Theoretical Analysis and Engineering Implications for the High Order Term Solutions of the Mode II Type Creep Crack

The high order term (HOT) solutions of crack tip field should be taken into account in engineering applications due to their potential influences on the fracture toughness as well as the crack growth rate. Towards this end, the high order asymptotic analysis of mode II crack in a power-law creeping material under the plane strain condition is presented theoretically in this paper. By comparing among the three order term solution, HRR field and finite element calculations, it can be found that the proposed three order term solution is able to characterize the full field of mode II creep crack tip accurately. The high order term solution of mode II creep crack relies on the creep exponent, which is different from that of mode I crack case. There are two independent terms among these three terms of asymptotic solution for mode II creep crack, which indicates that there exists the constraint effect for the plane strain mode II creep crack though the effect of high order term may not be as significant as the mode I crack case. Based on the theoretical analysis, a modified time-dependent failure assessment diagram (TDFAD) for mode II creep crack is proposed by considering the high order term solution.

Analysis of the High Order Terms on Periodic Solution Bifurcations of the Generalized Duffing Systems

This paper focuses on the effectsof the high order term in Duffing equation. Firstly the averaging equation andthe bifurcation equation are deduced through the multiple scale method.Secondly, the transition sets and several different bifurcation diagrams areobtained based on the singularity theory. The result shows that the high order term induces richer bifurcationcharacteristics.

Arithmetic expressions optimisation using dual polarity property

A method for optimisation of fixed polarity arithmetic expressions (FPAEs) based on dual polarity is proposed. The method exploits a simple relationship between two FPAEs for dual polarities. It starts from the zero polarity FPAE of the given function and calculates all FPAEs using the dual polarity route. Using one-bit check carries out conversion from one FPAE to another. Each term in an FPAE is processed by the proposed processing rule. Terms, which differ in a single position, can be substituted by a high order term (cube). Experimental results show efficiency of proposed method.