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A mesh reduction (regular) perturbation technique was developed to overcome inefficient and unviable analytical and “brute force” numerical solutions for structures with imperfections and for imperfection sensitive structures. Using this perturbation technique, a case study is presented to determine the effects of uncontrolled deviations in temperature on the stability of beam on elastic foundation. The study further explores the effects of imperfections on beams for five independent imperfection patterns, namely variability in initial shape, modulus of elasticity, moment of inertia, foundation stiffness, temperature, and their combined effects. The study demonstrates thermal imperfections behave in the same manner as other non-shape imperfections, while shape imperfections appear to be most sensitive. When thermal and shape imperfections were combined, all other imperfections were shown to have diminished effects.

Efficient regular perturbation solutions for beams subjected to thermal imperfections: a case study