Methods of improving reinforced concrete structures via numerical simulations

A method of improving reinforced concrete structure via numerically simulating structural behaviors obtained using finite element analysis (FEA) comprising:

• receiving characteristics of a reinforced concrete structure;
• creating a FEA model to represent the reinforced concrete structure that reflects the received characteristics in a computer system having a FEA application module installed thereon, the FEA model containing a plurality of solid elements defined by a plurality of solid element nodes and at least one beam element defined by a plurality of master beam element nodes, wherein the at least one beam element representing reinforcing steel bars are embedded inside the solid elements representing concrete, and the FEA model further containing a plurality of slave beam nodes along the at least one beam element such that each of the solid elements houses at least one slave beam node;
• obtaining, by the FEA application module, numerically simulated structural behaviors of the reinforced concrete structure by conducting a time-marching simulation using the FEA model, at each of a plurality of solution cycles of the time-marching simulation, proper coupling of the solid elements and the at least one beam element being ensured with following operations:
• obtaining slave beam nodal masses and velocities at each slave beam node from the corresponding master beam nodes;
• updating solid element nodal masses at each solid element node by accumulating respective contributions from relevant ones of the slave beam nodes with corresponding solid element shape functions;
• calculating updated slave beam nodal velocities at each slave beam node using said updated solid element nodal masses and momentums with the corresponding solid element shape functions;
• updating master beam nodal masses and momentums at each master beam node by accumulating respective contributions from the calculated slave nodal masses and velocities with corresponding beam element shape functions;
• and
• calculating the updated master beam nodal velocities at said each master beam node by dividing the updated master beam nodal momentums by the updated master beam nodal masses, respectively.