3D thermoelastic analysis of rotating disks having arbitrary profile based on a variable kinematic 1D finite element method

ABSTRACT A variable kinematic 1D finite element (FE) method is presented for 3D thermoelastic analysis of rotating disks with variable thickness. The principle of minimum potential energy is used to derive general governing equations of the disks subjected to body forces, surface forces, concentrated forces, and thermal loads. To solve the equations, the 1D Carrera unified formulation (CUF), which enables to go beyond the kinematic assumptions of classical beam theories, is employed. Based on the 1D CUF, the disk is considered as a beam, which can be discretized into a finite number of 1D elements along its axis. The displacement field over the beam’s cross section is approximated by Lagrange expansions. This methodology leads to an FE formulation that is invariant with respect to the order of expansions used over the cross sections, and thus the 3D problem reduces to a 1D problem. The effect of the cross section discretization on displacement and stress fields is investigated. Results obtained from this method are in good agreement with the reference analytical and finite difference solutions. The proposed innovative method can be very effective in the thermoelastic analysis of rotating disks.

[2]  Mohammad Saleem,et al.  THERMO ELASTIC ANALYSIS OF A FUNCTIONALLY GRADED ROTATING DISK WITH SMALL AND LARGE DEFLECTIONS , 2007 .

[3]  S S Manson.  Determination of elastic stresses in gas-turbine disks , 1947 .

[4]  Erasmo Carrera,et al.  Vibration Analysis of Thin/Thick, Composites/Metallic Spinning Cylindrical Shells by Refined Beam Models , 2015 .

[5]  Hamid Jahed,et al.  Loading and unloading behaviour of a thermoplastic disc , 2001 .

[6]  S. V. Wong,et al.  Thermoelastic solution of a functionally graded variable thickness rotating disk with bending based on the first-order shear deformation theory , 2009 .

[7]  Lihua You,et al.  Elastic-plastic stresses in a rotating solid disk , 1999 .

[8]  W. Marsden.  I and J , 2012 .

[9]  Vincenzo Vullo,et al.  Elastic stress analysis of rotating converging conical disks subjected to thermal load and having variable density along the radius , 2007 .

[10]  Susana Sterner.  A unified numerical approach for the analysis of rotating disks including turbine rotors , 1992 .

[11]  J. Reddy.  Mechanics of laminated composite plates and shells : theory and analysis , 1996 .

[12]  Erasmo Carrera,et al.  Finite Element Analysis of Structures Through Unified Formulation: Carrera/Finite , 2014 .

[13]  J. Reddy,et al.  Thermo elastic analysis of functionally graded rotating disks with temperature-dependent material properties: uniform and variable thickness , 2009 .

[14]  Abdel Magid Hamouda,et al.  ANALYSIS OF FUNCTIONALLY GRADED ROTATING DISKS WITH VARIABLE THICKNESS , 2008 .

[15]  Sunil Saigal,et al.  A unified numerical approach for the analysis of rotating disks including turbine rotors , 1994 .

[16]  Weiqiu Chen,et al.  Three-dimensional analytical solution for a rotating disc of functionally graded materials with transverse isotropy , 2007 .

[17]  Reza Naghdabadi,et al.  Thermoelastic analysis of a functionally graded rotating disk , 2007 .

[18]  Erasmo Carrera,et al.  A refined one-dimensional rotordynamics model with three-dimensional capabilities , 2016 .

[19]  Vincenzo Vullo,et al.  Elastic stress analysis of non-linear variable thickness rotating disks subjected to thermal load and having variable density along the radius , 2008 .

[20]  B. Sahari,et al.  Mechanical and thermal stresses in a functionally graded rotating disk with variable thickness due to radially symmetry loads , 2009 .

[21]  Erasmo Carrera,et al.  Analysis of Rotor Dynamic by One-Dimensional Variable Kinematic Theories , 2013 .

[22]  Erasmo Carrera,et al.  Variable Kinematic One-Dimensional Finite Elements for the Analysis of Rotors Made of Composite Materials , 2014 .

[23]  Erasmo Carrera,et al.  Refined One-Dimensional Formulations for Laminated Structure Analysis , 2012 .

[24]  Samuel S Manson.  Direct method of design and stress analysis of rotating disks with temperature gradient , 1950 .