Time-Differencing Fundamental Solutions for Plane Elastodynamics
Publication: Journal of Engineering Mechanics
Volume 148, Issue 8
Abstract
In this paper, new fundamental solutions for dynamic analysis of plane elastodynamics are developed. The governing dynamic differential equations are rewritten by replacing the accelerations with the corresponding displacements at different time steps via a suitable finite difference scheme. The known displacements in initial conditions or from previous time steps are treated as generalized new inertia terms. The unknown displacements at the current time step are added to the governing differential operator to form a new operator. The new time-dependent fundamental solutions are then derived with respect to the new differential operator. The required mathematical derivations are presented in detail. The corresponding integral equations and domain load treatments are also presented. Singular integrals of the derived fundamental solutions are also treated. Several numerical examples are solved to demonstrate the validity and the accuracy of the developed new solutions. The results demonstrated the accuracy of the developed new solutions compared to traditional time domain fundamental solutions.
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Data Availability Statement
All data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
This project was supported financially by the Science, Technology & Innovation Funding Authority (STIFA), Egypt, AHRC Grant No. 30794, and Basic and Applied Grant No. 37145. The authors would like to acknowledge the support of STIFA. The authors would like to thank M. Mubasher for preliminary and relevant programming work under the supervision of Professor Rashed.
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Published In
Journal of Engineering Mechanics
Volume 148 • Issue 8 • August 2022
Copyright
© 2022 American Society of Civil Engineers.
History
Received: Dec 31, 2021
Accepted: Mar 23, 2022
Published online: May 18, 2022
Published in print: Aug 1, 2022
Discussion open until: Oct 18, 2022
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