Systematic derivation of the fundamental solutions for couple stress theory

Document Type : Original Article


1 Engineering Mathematics Department, Military Technical College, Cairo, EGYPT.

2 Department of Basic Engineering Sciences, Shoubra-Faculty of Engineering, Benha University, EGYPT.

3 Department of Structural Engineering, Cairo University, Giza, EGYPT.



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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