10.1016/j.ijmecsci.2018.04.045

10.1016/j.ijmecsci.2018.04.045 Keywords: This article deals with the exact thermo-mechanical static responses of a curved circular beam by Green’s function Thermo-mechanical loading method. To find the solution, the related governing differential equations are found using the Hamilton’s princi- Circular curved beam ples. They are combined into two six-order ordinary inhomogeneous differential equations. To form the Green’s Green’s function method problem, the adjoint differential operator along with corresponding boundary conditions is found from the inner Adjoint differential problem product calculations. It is noteworthy that the lateral temperature distribution leads to both in-plane and out-of- In-plane and out-of-plane deformations plane deformations. This important point has not been mentioned in the previous studies. Moreover, the radially distributed temperature results in no out-of-plane displacements. Finally, the answers of some numerical tests confirmed the accuracy of the proposed solution method. 1. Introduction In the out-of-plane mode of deformation, Prathap and Naganarayana removed the spurious zero-energy modes by employing assumed consis- Curved beams are very applicable structures in several places due tent shear strain interpolation [11] . With the same technique, Choi and to their high carrying load capacity and beauty. Among various shapes, Lim derived two-nodded and three-nodded general curved beam ele- the simplicity of circular http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

10.1016/j.ijmecsci.2018.04.045

Elsevier — Jun 11, 2020

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Abstract

Keywords: This article deals with the exact thermo-mechanical static responses of a curved circular beam by Green’s function Thermo-mechanical loading method. To find the solution, the related governing differential equations are found using the Hamilton’s princi- Circular curved beam ples. They are combined into two six-order ordinary inhomogeneous differential equations. To form the Green’s Green’s function method problem, the adjoint differential operator along with corresponding boundary conditions is found from the inner Adjoint differential problem product calculations. It is noteworthy that the lateral temperature distribution leads to both in-plane and out-of- In-plane and out-of-plane deformations plane deformations. This important point has not been mentioned in the previous studies. Moreover, the radially distributed temperature results in no out-of-plane displacements. Finally, the answers of some numerical tests confirmed the accuracy of the proposed solution method. 1. Introduction In the out-of-plane mode of deformation, Prathap and Naganarayana removed the spurious zero-energy modes by employing assumed consis- Curved beams are very applicable structures in several places due tent shear strain interpolation [11] . With the same technique, Choi and to their high carrying load capacity and beauty. Among various shapes, Lim derived two-nodded and three-nodded general curved beam ele- the simplicity of circular

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