RELATIONS BETWEEN PROCESS OF CUTTING AND UNIQUENESS OF SOLUTIONS

Abstract

When an accurate stress analysis is to be made for excavation problems, it is desirable to make a step-by-step calculation by simulating the actual steps of excavation procedure. In this connection, there arise some fundamental questions as to whether the solutions are all identical when the order of cutting is changed, and whether the solution for multistage cutting equals that for a single-step cutting. To check the uniqueness of the solution for these different methods of cutting, the uniqueness proof was investigated by following the conventional method of approach which has been used extensively in the theory of elasticity and plasticity. The well-known theorem of virtual work was applied to the proof together with the stress-strain relationship of the material. It is shown that the uniqueness depends strongly upon the material properties, and that the sufficient condition for the uniqueness to be established is that the material is linear, time-independent and elastic throughout the cutting process.