab. 2, and the comparison of their geometries is showed in Fig. 7. The in-plane bending strain energy of the irregular grid shell is largely reduced, which is only 25% of the in-plane bending strain energy of the regular gridshell.

Table 2: Comparisons of the grid length and the strain energy between the regular grid and the irregular grid
	max. length[m]	min. length[m]	strain energy [kNm]	axial strain energy [kNm]	torsional strain energy [kNm]	out-of-plane bending strain energy [kNm]	in-plane be ding strain energy [kNm]
regular grid irregular grid	1.0003 1.0602	0.9996 0.9308	9.5E+01 6.7E+01	5.2E-01 3.2E-03	2.5E+01 2.6E+01	3.6E+01 3.3E+01	3.2E+01 8.2E+00