Miloslav Okrouhlík

Influence of 3D effects on the efficiency of percussive rock drilling

Abstract The aim is to investigate the influence of 3D effects on the efficiency of three processes for percussive rock drilling, viz., hammer drilling, down-the-hole drilling and churn drilling, each based on the use of tube-shaped members. A 3D axisymmetric finite element study is carried out for systems with idealised geometries. The efficiencies obtained are compared with formulae obtained from 1D analyses. It is found that the efficiencies based on 3D analyses are generally slightly lower than those based on 1D analyses. The difference is typically about 4% for hammer drilling, of the order of a percent or less for down-the-hole drilling, and practically non-existent for churn drilling. In the case of hammer drilling, the reduction of efficiency due to 3D effects is found to be slightly larger for tubes with relatively thin walls than for tubes with massive cross-sections. The lower efficiency in 3D is partially due to contributions to the kinetic and potential energies from components of velocity and stress which do not promote the performance of work on the rock. It is concluded that from a practical point of view, there is no need of 3D corrections of the 1D results for efficiency except possibly in the case of hammer drilling.

A contribution to the study of dispersive properties of one-dimensional Lagrangian and Hermitian elements

Abstract Dispersive properties of one-dimensional Lagrangian and Hermitian finite elements with higher-order polynomial shape functions are derived and presented. The available frequency regions of these elements and their save applicability in nonstationary dynamics is quantitatively ascertained. It is shown that for elastic bars modelled by Lagrangian elements of equal lengths all the necessary information pertaining the band-pass and cut-off frequencies is embedded in the mass and rigidity matrices of these elements. For Hermitian elements the existence of spurious modes is shown.

Dispersion and Time Integration Schemes in Finite-Element Analysis — A Practical Pictorial Manual

Using a simple physical model, i.e. propagation of stress waves in a thin elastic rod, we can show how the equivalent finite-element (FE) model can be treated by various methods (the central difference method, and the Newmark and Houbolt methods) to secure numerical integration in time and what differences, with respect to an ideal continuum model, can be expected. The FE histories of displacements, velocities, accelerations and strains, presented in pictorial form, are compared with those in an idealized elastic continuum. Differences due to time and space discretizations are shown and explained. Matlab programs are available at http://www.it.cas.cz/files/u1784/mtl.zip. Readers (especially novice finite-element users) are urged to modify the input parameters, observe the invoked changes and try to understand why and how they arise.

Why is the Stress Tensor Symmetric

The paper considers the meaning of stress and of other mechanical variables that are consensually defined and cannot be described or measured directly. Further, the stress tensor symmetry is discussed.

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.

Pollution‐free energy production by a proper misuse of finite element analysis

Notes that what applied scientists in classical continuum mechanics are doing is based on knowledge established by Newton, Cauchy, Euler, Rayleigh and others, and no really fundamental laws or principles in continuum mechanics have been “discovered” since. Newtonian mechanics provides a vital tool, which is still valid in all manners of ways from engineering to astronomy. Illustrates that we are not inventing completely new concepts of the world – rather, we are dealing with more and more precise models designed within the scope of Newtonian continuum mechanics. Nowadays, material non‐linearities, large strains and deformations, high‐velocity impact problems and others are routinely treated by sophisticated discrete tools, for example boundary elements, finite elements as expressed in Eulerian, Lagrangian and/or ALE formulations. Notes that modern methodologies are based on progress that is constantly being reported in finite element technology areas and that we should not believe in free‐energy production.