Optimal design of 3d frame structures taking into account the stress and multiple natural frequency constraints

The problem of determining the optimal cross-sectional parameters and joint positions of linearly elastic space frames with imposed stress and multiple frequency constraints was considered. The frame was assumed to be acted on by different independent load systems, including temperature and self-weight loads. The stress-state analysis includes tension, bending, shear and torsion of beam elements. The warping of beam elements was not taken into account in this problem. The sensitivity analysis of multiple frequencies was performed through analytic differentiation with respect to the joint positions and the sizes of the cross-sections of beam elements. The optimal design is attained through solving a sequence of quadratic programming problems.