Research On Stress Concentration In An Elastic Plane With Holes

In the past decades, considerable works have been done on the stress concentration around asingle hole in elastic solids. However, with the development of material science, more and morefunctional anisotropic materials, e.g. piezoelectric materials, are used in engineering, while in mostcases, multiple holes or flaws exist in these elastic materies. However, related studies on stressconcentration are mathematically concerned with multiply-connected region, which is more difficultand challenging. This thesis focuses on the stress concentration of an elastic plane with a single holeor holes under mechanical/thermal loads. The main contents are given below:Chapter1introduces the current situation of research on stress concentration in elastic solids.Chapter2introduces the elasticity theory of Muskhelishvili, Faber series and the basic equationsof thermopiezoelectricity.Chapter3mainly studies the problem of an isotropic plate with multiple holes where the size andlocation of the holes are arbitrary. By means of complex variable method and Taylor series expansion,the general solution for stress concentration around holes is solved. For the case of two holes,numerical examples are then given to discuss the effect of radius ratio, distance between two holes,and loading type on stress concentration.Chapter4, the stress field in an orthotropic plate containing two circular holes forced by theelastic rings is solved by means of Faber series when the plate is subjected to uniform tensile loads atinfinity. Then, solutions are presented for the cases of two holes, two elastic inclusions, and two rigidrings in the orthotropic plate as several special examples of the present work.In Chapter5given is the solution for a piezoelectric plate with a circular hole having thermallysemi-permeable surface when the plate is subjected to thermo-mechanical-electric loads. Finally, heatdistribution and stress concentration are derived and shown by numerical results.Chapter6concludes the present work and gives some prospects to the future work.