Abstract
This chapter is dedicated to the study of linear and nonlinear kinematics of elastic helicoidal beams and pretwisted (helicoidal) strips, their stress state, and specific rigidities. The pretwisted strip is an effective micronanostructural realization of the elastic helicoidal beams. We also evaluate the kinematics options of quasi-helicoids with coiled ribbon. The structure of naturally pretwisted strips was first introduced in the year 1888 by J. Perry, who attempted unsuccessfully to develop a theoretical model of the device. However, he predicted a very wide application of this system. Now, we are using it for different precision measuring systems and for modeling DNA molecules with explicit functional helical structure, as well. The author started scientific research of these structures back in the 1960s. In this chapter, we develop the mathematical apparatus for linear and nonlinear helicoidal sensors that we use for explicit functional helicoidal models (EFHM or, briefly, EHM) of DNA molecules presentation, and their parameters calculation.
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