It is well known that the main approaches of the analytical solving of the elasticity mixed plane problems for a semi-strip are based on the different representations of the equilibrium equations' solutions: the representations through the harmonic and by harmonic functions, through the stress function, Fadle-Papkovich functions and so on. The main shortcoming of these approaches is connected with the fact that to obtain the expression for the real mechanical characteristics, one should execute additional operations, not always simple ones. The approach that is proposed in this paper allows the direct solution of the equilibrium equations. With the help of the matrix integral transformation method applied directly to the equilibrium equations, the initial boundary problem is reduced to a vector boundary problem in the transformation's domain. The use of matrix differential calculations and Green's matrix function leads to the exact vector solution of the problem. Green's matrix function is constructed in the form of a bilinear representation which simplifies the calculations. The method is demonstrated by the solving of the thermoelastic problem for the semi-strip. The zones and conditions of the strain stress occurrence on the semi-strip's lateral sides, important to engineering applications, are investigated.

The stress state of the elastic fixed semi-strip with the regarding of the singularities at its edge is investigated in the article. The initial boundary problem is reduced to a vector boundary problem in the transformation's domain by the use of integral Fourier transformation. The one-dimensional vector boundary problem is solved exactly with the help of matrix differential calculations and Green's matrix apparatus. The problem's solving was focused at the solving of the singular integral equation (SIE) with the two fixed singularities at the ends of the integration's interval. The symbol of SIE was constructed and the generalized method of the SIE solving was applied. The stress' distributions of the semi-strip are investigated.

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