ABSTRACT
The Hybrid-type Penalty Method (HPM), developed by Takeuchi et al. (2009), refined the RBSM method for calculating the elastic deformations of elements using the Finite Element Method (FEM); a Lagrange multiplier was also introduced to satisfy the subsidiary condition of continuous displacement in the hybrid-type virtual work formulation. The HPM is suitable for analyzing the progressive failure of concrete structures, with the following features:
• Accurate deformation can be calculated before crack initiation because an elastic element (called a subdomain in HPM) is used. Even after crack initiation, it is important to accurately calculate the deformation within the elastic area between cracks.
