Multiobjective shape optimization of latticed shells for elastic stiffness and uniform member lengths

A multiobjective optimization approach is presented for shape design of latticed shells. The objective functions are the strain energy under static loads and the variance of member lengths. Numerical results are shown for the latticed shells with three types; namely, triangular grid, quadrilateral grid, and hexagonal grid. The topology of each grid is fixed, and the locations of control points or the nodal coordinates are considered as design variables. The constraint approach is used for multiobjective optimization. Optimization results show that the triangular-grid shell with uniform member lengths turn out to be a cylindrical surface with equilateral triangles. The optimal shapes for quadrilateral grids are highly dependent on the initial solutions, and there exists a kind of bifurcation for the set of local optimal solutions in the objective function space. Finally, various shapes with uniform member lengths are found for the latticed shells with hexagonal grids.