Optimization of lumping schemes for plane square quadratic finite element in elastodynamics

The effectiveness of explicit direct time-integration methods is conditioned by using diagonal mass matrix which entails significant computational savings and storage advantages. In recent years many procedures that produced diagonally lumped mass matrices were developed. For example, the row sum method and diagonal scaling method (HRZ procedure) can be mentioned. In this paper, the dispersive properties of different lumping matrices with variable mass distribution for the plane square 8-node serendipity elements are investigated. The dispersion diagrams for such lumping matrices are derived for various Courant numbers, wavelengths and the directions of wave propagation

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

AbstractNumerical 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

Periodic trends and easy estimation of relative stabilities in 11-vertex nido-p-block-heteroboranes and -borates

Density functional theory computations were carried out for 11-vertex nido-p-block-hetero(carba)boranes and -borates containing silicon, germanium, tin, arsenic, antimony, sulfur, selenium and tellurium heteroatoms. A set of quantitative values called “estimated energy penalties” was derived by comparing the energies of two reference structures that differ with respect to one structural feature only. These energy penalties behave additively, i.e., they allow us to reproduce the DFT-computed relative stabilities of 11-vertex nido-heteroboranes in general with good accuracy and to predict the thermodynamic stabilities of unknown structures easily. Energy penalties for neighboring heteroatoms (HetHet and HetHet′) decrease down the group and increase along the period (indirectly proportional to covalent radii). Energy penalties for a five- rather than four-coordinate heteroatom, [Het5k(1) and Het5k(2)], generally, increase down group 14 but decrease down group 16, while there are mixed trends for group 15 heteroatoms. The sum of HetHet′ energy penalties results in different but easily predictable open-face heteroatom positions in the thermodynamically most stable mixed heterocarbaboranes and -borates with more than two heteroatoms

The Use of Euler,s Method for Finite Element Solution of Problems of Viscoplasticity and Creep

Euler,s forward scheme with automatic subincrementation was used for integration of constitutive equations for voscoplasticity and creep. The time step length was set on the basis of an a posteriori error estimate. And number of testing was computed and a perfect match between the converged step length and the Cormeau formula for the citical time step was observed

How the liner material metallurgical texture affects the shaped charge jet break-up time

Since the hollow charge phenomenon was discovered in the 19$^{\rm th}$ century many discoveries have been made that have tumed the shaped charge jet formation and penetration mechanics into a status close to engineering. Still important questions remain to be answered. It was found by trial and error for example that by cold pressing copper to form the liner an increase in the jet break-up time was obtained. It is shown now that this production process prepares the internal metallurgical structure of the liner material for easy formation of shear bands. As a result the frequency of their formation increases, the jet breaks into larger number of fragments and the Vpl parameter value reduces. The evidence bringing to this conclusion is discussed in detail and recommendations for future studies are outlined