This paper focuses on the study of the stability of explicit time integration algorithm for dynamic problem by the Extended Finite Element Method(XFEM).A new enrichment scheme of crack tip is proposed within the framework of XFEM.Then the governing equations are derived and evolved into the discretized form.For dynamic problem,the lumped mass and the explicit time algorithm are applied.With different grid densities and different forms of Newmark scheme,the Dynamic Stress Intensity Factor(DSIF)is computed by using interaction integral approach to reflect the dynamic response.The effectiveness of the proposed scheme is demonstrated through the numerical examples,and the critical time stepping in different situations are listed and analyzed to illustrate the factors that affect the numerical stability.
Reinforcement corrosion directly affects the mechanical behavior of reinforced concrete structures.An electric corrosion test was conducted on a reinforced concrete test specimen,and a finite element model of the reinforcement corrosion damage was established.In addition,the damage behavior of reinforced concrete under different corrosion sediment distribution characteristics and different corrosion rates was studied.It was noted that when corrosion sediments are in a“semiellipse+semicircle”distribution,the results of numerical calculation are consistent with those obtained experimentally,reflecting the damage characteristics of reinforced concrete test specimens.Further,the results showed that the distribution characteristics of corrosion sediments greatly influence the damage behavior of reinforced concrete.In particular,when the corrosion sediments demonstrate a“semiellipse”distribution,reinforced concrete members may easily suffer from reinforcement damages.In the case of“semiellipse+semicircle”and“circle”distributions,the cohesive force between the reinforcements and concrete decreases:With the same corrosion rate,the damaged area expands with the increase in the number of reinforcements,which indicates a reduction in the cohesive force and thus,a reduction in the damage in the reinforcement area.This paper analyzes in-depth the effects of reinforcement corrosion expansion on the concrete damage behavior,provides references for practical engineering.
This paper focuses on the study of the stability of explicit time integration algorithm for dynamic problem by the Extended Finite Element Method(XFEM).A new enrichment scheme of crack tip is proposed within the framework of XFEM.Then the governing equations are derived and evolved into the discretized form.For dynamic problem,the lumped mass and the explicit time algorithm are applied.With different grid densities and different forms of Newmark scheme,the Dynamic Stress Intensity Factor(DSIF)is computed by using interaction integral approach to reflect the dynamic response.The effectiveness of the proposed scheme is demonstrated through the numerical examples,and the critical time stepping in different situations are listed and analyzed to illustrate the factors that affect stability.
