针对中职学生数学基础差、逻辑思维能力弱及数学概念理论性强、抽象难教、学生难学等问题,研究提出"生活应用激动机、已有认知导概念、归纳本质升思维、多角度分析明内涵、学以致用成技能"等策略,帮助学生进行数学概念认知建构,充分发挥线上线下混合式教学优势,借助在线学习平台前移课堂准备,拓展学生个性化学习时间和空间,巧设在线互动及评价激励,破解数学概念教学中的痛点问题,多维度提升概念教学效果.

By using integral transforms-dual integral equations,the dynamic problem of Yoffe type crack was studied subjected to antiplane shear impact in infinity orthotropic functionally graded materials.The shear moduli in two directions were assumed to vary in terms with power function form of two parameters of arbitrary times power.The stress field and strain field dynamic stress intensity factor at crack tip were obtained.And the influences of material inhomogenous coefficient and graded parameters and crack motion speed to dynamic stress intensity factor were analyzed in virtue of Matlab software.The result showes that the stress at the crack tip is of singularity as the same of homogenous material.And the dimensionless dynamic stress intensity factor decreases with the increase of motion speed of crack and rises with the increase of graded parameters.

A new multi-layered model was developed for the functionally graded materials with arbitrarily varying function parameter in the derection of thickness.By selecting the analyzed plane reasonably,the material′s parameter could successively vary in term with arbitrarily function in the derection of z axis.By using this mode and the function of complex variable method,the crack of anisotropic functionally graded materials was studied.The stress and strain fields and graded stress intensity factor near crack tip were firstly introduced.It shows that the stess remains the singular behavior of the inverse square root of r near the crack tip.So those methods which had been applied in homogeneous materials widely can be used to resolve those problems of FGMs.

The stress-strain field of interface crack tip in orthotropic bi-materials is determined by photoelastic coating in this paper,and the fracture mechanics parameters for interface crack are derived.Orthotropic bi- materials panel is made into a tension specimen,and metallic-aluminum coating is plated in the surface of unilateral polycarbonate coating to enhance the reflectivity of polycarbonate coating.Then the load along the interface prefabricated cracks of bi-materials is gradually increased,a series of clear equi-difference lines can be observed.Stress intensity factor can be calculated by using stress component expressions for interface crack in orthotropic bi-materials.The testing-result indicates that photoelastic coating can effectively analyze the problem for interface crack in orthotropic bi-materials.

Dynamic problems of Yoffe mode crack are studied under antiplane shear impact in infinite orthotropic functionally graded materials. The shear modules in two directions are assumed to vary in terms with power function form of dual parameters of arbitrary time power. By using integral transform-dual integral equations method, the stress field and dynamic stress intensity factor near crack tip are obtained. And the influences of material in homogenous coefficient and graded parameters and crack moving speed to dynamic stress intensity factor are analyzed in virtue of Matlab software. Results show that the dimensionless dynamic stress intensity factor will decrease with the increase of moving speed of crack, which is opposite to the result of the dynamic problem of infinite strip in FGM. And the dimensionless dynamic stress intensity factor will decrease with the increase of graded parameters and rise with the increase of material in homogenous coefficient.

The mechanics problem of Griffith is studied of an unbounded orthotropic functionally graded materials with finite length crack subjected to antiplane shear impact.The shear moduli in two directions were assumed to vary in terms with hyperbolic function.By using integral transformation and dual integral equations,the stress field and stress intensity factor were obtained.And the influence of material asymmetry parameter on stress intensity factor was analized.The results show that increasing shear moduli's gradient of FGM can restrain the driving force of crack expanding.