Systematic derivation of the fundamental solutions for couple stress theory
El-metwaly, A., Kamal, M., Rashed, Y. (2023). Systematic derivation of the fundamental solutions for couple stress theory. EKB Journal Management System, 20(20), 1-7. doi: 10.1088/1742-6596/2616/1/012001
A R El-metwaly; M A Kamal; Y F Rashed. "Systematic derivation of the fundamental solutions for couple stress theory". EKB Journal Management System, 20, 20, 2023, 1-7. doi: 10.1088/1742-6596/2616/1/012001
El-metwaly, A., Kamal, M., Rashed, Y. (2023). 'Systematic derivation of the fundamental solutions for couple stress theory', EKB Journal Management System, 20(20), pp. 1-7. doi: 10.1088/1742-6596/2616/1/012001
El-metwaly, A., Kamal, M., Rashed, Y. Systematic derivation of the fundamental solutions for couple stress theory. EKB Journal Management System, 2023; 20(20): 1-7. doi: 10.1088/1742-6596/2616/1/012001

Systematic derivation of the fundamental solutions for couple stress theory

International Conference on Aerospace Sciences and Aviation Technology
Volume 20, Issue 20, May 2023, Page 1-7  XML PDF (1.57 MB)
Document Type: Original Article
DOI: 10.1088/1742-6596/2616/1/012001
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Authors
A R El-metwaly email 1; M A Kamal2; Y F Rashed3
1Engineering Mathematics Department, Military Technical College, Cairo, EGYPT.
2Department of Basic Engineering Sciences, Shoubra-Faculty of Engineering, Benha University, EGYPT.
3Department of Structural Engineering, Cairo University, Giza, EGYPT.
Abstract
Classical elasticity theory failed to produce accurate results given in agreement with the experimental results. As this theory fails at stress concentration near the gaps or holes, or materials with significant microstructure contributions as soil, composite material, and polymer material generally in aerospace materials. In order to improve accuracy, the consistent couple stress theory is used. In the consistent couple stress theory, the microrotation and macro rotation are equal, where the macro rotation is half the curl of displacement, and the couple stress tensor is skew-symmetric. In this paper, the fundamental solutions for couple stress elasticity are derived in a systematic way via the H¨ormander technique. The used technique is characterized by its ease and also develops the Galerkin tensor used in many applications, for example, the transformation of domain integral, computing the body force in the domain without discretization. All necessary kernels for displacements and tractions are derived and given in terms of a generalized Galerkin tensor for further use.
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