Silindirik olmayan viskoelastik helisel çubukların karışık sonlu eleman yöntemi ile dinamik analizi

In the case of an elastic material behavior, deformed structure recovers its original shape and size after unloading. The elastic behavior is time independent. The strains measured in a of viscous matrial depend on the speed and intensity of the loading. The viscous behavior is time dependent.Viscoelastic materials exhibit both viscous and elastic effects. In fact, due to internal friction, the material shows some viscous behavior. Thus, for more realistic analysis the viscous behavior should be taken into account. In the literature, There are many models for defining viscoelastic behavior, such as Kelvin, Maxwell and standard model. In this study standard model is prephered due to its suitability for structural analysis. The viscoelastic materials has been used for so long, and they are preffered for specific applications, such as, to support structures, mechanical equipments, vibration isolatars which are used for reducing the external forces e.g. associated with an earthquake or impact forces. In the literature, the studies about viscoelastic isolator have significance for increasing the strength of the structures against the earthquake. For this purpose, viscoelastic helical springs are used to absorb the energy, transfer the forces or reduce the vibration. Helical springs have varios geometries. These may be cylindrical or non-cylindrical, e.g., conical, barrel and hyperboloidal springs. Especially, viscoelastic helices take important place in defence industry. In this thesis, based on Timoshenko beam theory the dynamic analysis of non-cylindrical viscoelastic helices is investigated. Viscoelastic behavior is modelled by using standard model. By applying the Laplace transformation to the functional, it is carried to the frequency domain. Using the correspondence principle, the constitutive equations of the linear viscoelastic material is identified in the frequency domain. Afterward, applying the variational method to the Laplace transformed functional a mixed finite element is generated. Geometrical properties of conical, barrel and hyperboloidal helical rods are calculated based on the exact expressions, e.g., differential arc length and curvatures are determined directly by using the respective axis function of the helical bar. The numerical results obtained after the finite element solution are transformed back to time space by the numerical solution of the modified Durbin's algorithm. This thesis is composed of six chapters. Chapter 1 is about literaure survey. In Chapter 2, a brief explanation about the Laplace transformation and the inverse Laplace transformation algorithm of modified Durbin's algorithm is given. In Chapter 3, the mechanical viscoelatic model, namely the Standard model, and the application of the correspondance principle is explained. In Chapter 4, the noncylindrical helical bar geometry is defined by means of the exact expressions, the functional in Laplace space is derived, the finite element formulation is given. The numerical investigation is presented in Chapter 5. A new mixed finite element approach, based on precise definition of the non-cylindrical helical geometry, is verified with the examples existing elastic problems in the literature. Afterward, a convergenge analysis is performed on a viscoelastic hyperbolic helix and finally some viscoelastic benchmark examples are solved. Through the analysis, the time dependent behavior of the cantilever hyperboloidal helix is investigated for some of the viscoelastic parameters, namely, three different values of retardation time of relaxation function associated with the shear modulus, three different values of the ratio of instantaneous value of relaxation function associated with the shear modulus. Also viscoelastic behaviour of three different cross-sectional areas, all having the same net area, namely, a solid circular section, hollow circular section and a thin-walled hollow circular section are investigated. All the results are either tabulated or given as graphics. Discussion of the results are given in Chapter 6.