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Abstract <p>In this paper, the principle of obtaining conditions for matching input data is formulated. A&#xa0;set of matching conditions is obtained, failure to fulfill which leads to large unavoidable errors in the corners of the rectangle. The problem is solved in analytical form using the method of universal fast expansions. The obtained approximate analytical solution is compared with the test one, the error in determining the plate deflection, torque and bending moments, shear forces and stress tensor components is investigated. It is found that when using a sixth-order boundary function and only one term in the cosines and one term in the sines in the Fourier series in universal fast expansions, the accuracy of the obtained solution significantly exceeds the accuracy of specifying the input parameters of the problem determined by the concept of a continuous medium. In this case, the approximate analytical solution can formally be considered exact.</p>

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Rectangular Plate on an Elastic Base with Arbitrary Boundary Conditions and Arbitrary Load

  • 期刊论文

  • 发表日期：

    2025年8月1日

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  • A. D. Chernyshov,
  • V. V. Goryainov

摘要

Abstract

In this paper, the principle of obtaining conditions for matching input data is formulated. A set of matching conditions is obtained, failure to fulfill which leads to large unavoidable errors in the corners of the rectangle. The problem is solved in analytical form using the method of universal fast expansions. The obtained approximate analytical solution is compared with the test one, the error in determining the plate deflection, torque and bending moments, shear forces and stress tensor components is investigated. It is found that when using a sixth-order boundary function and only one term in the cosines and one term in the sines in the Fourier series in universal fast expansions, the accuracy of the obtained solution significantly exceeds the accuracy of specifying the input parameters of the problem determined by the concept of a continuous medium. In this case, the approximate analytical solution can formally be considered exact.