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Single variable-based unified numerical model for plane elastic problems of stress analysis in Cartesian and polar coordinate systems

Published Online:pp 311-341

A unified numerical model for stress analysis of plane problems of structural mechanics in Cartesian and polar coordinate systems is presented. The traditional two-variable problem of stress analysis is reduced to a single-variable problem through the use of a scalar potential function defined in terms of the displacement components. The resulting mathematical formulations for Cartesian and the polar coordinate systems differ significantly in terms of derivatives and coefficients present. However, they are discretised in a fashion so that they can be expressed as a single set of difference equations applicable to both coordinate systems. The resulting unified numerical model handles the problems of straight and curved geometries using Cartesian and polar coordinate systems, respectively. The model is validated against the analytical solutions of known problems in both coordinate systems. Finally, the effects of the initial curvature on stresses and displacements in both ends fixed beams with and without intermediate supports are discussed.


unified numerical model, stress analysis, plane problems of elasticity, finite-difference method, effect of curvature, both ends fixed beam, intermediate support