Abstract
A general solution of a mixed boundary value problem in the plane elasticity is obtained for the boundary condition; one of two displacement components and one of two external force components are given on a part of the boundary. The part of the boundary is a straight line. A mapping function of a sum of fractional expressions and the complex stress functions are used. A closed solution can be obtained. As an example, a semi-infinite plate with a simple support on a part of the boundary is analyzed. The analysis is carried out for the states before and after the crack initiation at an end of the simple support. The loading condition is that the constant tensile load applies on the simple support. The stress distribution, the stress intensity factor and the resultant moment on the simple support are obtained.
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