Fıçı Tipi Doğrusal Viskoelastik Helislerin Dinamik Davranışı

Konferans Bildirisi -- Teorik ve Uygulamalı Mekanik Türk Milli Komitesi, 2015Conference Paper -- Theoretical and Applied Mechanical Turkish National Committee, 2015Bu çalışmada, viskoelastik parametrelerin dairesel kesitli fıçı (barrel) tipi doğrusal viskoelastik helislerin dinamik davranışı üzerindeki etkileri Timoshenko çubuk kuramını esas alan bir karışık sonlu eleman algoritması kullanılarak incelenmiştir. Helisin iki ucundan tutulu ve dinamik olarak adım tipinde düzgün yayılı yük etkisinde olduğu varsayılmıştır. Doğrusal viskoelastik malzemede, kayma şekil değiştirmelerinin standart modele ve hacimsel şekil değiştirmelerinin ise Kelvin modele uygun davranış gösterdiği kabul edilmiş ve karşıgelim ilkesi kullanılarak malzeme özellikleri çözüm algoritmasına eklenmiştir. Helis probleminin çözümü Laplace uzayında gerçekleştirilmiş ve sonuçlar geliştirilmiş Durbin dönüşüm algoritması kullanılarak zaman uzayına taşınmıştır. Doğrusal viskoelastik fıçı tipi helislerin dinamik davranışına ait sayısal sonuçlar detaylı olarak irdelenmiştir.In this study, the effects of viscoelastic parameters on the dynamic behavior of a linear viscoelastic circular cross-sectioned barrel type helix is investigated by using the mixed finite element method based on the Timoshenko beam theory. The helix is assumed to be fixed from both ends and subjected to dynamic step type of vertical distributed loading. The linear viscoelastic material exhibits standard type of distortional behavior and Kelvin type of bulk compressibility, and, the material properties are implemented into the formulation through the use of the correspondence principle. The solutions of the helix problem are obtained in the Laplace space and the results are transformed back to the time domain numerically by means of the Modified Durbin's transformation algorithm. Numerical results for the dynamic behavior of linear viscoelastic barrel type helix are discussed extensively

Konik Tipi Viskoelastik Helislerin Farklı Yüklemeler Altındaki Dinamik Davranışı

Konferans Bildirisi -- Teorik ve Uygulamalı Mekanik Türk Milli Komitesi, 2015Conference Paper -- Theoretical and Applied Mechanical Turkish National Committee, 2015Bu çalışmanın amacı, Timoshenko çubuk kuramına dayalı karışık sonlu eleman formülasyonu kullanılarak daire kesitli konik tipi doğrusal viskoelastik helislerin düzgün yayılı yük etkisinde dinamik davranışını araştırmaktır. Doğrusal viskoelastik malzemenin kayma modülü standart model ile tanımlanmış ve Poisson oranı elastik alınmıştır. Sonlu eleman çözümlemesi Laplace uzayında gerçekleştirileceği için, viskoelastik malzeme özellikleri karşıgelim ilkesi kullanılarak belirlenmiş ve. Laplace uzayında elde edilen sonuçlar, geliştirilmiş Durbin dönüşüm algoritması kullanılarak zaman uzayına taşınmıştır. Örnek problemlerde iki farklı sınır koşulu kullanılmıştır: bir ucundan tutulu diğer ucu serbest helis ve iki ucu tutulu helis. Her iki durum için adım ve impulsif tiplerinde (dikdörtgen, sinüzoidal, dik üçgen ve üçgen formlarında olmak üzere) düşeyde etkiyen dinamik yayılı yüklemeler etkisindeki helislerin dinamik davranışı incelenmiştir.The objective of this study is to investigate the dynamic behavior of a linear viscoelastic conical type helical bar having a solid circular cross-section subjected to vertical distributed loading by using the mixed finite method based on Timoshenko beam theory. It is assumed that, the linear viscoelastic material exhibits the standard type of distortional behavior while having elastic Poisson's ratio. The finite element analysis is carried out in Laplace space, the material properties are implemented into the formulation through the use of the correspondence principle. The results are transformed back to the time domain numerically by using of the Modified Durbin's transformation algorithm. Two different cases of boundary conditions are considered in the sample problems: helix fixed from one end (cantilevered) and helix fixed from two ends. For each case, the dynamic responses of the helices are determined for step and impulsive types (having rectangular, sinusoidal, right triangular and triangular forms) of dynamic vertical distributed loadings

