New Algorithm and New shear-lock free finite elements

Dear all,

(1)              Development of shear-lock free finite elements

In this research work, new finite elements based on the Timoshenko beam / Reissner-Mindlin plate theories using novel shape functions, in which a new concept, Convergence Factor (CF), is introduced to accelerate convergence rate and following standard finite element procedure, are developed for the analysis of beams and plates under transverse loads. All these elements are isoparametric and they can be used for the analysis of thin to very thick beams/plates without shear lock problem and special integration scheme for various values of aspect ratios. A comparison study among the finite elements based on the higher order shear deformation theories developed by me and the new finite elements based on the Timoshenko beam / Reissner-Mindlin plate theories is carried out and the following observations are made.

The finite elements based on the higher order shear deformation theories developed by me using standard finite element shape functions (Lagrangian shape functions) estimate the maximum displacement accurately for very thick to moderately thick beams. As the aspect ratio of the beam increases, it converges very slowly to the exact solution. In contrast to this, the finite elements based on the same higher order shear deformation theories using the new shape functions predict the maximum displacement accurately for thin to very thick beams and the convergence rate is faster than the former case.

The performance of the finite elements based on the Timoshenko beam theory for very thick to thin beam is excellent and similar observations are made in the case of plates also.

(2)                 Numerical Algorithm

Recently I have developed an efficient numerical algorithm based on the Newton-Raphson  method to find out the roots of real-valued functions in one variable.  Many real valued functions were tested to assess the performance of the algorithm and it shows that the convergence rate is very faster than the above method. This work will be extended to the problems involving many variables to examine computational efficiency and solution accuracy.

 P.Subramanian