Regularization of Inverse Problems in Reinforced Concrete Fracture

Abstract

Reinforced concrete beams with flexural cracks are simulated by the bridged crack model. The weight function method of determining stress intensity factors has been followed to derive a transformation between the crack bridging force (the rebar force) and the crack opening displacements (CODs). The matrix of the transformation is then approximated by its finite difference equivalent within finite dimensional vector spaces. Direct problem of the transformation solves for CODs, which require a known rebar force. Alternatively, the inverse problem works out the rebar force from known CODs. However, the inverse transformations of such convolution type integral equations become