Influence of inclusion sizes on the stress state of plate elements underdynamic loading
DOI:
https://doi.org/10.36910/6775-2410-6208-2025-14(24)-44Keywords:
stress state, dynamic loading, inclusion, integral equation method, uniaxial tensionAbstract
The article presents the results of a study on the assessment of the influence of rigid inclusions on the stress state of plate elements of structures under the action of uniaxial dynamic loading. To solve the problem, the method of boundary integral equations and the apparatus of the theory of functions of a complex variable were used. This approach allowed reducing the solution of the problem to a system of singular integral equations. The selection of irregular features of the integrand functions and the use of the Plemel-Sohotsky formulas at the limit transition allowed us to write the integral equations in a form convenient for numerical solution.
The use of the conformal mapping method allowed us to apply the proposed approach to study the stress state of plate elements with inclusions of practically arbitrary smooth shape. For numerical implementation, the methods of mechanical quadrature and collocation were used. The numerical analysis of the stress state was carried out on the basis of the study of the distribution of dynamic stresses in infinite plates with rigid inclusions of rectangular forms under the action of axial impulse loading. Comparison of numerical results allowed us to analyze the concentration of stresses for inclusions of various shapes. An analysis of the distribution of dynamic stresses at the boundary between the inclusion and the matrix at different stages of load application was also carried out. Based on numerical calculations, it was established that with increasing inclusion length, the stress distribution changes. It was also established that during high-frequency oscillations, the values of both hoop and normal stresses are practically the same and do not depend on the inclusion size. Based on the corresponding results, points on the boundary of the inclusion and the plate element with the maximum concentration of stresses were determined. This approach allows us to ensure the strength and reliability of the corresponding connection elements.
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