Abstract
The use of the classical Sturm theorem (based on Sturm's sequences) in elementary algorithmic algebra for the determination of the number of distinct real zeros of a polynomial in a real finite or infinite interval, is suggested for making decisions in elementary elasticity problems, including polynomial equations and inequalities. In these cases, the decision really depends on whether a polynomial equation has a real zero or not in a real interval. The use of this method is generalized from elementary problems in computational/algebraic geometry to applied mechanics. The approach is illustrated in four elasticity problems: an elementary straight beam problem above an obstacle (to decide whether the beam comes into contact with the obstacle or not), a straight crack problem under a known loading distribution (to decide whether the crack edges come into contact or not), a problem concerning a stress component in a finite circular elastic medium (to decide whether this component reaches a critical value or not) and finally, a problem concerning the classical caustic about a crack tip in fracture mechanics (to decide whether the caustic is surrounded by the circumference of a concrete circle or not). Additional applications and possibilities are also suggested in brief.
Published Version
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call