Reducing material to gain load capacity

Abstract

This research investigates whether a decrease in area or volume of material without changing the configuration can lead, to an increase in the load capacity of a structure. If true, this study explores how this happens. At first, simple cases such as springs on rotating bars and simple truss structures were studied in an attempt to selectively modify the area of members by changing their stiffness in order to find examples of this concept. An approach was developed using Mathematica to solve this constrained optimization problem. The constraints are that the configuration remains the same while the area or volume may only stay the same or decrease. The first two cases that were analyzed included a structure consisting of three members supported by pins and springs connected in parallel on a rotating rigid bar and subjected to a vertical point load at a specific location. The results obtained from both these examples indicated that the proposition is possible. Therefore, other cases were analyzed to extend those cases. The next step was executed through creating a program that implements the direct stiffness method to solve general cases of springs on multiple rotating rigid bars. The results provide insight into the mechanism of stress concentration and may provide ideas on how to improve material at the micromechanical level.