D. Gabriel

Dispersion of elastic waves in the contact-impact problem of a long cylinder

Numerical dispersion of two-dimensional finite elements was studied. The outcome of the dispersion study was verified by the numerical and analytical solutions to the longitudinal impact of two long cylindrical bars. In accordance with the results of the dispersion analysis it was demonstrated that the quadratic elements showed better accuracy than the linear ones.

Stress Accuracy Of Parabolic Finite ElementsIn Contact Problems Analysis

The paper presents the stress distribution errors discovered while analysing contact problems with parabolic finite elements. Usage of parabolic instead of linear finite elements in finite element analysis usually results in more accurate stresses. On the other hand usage of parabolic finite elements would result in jagged stress distribution. The jagged stress distribution occurs using either Penalty function method or Lagrange multiplier method. Stress distribution errors were discovered also in analysis where Gauss integration point positions were used for contact analysis. Series of contact problems analyses with special attention to stress accuracy will be presented in the paper. Presented contact problems were analysed with different commercial and non-commercial finite element systems. Obtained results of contact problems analysis with parabolic finite elements will be compared to contact problems analysis with linear finite elements. Results of contact problems analysis using finite elements will then be compared to results obtained with theoretical solution or experimental data. The possible reasons for stress errors will be discussed and some workaround for this problem will be proposed. Transactions on Engineering Sciences vol 24,

ESTIMATION OF STABILITY LIMIT BASED ON GERSHGORIN'S THEOREM FOR EXPLICIT CONTACT-IMPACT ANALYSIS SIGNORINI PROBLEM USING BIPENALTY APPROACH

Abstract. The stability properties of the bipenalty method presented in Reference [4] is studied in application to one-dimensional bipenalized Signorini problem. The attention has been paid on the critical Courant numbers estimation based on Gershgorin’s theorem. It is shown that Gershgorin’s formula overestimates maximum eigenfrequency for all penalty ratios with exception of the critical penalty ratio. Thus, smaller safer values of critical Courant numbers are obtained in comparison with exact ones calculated from the solution of eigenvalue problem.

STUDIES IN NUMERICAL STABILITY OF EXPLICIT CONTACT-IMPACT ALGORITHM TO THE FINITE ELEMENT SOLUTION OF WAVE PROPAGATION PROBLEMS

Abstract. In dynamic transient analysis, recent comprehensive studies have shown that using mass penalty together with standard stiffness penalty, the so-called bipenalty technique, preserves the critical time step in conditionally stable time integration schemes. In this paper, the bipenalty approach is applied in the explicit contact-impact algorithm based on the pre-discretization penalty formulation. The attention is focused on the stability of this algorithm. Specifically, the upper estimation of the stable Courant number on the stiffness and mass penalty is derived based on the simple dynamic system with two degrees-of-freedom. The results are verified by means of the dynamic Signorini problem, which is represented by the motion of a bar that comes into contact with a rigid obstacle.

Symmetry preserving algorithm for a dynamic contact-impact problem

In the finite element method, the contact constraints can be introduced either before or after the fi- nite element discretization has been performed, leading to the so-called pre-discretization or postdiscretization techniques [1]. In the paper [2] we focused on the pre-discretization approach, showing this technique to lead naturally to the use of surface integration points as contactors. It was shown that the proposed method preserved the symmetry of the algorithmic approximation with respect to contact boundaries. On the outcome there was nothing like a master or slave definition of contact surface.