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First Principles Derivation of Displacement and Stress Function for Three-Dimensional Elastostatic Problems, and Application to the Flexural Analysis of Thick Circular Plates | ||
| Journal of Computational Applied Mechanics | ||
| مقاله 19، دوره 51، شماره 1، شهریور 2020، صفحه 184-198 اصل مقاله (797.64 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22059/jcamech.2020.295989.471 | ||
| نویسندگان | ||
| Hyginus Nwankwo Onah1؛ Michael Ebie Onyia1؛ Benjamin Okwudili Mama1؛ Clifford Ugochukwu Nwoji1؛ Charles Chinwuba Ike* 2 | ||
| 1Department of Civil Engineering, University of Nigeria, Nsukka, Enugu State, Nigeria | ||
| 2Department of Civil Engineering, Enugu State University of Science and Technology, Enugu State, Nigeria | ||
| چکیده | ||
| In this study, stress and displacement functions of the three-dimensional theory of elasticity for homogeneous isotropic bodies are derived from first principles from the differential equations of equilibrium, the generalized stress – strain laws and the geometric relations of strain and displacement. It is found that the stress and displacement functions must be biharmonic functions. The derived functions are used to solve the elasticity problem of finding stresses and displacement fields in a thick circular plate with clamped edges for the case of uniformly distributed transverse load over the plate domain. Superposition of second to sixth order Legendre polynomials which are biharmonic functions are used in the thick circular plate problem as the stress function with the unknown constants as the parameters to be determined. Use of the stresses and displacement fields derived in terms of the stress and displacement function yielded the stress fields and displacement fields in terms of the unknown constants of the biharmonic stress function. Enforcement of the boundary conditions yielded the unknown constants, leading to a complete determination of the stress and displacement function for the stress fields and the displacement fields. The solutions obtained are comparable to solutions in the technical literature. | ||
| کلیدواژهها | ||
| stress function؛ displacement function؛ biharmonic function؛ three dimensional elasticity problem؛ Legendre polynomial؛ thick circular plate problem؛ stress fields؛ displacement fields | ||
| مراجع | ||
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