PSI - Issue 28

O. Pozhylenkov et al. / Procedia Structural Integrity 28 (2020) 458–463 Author name / Structural Integrity Procedia 00 (2019) 000–000

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1.1. Problem statement

Fig. 1. Geometry of the problem The elastic rectangular domain � � , � � meets a load at the upper face of the domain, the lower side is under condition of ideal contact, the left side is under condition of ideal contact too, displacements at the right side of the domain is equal to zero � � � � ��� � �� � � � � � � � �� � � � � �0, � � �� �0, � � � � � � � � � � (1) It is required to estimate the stress state of the rectangular domain � � , � � satisfying the boundary conditions (1) and the equilibrium equations �� � � � ∗∗ � � � � � �� � � � �∗ � �� � �� � � � ∗∗ � � � � � ∗∗ � � � �∗ � �� � (2) Here we use next notation � � � � � � , � � � � � � , � � � � �� � �� � �� , ∗ � � � �� � �� � �� , � � �� � �� 1.2 Problem solving The Fourier`s transforms are applied to the equations (2) with following scheme: � � � � � � � � � � � � � ∗ sin � � � � � ∗ ��s � � � � � � � � � �� � 1 2 � (3) It leads to the non-homogeneous system of the ordinary differential equations in the transform`s domain: ��� � � � �� � � � � � �� �� � � � � � � � �� � � � ∗ sin� � � ∗ ��1 � � � � �� �1 � � � � �� � � � � � � �� � � �