Stress And Displacement Analysis Of A Three Phase Plate With Concentric Circular Inclusion:a Complex Function Study

Fracture mechanism is highly related to the defects of materials. These defects usuallytake the form of inclusions, holes and micro cracks. For some specific plane inclusionproblems plate medium model with the loading at infinity is usually adopted. Complexvariable function has become a powerful method for solving such problems.In this thesis, by using the complex variable function method we can express AIRYstress function in elastic theory as the linear combination of two arbitrary analytical functions,called complex potentials. Thus, solution of Airy stress function is attributed to the solution ofthe two analytic functions. Further, according to the characteristics of the domains of themodel, which can be the finite simply connected domain, finite multiply connected domainand infinite multiply connected domain, we expand the two arbitrary analytic functions intocomplex series. Moreover, the coefficients of the series are determined by the continuityconditions of the stresses and the displacements at the interfaces of different domains. Thefields of the stresses and displacements are formulated by two analytical functions. As theexample, we substitute the material constants into the formulas and give the graphs of thefields by computer simulation.The thesis consists of four chapters. In Chapter1we first summary the significant of thestudy on material inclusion; then we review the developments of plane elastic problems byusing complex function method. After the brief introduction of the software,MATHEMETICA, used in this study we present the contents investigated in this paper. Thebasic theories of plane elastic problems and complex function are discussed in chapter2firstly. Then we deduced the expressions of complex function for plane elastic problem. Wegive formulas of the stresses and displacements distributions for the model of a plate withcircle hole and for the two phase circle inclusion. And we deduced the formula for theproblems of a three-phase circular inclusion subjected to biaxial loading by the symbolicoperation system of MATHEMETICA. Finally, some conclusions are drawn in chapter4.