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A simple coupled method, called “finite element discretized symplectic method” is introduced into the mode III fracture analysis of a V-notched magneto-electro-elastic (MEE) bimaterial. High-accuracy generalized intensity factors and energy release rate are computed to evaluate the singularities of mechanical, electric and magnetic fields. The present method is carried out in two steps. In the first step, the physical domain is meshed by the conventional element for MEE media and is divided into a finite size singular region near the notch tip and a regular region far away from the notch tip. In the second step, analytical symplectic eigenfunctions are employed to transform the large number of nodal unknowns in the singular region into a small set of undetermined coefficients of a symplectic series; the nodal unknowns in the regular region remain as usual. Consequently, the computational cost is enormously reduced and fracture parameters are actually the first three coefficients of the series. Explicit expressions in the singular fields are obtained simultaneously. Numerical results are compared with the existing solutions and found to be in good agreement. Some new results are given also.

Stress singularities arising at the multi-material interface in a V-notched plate under bending are studied in the frame work of a Hamiltonian-based method. Exact solutions of V-notched multi-material plates are expressed in an analytical symplectic series. Newly defined generalized stress intensity factor (GSIF) are introduced to evaluate fracture behaviors of the V-notched plate. A highly accurate finite element discretized symplectic method is employed to compute the GSIFs and to obtain the explicit expressions of singular stresses near the notch tip. Comparisons are presented to show the accuracy and efficiency of the present work. Some new results are also provided.

A finite element discretized symplectic method is presented for the determination of modes I and II stress intensity factors (SIFs) for cracked bimaterial plates subjected to bending loads using Kirchhoff’s theory and symplectic approach. The overall plate is meshed by conventional discrete Kirchhoff theory elements and is divided into two regions: a near field which contains the crack tip and is enhanced by the symplectic series expansion and a far field which is far away from the crack tip. Based on the analytical solutions of global displacement, numerous degrees of freedom are transformed to a small set of undetermined coefficients of the symplectic series through a displacement transformation, while those in the far field remain unchanged. The SIFs can be obtained directly from coefficients of eigensolution (Re $$\mu < 1$$ ), and no post-processing or special singular element are required to develop for extracting the SIFs. Numerical examples are presented and compared with existing results to demonstrate the efficiency and accuracy of the method.

An interface V-shape notch under bending loads is evaluated by a finite element discretized symplectic method. The stress intensity coefficients are extended to represent the singularities of notch-tip stress fields. The bimaterial notched plate is first meshed by conventional finite elements. Analytical symplectic eigenvectors are then used as the global interpolation functions so that the evaluation of stress singularities is reduced to solving undetermined coefficients of the symplectic series. Explicit expressions of stress fields and stress intensity coefficients are finally achieved simultaneously. Numerical examples are presented to validate the accuracy of the proposed method and new results are also given.

As far as the impact of air pollutants on human heath being is concerned, ozone (O3) is one of the most pollutant sources, and, in particular, the ground level ozone is responsible for a variety of adverse effects on both human being and plant life. To protect the population from such adverse health effects, early information and precautions about the high ozone level need to be ascertained. In this study, statistical characteristics of ground level ozone is analyzed according to field monitoring data in mixed residential, commercial and industrial areas, e.g., Tsuen Wan area in Hong Kong. The study deals with the characteristics of hourly and daily mean ozone levels under different climatic conditions such as temperature, solar radiation (SR), wind speed (WS), and other pollutant concentration levels. The study aims to investigate the importance of meteorological factors and their impact on relevant pollutant concentration levels from a chemical aspect. Further, reasons for the spatial and temporal variation of ozone levels are discussed. All these results will provide a physical basis for accurately predicting ozone concentration in similar research. Keywords: Chemical, Climatic condition, Environment, Ozone level, Pollutant monitor