Stress-strain state near the wedge top with rigidly fastened sides

Deformable bodies containing wedge form elements with rigidly fastened sides under temperature loading are investigated. Stress-strain state research method based on identifying a singular point with a representative volume of the body is offered. This approach (in contrast to the commonly used asymptotic methods) makes it possible to formulate essential restrictions at а singular point. It is shown that typically the number of restrictions in the singular point is redundant (larger than usual at the body surface). This situation causes a new (compared to classical) formulation of the problem of solid mechanics contained at a singular point. The investigation of restrictions for the composite wedge with rigidly fastened sides in the vicinity of its top is done. Combinations of material and geometric parameters of construction elements that lead to various variants for problem formulation in solid mechanics are revealed. The critical values of set parameters at which the stress at the singular point increases indefinitely are identified. Load parameters conditions under which a singular point ceases to show singular behavior are formulated. Stress distributions problem near the top of composite wedge with 180 degrees vertex angle under the temperature loading is solved by the iterative numerical-analytical method. The comparison of the solutions obtained by the iterative technique and the classical finite element method is performed. It is shown that the iterative solution matches with all the singular point definable restrictions. Outside a singular point small neighborhood it matches with classical method decisions. But the classical asymptotic solution of the finite element method in the singular point small neighborhood cannot be declared allowed, since it does not satisfy the constraints formulated for such points. This makes it possible to evaluate the region near the critical point, which has no correct asymptotic solution. The typical size of such region is of five to ten characteristic size of the representative volume of the deformable body material. When material parameters approximate to the critical combination, the stress components demonstrate the singular character. The greatest stress value is reached not at the singular point, but at its proximate neighborhood.