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# BEM Solutions for 2D and 3D Dynamic Problems in Mindlin's Strain Gradient Theory of Elasticity

A. Papacharalampopoulos2, G. F. Karlis2, A. Charalambopoulos3, D. Polyzos4

This paper is dedicated to the memory of Professor Ioannis Vardoulakis.
Department of Mechanical and Aeronautical Engineering, University of Patras, GR-26500 Patras, Greece
Department of Materials Science and Engineering University of Ioannina, Dourouti, Ioannina, Greece
Department of Mechanical and Aeronautical Engineering, University of Patras, GR-26500 Patras, Greece & Institute of Chemical Engineering and High Temperature Process, ICETH-FORTH, Rio, Greece

Computer Modeling in Engineering & Sciences 2010, 58(1), 45-74. https://doi.org/10.3970/cmes.2010.058.045

## Abstract

A Boundary Element Method (BEM) for solving two (2D) and three dimensional (3D) dynamic problems in materials with microstructural effects is presented. The analysis is performed in the frequency domain and in the context of Mindlin's Form II gradient elastic theory. The fundamental solution of the differential equation of motion is explicitly derived for both 2D and 3D problems. The integral representation of the problem, consisting of two boundary integral equations, one for displacements and the other for its normal derivative is exploited for the proposed BEM formulation. The global boundary of the analyzed domain is discretized into quadratic line and quadrilateral elements for 2D and 3D problems, respectively. Representative 2D and 3D numerical examples are presented to illustrate the method, demonstrate its accuracy and efficiency and assess the gradient effect on the response.

## Cite This Article

APA Style
Papacharalampopoulos, A., Karlis, G.F., Charalambopoulos, A., Polyzos, D. (2010). BEM solutions for 2D and 3D dynamic problems in mindlin's strain gradient theory of elasticity. Computer Modeling in Engineering & Sciences, 58(1), 45-74. https://doi.org/10.3970/cmes.2010.058.045
Vancouver Style
Papacharalampopoulos A, Karlis GF, Charalambopoulos A, Polyzos D. BEM solutions for 2D and 3D dynamic problems in mindlin's strain gradient theory of elasticity. Comput Model Eng Sci. 2010;58(1):45-74 https://doi.org/10.3970/cmes.2010.058.045
IEEE Style
A. Papacharalampopoulos, G.F. Karlis, A. Charalambopoulos, and D. Polyzos "BEM Solutions for 2D and 3D Dynamic Problems in Mindlin's Strain Gradient Theory of Elasticity," Comput. Model. Eng. Sci., vol. 58, no. 1, pp. 45-74. 2010. https://doi.org/10.3970/cmes.2010.058.045

Copyright © 2010 The Author(s). Published by Tech Science Press.
This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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