Stochastic strength analysis of compression headless screw

Abstract

This article deals with strength and stiffness analysis of headless screw. This issue was solved in cooperation with engineering industry and doctors. The problem was solved using a stochastic approach, which utilizes the field of random events (simulations), which are applied for determination of input values. The prototype of headless (Herbert) screw Ti4.0/1.4x30/75 was used for solving this problem. Mathematical equations for analytical calculation of the maximal equivalent stress in screw were established. This issue is statically indeterminate problem in compressive and tensile stresses and needs one more equation (i.e. the condition of deformation), which describes relationship between extension of screw and contraction of bone. Resulting values are not defined for one specific model, but the simulation is taking into account a large amount of random samples (specifically 5x10(6) random simulations), which are distributed by bounded histograms. Furthermore, the probabilistic functions of simulated screw were determined. Due to stochastic strength analysis of headless screw, it meets reliability conditions for practical application in osteosynthetic treatment, see [Frydrysek 2016]