Задачи устойчивости круговых арок с неудерживающими связями

Abstract

The work deals with the problems of stability of arches and arch systems supported by inextensible threads that cannot withstand compressive forces. These questions relate to contact problems of elastic structures with an unknown region of active interaction of their elements, and the study is reduced to the search and analysis of bifurcation points ofsolutions to variational problems in the presence of inequality constraints on the sought functions. The paper considers the problem of stability of an arch supported by threads, one end of which is attached to some point of the arch, the other to the projection of this point on the chord connecting its ends. In the numerical solution, the problem is reducedto finding a load parameter in which the nonconvex quadratic programming problem with constraints on variables in the form of inequalities has a non-unique solution. Numerical calculations have shown that even with a small number of reinforcing threads, the critical load approximately doubles.