This paper presents an analytical method for determining the bending stresses and deformations in prismatic, noncircular profile shafts with trochoidal cross sections. The so-called higher trochoids can be used as form-fit shaft-hub connections. Hybrid (mixed) higher trochoids (M-profiles) were developed for the special application as a profile contour for the form-fit shaft and hub connections in an earlier work by the author. M-profiles combine the advantages of the two standardised polygonal and spline contours, which are used as shaft-hub connections for the transmission of high torques. In this study, the geometric and mechanical properties of the higher hybrid trochoids were investigated using complex functions to simplify the calculations. The pure bending stress and shaft deflection were determined for M-profiles using bending theory based on the theory of mathematical elasticity. The loading cases consisted of static and rotating bends. Analytical, numerical, and experimental results agreed well. The calculation formulas developed in this work enable reliable and low-cost dimensioning with regard to the stresses and elastic deformations of profile shafts subjected to bending loads.
Problem statement: Improper understanding of material behavior prevents the efficient and correct usage of available materials and consequently, increases the construction and maintenance costs and even unsuitable construction. Considering the necessity of exact investigation about material behavior, several researches have been carried out in this field but the majority of these researches did not propose a general method for prediction of granular material behavior. Furthermore, many of the methods proposed by researchers are not able to present the properties such as the orientation of failure mechanism of propagating plasticity in materials. Approach: In this study, a general method was proposed for multi-laminate simulation to predict the behavior of materials. The general applicability of this method for prediction of granular material is one of its significant advantages. The study was carried out in the framework of multi-plane pattern which is able to predict anisotropic behavior, consider the effect of stress and strain axis rotations in plasticity, consider the semi-micro mechanical history and finally predict the orientation of failure mechanism. The method was presented in a matter that there is no limitation for different shapes of stress-strain curves. Results: It was concluded that using this method, fundamental properties of material such as material fracture, orientation of failure, anisotropic behavior of material, separation of behavior in several planes and rotation of principle axis of stress and strain during nonlinear behavior can be determined. Conclusion/Recommendations: This method can be used for complicated material behavior simulation under seismic loading, cyclic loading or fatigue effects. For future works, the method can be extended by increasing the number of planes. Higher-order equations can also be used to have a more accurate approximation of stress-strain curve.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.