The Problems on the concentration in the strip-plates containing a rectangular hole

The boundary-value problem of stress accumulation in the simply- and rigidly-supportedstrip-plate with a rectangular hole or a rectangular inclusion has been formulated for the plainstrain state. The formulation is established in the framework of exact equations of theelasticity theory. Then, another boundary-value problem of stress accumulation in the simply-supported pre-stressed strip-plate with a rectangular hole has been elaborated to determine theeffect of the pre-stress when additional load is introduced. This problem is formulated byutilizing the exact equations of the linearized elasticity theory in plain strain state.The associated algorithms and computer programs have been developed for the abovementioned problem formulations, in order to model them with the finite element method andto perform numerical analyses. In the non-pre-stressed case, it was studied in the statedboundary-value problem to determine the effect of the geometric and material discontinuitieson the stress accumulation in the strip-plate with respect to the parameters of geometry andmaterial. In the pre-stressed case, it was determined for the given boundary-value how arectangular hole affects the stress accumulation in the strip-plate, in relation with dependencyon the parameters of geometry and material, and the amount of pre-stress.The associated graphics and the numerical analyses have been presented in the conclusion.Keywords: Finite element method, rectangular hole or rectangular inclusion, stressconcentration, composite material, pre-stress.xii