Non-standard problems of homogeneous structural elements with wedge shape features in the plane case

A new type of solid mechanics problems – non-standard ones – is distinguished. Their distinctive feature is the redundancy of restrictions on status parameters at at least one point on the body boundary. It is shown that the use of standard methods in solving non-standard problems does not guarantee the fulfillment of all specified conditions. The most important cases of nonstandard restrictions in flat homogeneous structural elements with singularities in the form of wedges are presented. Wedge side loading is studied in the following cases: free from stress, rigidly clamped, sliding without friction along a rigid surface, and surface power loaded. An iterative converging numerical-analytical method for studying problems of this type is proposed. At each step of the iterative process converging to the solution of the non-standard problem, the inverse problem in displacements is solved. An illustrative example shows the essential difference between the standard and iterative solutions of the non-standard problem in a vicinity of the wedge tip.