Application of scaled boundary finite element method in static and dynamic fracture problems

The scaled boundary finite element method （SBFEM） is a recently developed numerical method combining advantages of both finite element methods （FEM） and boundary element methods （BEM） and with its own special features as well. One of the most prominent advantages is its capability of calculating stress intensity factors （SIFs） directly from the stress solutions whose singularities at crack tips are analytically represented. This advantage is taken in this study to model static and dynamic fracture problems. For static problems, a remeshing algorithm as simple as used in the BEM is developed while retaining the generality and flexibility of the FEM. Fully-automatic modelling of the mixed-mode crack propagation is then realised by combining the remeshing algorithm with a propagation criterion. For dynamic fracture problems, a newly developed series-increasing solution to the SBFEM governing equations in the frequency domain is applied to calculate dynamic SIFs. Three plane problems are modelled. The numerical results show that the SBFEM can accurately predict static and dynamic SIFs, cracking paths and load-displacement curves, using only a fraction of degrees of freedom generally needed by the traditional finite element methods.

THE MECHANICAL METHOD OF CONSTRUCTING THE DISPLACEMENT FUNCTIONS IN ELASTICITY

In this Paper we have proven the general solution to the equations of linear operatorsAu=f as u=Cv+e . where v satisfies the equation Dv=g and D is adiagonal matrix. Basing on the consstructive proof of Hilbert Nullstellensat=. we haregiven the mechanical method of constucting C. D and e.and some of the mechanicalalgorithm displacement functions in elasticity are given by this method also .

Characterization of particulate products for aging of ethylbenzene secondary organic aerosol in the presence of ammonium sulfate seed aerosol

Aging of secondary organic aerosol（SOA） particles formed from OH– initiated oxidation of ethylbenzene in the presence of high mass（100–300 μg/m^3） concentrations of（NH_4）_2SO_4seed aerosol was investigated in a home-made smog chamber in this study.The chemical composition of aged ethylbenzene SOA particles was measured using an aerosol laser time-of-flight mass spectrometer（ALTOFMS） coupled with a Fuzzy C-Means（FCM） clustering algorithm.Experimental results showed that nitrophenol,ethyl-nitrophenol,2,4-dinitrophenol,methyl glyoxylic acid,5-ethyl-6-oxo-2,4-hexadienoic acid,2-ethyl-2,4-hexadiendioic acid,2,3-dihydroxy-5-ethyl-6-oxo-4-hexenoic acid,1H-imidazole,hydrated N-glyoxal substituted1H-imidazole,hydrated glyoxal dimer substituted imidazole,1H-imidazole-2-carbaldehyde,N-glyoxal substituted hydrated 1H-imidazole-2-carbaldehyde and high-molecular-weight（HMW） components were the predominant products in the aged particles.Compared to the previous aromatic SOA aging studies,imidazole compounds,which can absorb solar radiation effectively,were newly detected in aged ethylbenzene SOA in the presence of high concentrations of（NH_4）_2SO_4seed aerosol.These findings provide new information for discussing aromatic SOA aging mechanisms.