A new numerical method,scaled boundary isogeometric analysis(SBIGA)combining the concept of the scaled boundary finite element method(SBFEM)and the isogeometric analysis(IGA),is proposed in this study for 2D elastostatic problems with both homogenous and inhomogeneous essential boundary conditions.Scaled boundary isogeometric transformation is established at a specified scaling center with boundary isogeometric representation identical to the design model imported from CAD system,which can be automatically refined without communication with the original system and keeping geometry invariability.The field variable,that is,displacement,is constructed by the same basis as boundary isogeometric description keeping analytical features in radial direction.A Lagrange multiplier scheme is suggested to impose the inhomogeneous essential boundary conditions.The new proposed method holds the semi-analytical feature inherited from SBFEM,that is,discretization only on boundaries rather than the entire domain,and isogeometric boundary geometry from IGA,which further increases the accuracy of the solution.Numerical examples,including circular cavity in full plane,Timoshenko beam with inhomogenous boundary conditions and infinite plate with circular hole subjected to remotely tension,demonstrate that SBIGA can be applied efficiently to elastostatic problems with various boundary conditions,and powerful in accuracy of solution and less degrees of freedom(DOF)can be achieved in SBIGA than other methods.
This paper aims at exploring the effects of anti-seismic reinforcement with the fiber-reinforced polymer （FRP） material bonded to the dam surface in dam engineering. Time-history analysis was performed to simulate the seismic failure process of a gravity dam that was assumed to be reinforced at the locations of slope discontinuity at the downstream surface, part of the upstream face, and the dam heel. A damage model considering the influence of concrete heterogeneity was used to model the nonlinearity of concrete. A bond-slip model was applied to the interface between FRP and concrete, and the reinforcement mechanism was analyzed through the bond stress and the stress in FRP. The results of the crack pattern, displacement, and acceleration of the reinforced dam were compared with those of the original one. It is shown that FRP, as a reinforcement material, postpones the occurrence of cracks and slows the crack propagation, and that cracks emanating from the upstream surface and downstream surface are not connected, meaning that the reinforced dam can retain water-impounding function when subjected to the earthquake. Anti-seismic reinforcement with FRP is therefore beneficial to improving the seismic resistant capability of concrete dams.
