Analytical solutions and numerical procedures for minimum-weight Michell structures
Date of Original Version
A power-series method developed for plane-strain slip-line field theory is applied to the construction of minimum-weight Michell frameworks. The relationship between the space and force diagrams is defined as a basis for weight calculations. Analytical solutions obtained by the method are shown to agree with known solutions that were obtained through virtual displacement calculations. Framework boundary conditions are investigated, and matrix operators used in slip-line field theory are shown to apply to the force-free straight framework boundary-value problem. The matrix operator method is used to illustrate the transition from circular arc-based to cycloid-based Michell solutions. Finally, an example is given in the use of the method for evaluation of support boundary conditions.
Journal of the Mechanics and Physics of Solids
Dewhurst, Peter. "Analytical solutions and numerical procedures for minimum-weight Michell structures." Journal of the Mechanics and Physics of Solids 49, 3 (2001): 445-467. doi:10.1016/S0022-5096(00)00053-3.