ABSTRACT
Solutions to some engineering problems in Cartesian coordinates are obtained by finding appropriate stress functions for plane strain and plane stress conditions. Stress functions in the form of algebraic polynomials are chosen to solve the problems of a retaining wall subjected to hydrostatic pressure, a simply supported beam subjected to uniformly distributed load, and a cantilever beam under end force. The results are compared with those obtained from elementary strength-of-materials solutions. Use of stress functions in the form of trigonometric series is demonstrated by solving plane problems of bars subjected to two equal and opposite forces in the lateral and axial directions. The solutions are obtained by employing the semi-inverse method. The problem of a dam or a retaining wall subjected to pressure due to water or loose material could be considered to be a plane strain problem. Laterally loaded beams are basic components of engineering structures.
