Sustainability problems of circular arcs with non-retaining links

The work deals with the problems of stability ofarches and arch systems supported by inextensiblethreads that cannot withstand compressive forces.These questions relate to contact problems of elasticstructures with an unknown region of active interaction of their elements, and the study is reducedto the search and analysis of bifurcation points ofsolutions to variational problems in the presenceof inequality constraints on the sought functions.The paper considers the problem of stability of anarch supported by threads, one end of which is attached to some point of the arch, the other to theprojection of this point on the chord connecting itsends. In the numerical solution, the problem is reduced to finding a load parameter in which the non-convex quadratic programming problem with constraints on variables in the form of inequalities hasa non-unique solution. Numerical calculations haveshown that even with a small number of reinforcingthreads, the critical load approximately doubles.