Solution of Finite-Displacement Small-Strain Elasticity Problems by Removal of Rigid Body Displacements

Abstract

If rigid body displacements are properly separated from a fmite-displacement small-strain problem, the remaining deformation is within the scope of the small displacement theory. For this purpose, the rigid body displacement of each sufficiently small subdomain of an elastic body must be removed independently from other subdomains before the actual deformation occurs. This paper presents a rigorous and straightforward theoretical formulation for a numerical solution procedure based on this concept. The simplicity of the formulation is due to the fact that it is developed for a general three-dimensional solid rather than structural elements as in the past works.

Evaluating the Nonlinear Dynamic Stiffness of Rail Pad using Finite Element Method

“…The rigid body displacement, which occurred at 20 kN, 30 kN, and 40 kN, was corrected for accurate results. This was a common problem for geometrically nonlinear small-strain conditions [26]. As a percentage error below 10%, it was concluded that the simulation model could be accepted.…”

Nonlinear Static Stiffness of Rail Pads for Different Materials and Thicknesses using Finite Element Method

“…The percentage error between simulation and previous experimental data was tabulated in Table 3. The higher percentage errors at loads 10 kN and 20 kN were due to rigid body displacement, which is a common problem for geometrically nonlinear small-strain condition [19]. This problem could been neglected since the average value of percentage error was 6.5% which was considered as an acceptable range to verify the accuracy of the model simulation.…”