Limit angular velocities of variable thickness rotating disks

Elastic and plastic limit angular velocities are calculated for rotating disks of variable thickness in power function form. Analytical solution is obtained and used to calculate elastic limit angular velocities of variable thickness rotating annular disks and annular disks with rigid inclusion. An efficient numerical solution procedure is designed and used to obtain the elastic limit angular velocities of variable thickness rotating solid disks. Von Mises yield criterion and its flow rule is used to estimate plastic limit angular velocities. Both linear and nonlinear hardening material behaviors are treated numerically. The results are verified by comparing with those of uniform thickness rotating solid disks available in the literature. Elastic and plastic limit angular velocities are found to increase with the reduction of the disk thickness at the edge as well as the reduction in the disk mass due to the shape of the profile

A unified approach for the formulation of interaction problems by the boundary element method

A unified formulation is presented, based on boundary element method, in a form suitable for performing the interaction analyses by substructure method for solid-solid and soil-structure problems. The proposed formulation permits the evaluation of all the elements of impedance and input motion matrices simultaneously at a single step in terms of system matrices of the boundary element method without solving any special problem, such as, unit displacement or load problem, as required in conventional methods. It eliminates further the complicated procedure and the need for using scattering analysis in the evaluation of input motion functions. To explain the formulation, it is first given for an inclusion interacting with an infinite surrounding medium under the influence of a seismic input, where both the inclusion and surrounding medium are treated as viscoelastic. It is shown that the formulation for a rigid inclusion may be obtained from that for flexible inclusion as a special case through a transformation. Then, the formulation is extended to other types of interaction problems: a multi-inclusion problem and an interaction problem involving a foundation embedded in a viscoelastic half-space. It is found that the proposed formulation remains essentially the same for all kinds of interaction problems and it can be used not only in regular interaction analysis, but also in the analysis involving diffraction of waves in a medium containing holes. Copyright (c) 2005 John Wiley & Sons, Ltd

Stress distributions in energy generating two-layer tubes subjected to free and radially constrained boundary conditions

Analytical solutions are obtained for thermally induced axisymmetric elastic and elastic-plastic deformations in heat generating composite tubes having a free inner and a radially constrained outer boundaries. Tresca's yield condition and its associated flow rule are used to determine the elastic-plastic response of the assembly. Depending on the physical properties of the materials used, eight different plastic regions with different mathematical forms of the yield condition may occur in the assembly. The closed form solutions for these plastic regions are obtained by assuming linearly hardening material behavior. Various numerical examples are handled using thermal and mechanical properties of real engineering materials

Silindirik Helislerin Farklı Viskoelastik Modellemelerinin SE Analizi

Konferans Bildirisi -- Teorik ve Uygulamalı Mekanik Türk Milli Komitesi, 2011Conference Paper -- Theoretical and Applied Mechanical Turkish National Committee, 2011Bu çalışmada, dik kesiti kare ve daire olan, silindirik viskoelastik helislerin farklı viskoelastik modeller için Timoshenko çubuk varsayımı kullanılarak sonlu eleman analizi yapılmıştır. Fourier dönüşüm yöntemi kullanılarak yapılan analizde, helisel viskoelastik çubuklar için fonksiyonel Fourier uzayında elde edilmiştir. İki düğüm noktalı eğrisel çubuk elemanı için, eleman matrisleri elde edilmiş ve Fourier uzayında karışık sonlu eleman çözümü yapılarak, zaman uzayına geri dönüş için Fast Fourier dönüşümü (FFT) kullanılmıştır. Silindirik helis problemi Kelvin ve standart modeller için çözülmüştür

Dynamic analysis of linear viscoelastic cylindrical and conical helicoidal rods using the mixed FEM

The objective of this study is to investigate the influence of the rotary inertia on dynamic behavior of linear viscoelastic cylindrical and conical helixes by means of the Laplace transform-mixed finite element formulation and solution. The element matrix is based on the Timoshenko beam theory. The influence of rotary inertias is considered in the dynamic analysis, which is original in the literature. Rectangular, sine and step type of impulsive loads are applied on helices having rectangular cross-sections with various aspect ratios. The Kelvin and standard models are used for defining the linear viscoelastic material behavior; and by means of the correspondence principle (the elastic-viscoelastic analogy), the material parameters are replaced with their complex counterparts in the Laplace domain. The analysis is carried out in the Laplace domain and the results are transformed back to time space numerically by modified Durbins algorithm. First, the solution algorithm is verified using the existing open sources in the literature and afterwards some benchmark examples such as conical viscoelastic rods are handled. © 2014 Elsevier Ltd.36130 National Council for Scientific Research: 111M308This research is supported by the Scientific and Technological Research Council of Turkey under Project no. 111M308 and by the Research Foundation of ITU under Project no. 36130 . These supports are gratefully acknowledged by the authors