Eytan Kochavi

Numerical solution of field problems by nonconforming Taylor discretization

Abstract An algorithm for the numerical solution of field problems is presented. The method is based on expanding the unknown function in a Taylor series about some nodal points so that the coefficients of the series for the various nodes are considered as unknowns. Discrepancy between the values resulting from Taylor expansions about distinct nodes is allowed if it is on the same order of magnitude as the estimated error resulting from the discretization. This enables considerable savings in computation effort in addition to the advantage of specifying the accuracy of the obtained solution. Geometrical flexibility, which enables handling complex boundaries for a large variety of field problems, is another advantage of the proposed scheme. The algorithm is applied to nonlinear steady-state heat-conduction. A test case is treated numerically, and for the evaluation of the scheme the results are compared with the analytical solution.

Modified algorithms for nonconforming taylor discretization

Abstract Algorithms for solving partial differential equations which extend previous applications of the nonconforming Taylor discretization method (NTDM) are presented. In one modification the number of interrelated grid points is variable, thus enabling additional geometric flexibility. Another modification is the approximation of the governing differential equation using the method of weighted residuals. A simple one-dimensional test case with a known analytic solution is solved using this code. The results demonstrate that precision is enhanced when using the method of weighted residuals with an increased number of interrelated points. The algorithm is applied as a general purpose two-dimensional code for nonlinear steady state heat-conduction. Two-dimensional examples with complex geometry and boundary conditions are then solved both by the NTDM and by the finite elements method (FEM). The results obtained by the two methods are compared.

Small-Scale Blast Wave Experiments by Means of an Exploding Wire

The effort invested in improving our understanding of the physics of high energy explosion events has tremendously increased in the past few decades. Moreover, the dramatic increase in computer capabilities over the last two decades made the numerical simulation approach the dominant tool for investigating blast wave related phenomena and their effects. However, both large- and small-scale field tests are still in use. In the following, we present an experimental tool capable of better resolving and studying the blast–structure interaction phenomenon. In addition, this experimental tool can assist in validating numerical simulations of these phenomena prior to applying them to simulate large-scale events. The experimental tool uses an exploding wire technique to generate small-scale cylindrical and spherical blast waves. This approach permits safe operation, high repeatability, and usage of advanced diagnostic systems that cannot be used in large-scale field experiments. The system was calibrated using an analytical model, an empirical model, and a numerical simulation. To ensure that spherical blast geometry was achieved, a set of free air blast experiments in which high-speed photography was used to monitor the blast wave structure was conducted. Furthermore, by using similitude analysis the results obtained from small-scale experiments can be applied to full-scale problems. It has been clearly shown that an exploding wire system offers an inexpensive, repeatable, safe, easy to operate, and effective experimental tool for studying phenomena involving blast–structure interactions.

Exploration of Methods in the Exploding Wire Technique for Simulating Large Blasts

Small-scale modeling of explosive events has become an important tool in the investigation of blast wave-structure interactions. In this approach, a full-scale model is miniaturized and subjected to “gram-scale” explosions from detonated micro-charges. While offering a cheaper, faster, and ultimately more manageable alternative to full-scale field tests, small-scale testing also offers better reliability and accuracy in more complex scenarios where numerical simulations become limited. Nevertheless, small-scale experiments introduce other difficulties due to the reliance on the well-known Cranz-Hopkinson “cube-root” scaling law. This scaling relationship is suitable for self-similar open-field experiments but does not necessarily apply to urban scenarios. Additionally, chemical explosive charges of such small quantities might be susceptible to changes in parameters such as the explosive compound compression strength, the humidity of the explosive and of the surrounding atmosphere, the method of ignition, etc. Logistically, the handling and preparing of the experimental setup with these small chemical explosives requires specially trained personnel and permits. To overcome these challenges, the exploding wire (EW) technique offers an elegant substitute to using small chemical charges in scaled-down modeling.

Numerical Modeling of Composite Concrete Walls

Dynamic tests of three reinforced concrete samples and six Dynablok samples were performed in the blast simulator facility at the University of California San-Diego (UCSD). The purpose of these tests was to evaluate the performance of a novel protective wall design. These tests were numerically simulated at the Protective Technologies Research and Development Center (PTR&DC) of the Ben-Gurion University (BGU) in Beer-Sheva, Israel. The simulations were carried out using two commercial hydro-codes: LS-Dyna and Dytran. The purpose of these simulations was to calibrate the parameters of the material models available in the above codes. Once calibrated, the simulation results showed good agreement with the test results for largely deflected yet moderately damaged specimens.Copyright

Evaluation of Numerical Methods for Simulation of Weak Impact

ABSTRACT An elastic cantilever beam subjected to weak impact is investigated with focus on its ability to absorb the impact energy. It was found that the location of impact along the beam has a significant influence on the kinetic energy absorbed. It was established in both, using an experimental setup and numerical computations. A reduced degrees of freedom analytical model of this simple continuous system is analyzed in order to explain its quite complicated behavior. The same impact spot, at which the maximum impact energy was absorbed, was predicted by the analytical model. At this location 90% of the kinetic energy is absorbed in the form of elastic beam vibrations. The results of this demonstration may be used for designing an elastic kinetic energy absorbing system. INTRODUCTION There are many applications for which mechanical systems are designed to absorb the impact energy. As in cars that should provide safety for passengers during impact, or in casks used for safe transportation of hazardous materials. In such applications it is common to use sacrificial parts of the structure which undergo permanent plastic deformation. However, in cases where a system has to sustain a large number of repeated impacts, the absorbing part is limited to the elasticity of the material. In this work we suggest and examine a very basic and simple system, namely, an elastic cantilever beam subjected to an impacting weight. To effectively describe the amount of kinetic energy absorbed by the beam during impact we make use of the widely used term, restitution coefficient. This is the ratio of the final to the initial relative velocities between two bodies involved in an impact. Particularly, when a weight bounces from an elastic foundation the restitution coefficient is the absolute ratio of the rebound to the impact velocities. This provides a simple and meaningful measure for the amount of elastic energy absorbed by the elastic substance. When a sufficiently heavy weight interacts with an elastic cantilever beam the process will possibly involve a sequence of many short impacts. A discussion concerning the dynamics of repeated impacts is given by [1,2] who defines an impact oscillator as a system which is driven in some way and which also undergoes intermittent sequence of contacts with motion limiting constraints. In [3] the behavior of a forced one-dimensional impact oscillator is investigated. In agreement with the above-mentioned works, we find that during the interaction period, the motions of both the weight and the beam are extremely complicated and strongly depend on the initial conditions and the local properties at the contact area. We further note that [4,5] mention three primary vibrations. In both works it is concluded that during weak impacts the amount energy dissipated due to the generation of elastic waves is negligible.