Non-linear bending of a rod

Abstract

In this report, literature research on non-linear bending of a rod as well as soft materials such as hydrogel were conducted. Relevant information as well as required equations was used in the study of this report. The information from the literature research were investigated and checked by proof of calculation, plotting of graphs and checking for error of approximation. After that, simulations were done using software, Mathematica, which can be used to simulate the deflections and angle of deflections by using the necessary equations and inputting the parameters. This allows a detailed parametric study where individual parameter can be studied on the effects it have on the beam deflection along Y-axis (δy) and deflection angle (θ) by varying the individual parameter and fixing the remaining parameters’ values. The parametric study is split into 3 categories. First is Material Constants where the relationship between Young’s Modulus (E) of the material and δy and θ under fixed force and moment loading is studied. The result shows an inverse and exponential relationship. The second category is dimension changes where dimensions such as length (l), breadth (b) and height (h) of the beam are varied individually and combined in different scenarios to investigate the relationship between the dimensions and the δy and θ. In general, we deduce that a beam of larger dimension will result in smaller δy and θ compared to a beam of smaller dimensions even when the ratio of b: h: l is kept constant. Even though the relationships of individual dimensions to δy and θ might be different, but as a whole, they portray an inverse and exponential relationship to δy and θ. The third and last category will be force and moment loading. This is further broken down into study of 3 individual parameters, transverse force loading, axial force loading and moment loading. The transverse force loading portrays a direct and linear relationship to δy as well as θ. The axial force loading shows an inverse and exponential relationship to δy and θ. Lastly, the moment loading exhibits a direct and linear relationship to δy and θ. These parametric studies will be very useful for designing materials for specific applications where specific deformations and deformation angles have to be met during a specific environment condition.