Stability Of The First And Second Fundamental Problems In Plane Elasticity

This dissertation proposes and devotes to the investigation of stability of the first and second fundamental problem on finite domain in elasticity. At first, the fundamental problems are changed to analytic boundary problems via introducing two holomorphic functions and further to Sherman-Lauricella equations by the Cauchy type integral ex-pression of holomorphic function, then the stability of solution to Sherman-Lauricella equations are discussed by the properties of high order difference quotient function. By dint of derivation rule for line integrals, the stability of the solutions to Sherman-Lauricella equations and the stability of Cauchy type integral with respect to the smooth pertur-bation for integral curve and the Sobolev type perturbation for density function, we discuss the stability of the first fundamental problem when the smooth perturbation for the boundary of elastic domain and the Sobolev type perturbation for the external load happen, and the error of perturbation for the complex functions are estimated, further, the error of perturbation for the stress and displacement are then estimated too. Analo-gously, we discuss the stability of the second fundamental problem, and then the error of perturbation for the stress and displacement are estimated.The dissertation consists of seven Chapters as follow:In Chapter1. the background of this dissertation work is introduced, the difficulties and solutions in the course of the study are stated, as well as the main results of this dissertation are given; In Chapter2, perturbed curve and perturbed function are defined, the concept of n order Sobolev type perturbation for function is proposed:In Chapter3, derivative condition for a kind of line integral and derivation rule are shown; In Chapter4, continuity theorem of n order difference quotient function and its arbitrary order derivative are got, estimates of n order difference quotient function and its arbitrary order derivative are given:In Chapter5. by using maximum modulus principle and Privalov theory, the stability of Cauchy type integral is discussed when smooth perturbation for curve and n order Sobolev type perturbation lor kernel density function happen, and error perturbation for Cauchy type integral is then estimated: In Chapter6. the stability of the first fundament al problem is discussed, error of perturbation for the stress and displacement are estimated: In Chapter7. the stability of the second fundamental problem is discussed, the error estimation for the stress and displacement are obtained.