Modelling of the Effect of Piece-Wise Potential Volume Forces in the Photo-Elasticity Method

Abstract

Abstract The authors note a special feature complicating the direct modelling process in the photo-elasticity method (using the models made from widely-used epoxy materials) with volume forces even of the simplest kind (mass forces). This problem is more complicated than the problems with constant parameters ν, E, γ, α in the whole body. The authors give some additional relationships between the similarity factors, the use of which may create some restrictions and difficulties in the process of modelling non-uniform problems through traditional methods. The authors use the theoretical principles of mechanics of deformable rigid bodies and show that the solution of the problem in case, when the volume forces in different domains of the body have different potential values, may be reduced to the solutions of the problems with potential volume forces and to the solution of the problem with given stress values. The authors have developed both methodology and engineering questions of modelling piece-wise potential volume forces using the equivalence of effects. They note that the methods of solution of the problems with the loadings substituting the volume forces have been developed in full and give efficient results.