Bending by Concentrated Force of a Cantilever Strip Having a Through-thickness Crack Perpendicular to Its Axis

Abstract

The article focuses on the bending problem for a cantilever beam with a straight through-thickness crack, perpendicular to its axis under bending by concentrated force. Depending on the crack location in relation to the axis, crack faces may be in three states: perfect contact, particular contact, or noncontact. Using the theory of functions of complex variable and complex potentials, the considered problem was reduced to a linear conjunction one. An analytical solution of the problem was obtained. In the case of particular contact, the length of the contact area and stress intensity factors were determined. The ultimate force that causes beam destruction was determined. Numerical analyses of the problem were also performed.

Keywords

• cantilever beam
• concentrated force
• crack
• complex potentials
• stress intensity factor
• ultimate force.