The solution of system of integral differential equations and its application in the theory of elasticity

摘要

A contact problem of the theory of elasticity of infinite compound and infinite orthotropic plates with an elastic semi-infinite or finite inclusion of variable rigidity is considered. The problem is reduced to the system of integral differential equations with variable coefficient of singular operator. If such coefficient varies with power law we can manage to investigate the obtained equations, using the methods of analytical functions to get exact solutions and to establish behavior of unknown contact stresses at the ends of elastic inclusion. In some case using the method of orthogonal polynomials we obtain the dual infinite system of linear algebraic equations. We can manage to investigate the obtained system on the quasi-regularity and the method of reduction for approximate solution is developed. A contact problem of the theory of elasticity of infinite compound and infinite orthotropic plates with an elastic semiinfinite or finite inclusion of variable rigidity is considered. The problem is reduced to the system of integral differential equations with variable coefficient of singular operator. If such coefficient varies with power law the author can manage to investigate the obtained equations, using the methods of analytical functions to get exact solutions and to establish behavior of unknown contact stresses at the ends of elastic inclusion. In some case using the method of orthogonal polynomials he obtains the dual infinite system of linear algebraic equations. The method of reduction for approximate solution is developed.