Methods of improving reinforced concrete structures via numerical simulations
Characteristics of a reinforced concrete structure are received. FEA model is created in a computer system accordingly. FEA model contains solid elements defined solid nodes and beam elements defined by master beam nodes. Beam elements representing reinforcing steel bars are embedded inside solid elements representing concrete. Each beam element straddles one or more solid elements. Slave beam nodes along the at least one beam element are created such that each of the solid elements houses at least one slave beam node. Numerically-simulated structural behaviors of the reinforced concrete structure are obtained at each solution cycle of the time-marching simulation. Proper coupling of solid elements and at least one beam element are ensured. Exchanges of masses and momentums between a slave beam node and corresponding solid element nodes is conducted with both consistent and non-consistent portions. Reinforced concrete structure is adjusted to alleviate weakness indicated in the numerically-simulated structural behaviors.
1. 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.
2. The method of claim 1 , wherein said calculating updated slave beam nodal velocities at each slave beam node further comprises:
calculating updated solid element nodal velocities by dividing the updated solid element nodal momentums by the respective updated solid element nodal masses; and
deriving updated slave beam nodal velocities by accumulating contributions from the respective updated solid element nodal velocities with the corresponding solid element shape functions.
3. The method of claim 1 , said obtaining slave beam nodal masses and velocities at each slave beam node from the corresponding master beam nodes further comprises evenly distributing total mass of the corresponding master beam nodes to the slave beam nodes.