Two-dimensional isostatic meshes in the finite element method

In a Finite Element (FE) analysis of elastic solids several items are usually considered, namely, type and shape of the elements, number of nodes per element, node positions, FE mesh, total number of degrees of freedom (dot) among others. In this paper a method to improve a given FE mesh used for a particular analysis is described. For the improvement criterion different objective functions have been chosen (Total potential energy and Average quadratic error) and the number of nodes and dof's of the new mesh remain constant and equal to the initial FE mesh. In order to find the mesh producing the minimum of the selected objective function the steepest descent gradient technique has been applied as optimization algorithm. However this efficient technique has the drawback that demands a large computation power. Extensive application of this methodology to different 2-D elasticity problems leads to the conclusion that isometric isostatic meshes (ii-meshes) produce better results than the standard reasonably initial regular meshes used in practice. This conclusion seems to be independent on the objective function used for comparison. These ii-meshes are obtained by placing FE nodes along the isostatic lines, i.e. curves tangent at each point to the principal direction lines of the elastic problem to be solved and they should be regularly spaced in order to build regular elements. That means ii-meshes are usually obtained by iteration, i.e. with the initial FE mesh the elastic analysis is carried out. By using the obtained results of this analysis the net of isostatic lines can be drawn and in a first trial an ii-mesh can be built. This first ii-mesh can be improved, if it necessary, by analyzing again the problem and generate after the FE analysis the new and improved ii-mesh. Typically, after two first tentative ii-meshes it is sufficient to produce good FE results from the elastic analysis. Several example of this procedure are presented.

Coupled Biomechanical Response of the Cornea Assessed by Non-Contact Tonometry. A Simulation Study

The mechanical response of the cornea subjected to a non-contact air-jet tonometry diagnostic test represents an interplay between its geometry, the corneal material behavior and the loading. The objective is to study this interplay to better understand and interpret the results obtained with a non-contact tonometry test. A patient-specific finite element model of a healthy eye, accounting for the load free configuration, was used. The corneal tissue was modeled as an anisotropic hyperelastic material with two preferential directions. Three different sets of parameters within the human experimental range obtained from inflation tests were considered. The influence of the IOP was studied by considering four pressure levels (10–28 mmHg) whereas the influence of corneal thickness was studied by inducing a uniform variation (300–600 microns). A Computer Fluid Dynamics (CFD) air-jet simulation determined pressure loading exerted on the anterior corneal surface. The maximum apex displacement showed a linear variation with IOP for all materials examined. On the contrary, the maximum apex displacement followed a cubic relation with corneal thickness. In addition, a significant sensitivity of the apical displacement to the corneal stiffness was also obtained. Explanation to this behavior was found in the fact that the cornea experiences bending when subjected to an air-puff loading, causing the anterior surface to work in compression whereas the posterior surface works in tension. Hence, collagen fibers located at the anterior surface do not contribute to load bearing. Non-contact tonometry devices give useful information that could be misleading since the corneal deformation is the result of the interaction between the mechanical properties, IOP, and geometry. Therefore, a non-contact tonometry test is not sufficient to evaluate their individual contribution and a complete in-vivo characterization would require more than one test to independently determine the membrane and bending corneal behavior.

Effects of Fe addition on the mechanical and thermo-mechanical properties of SiC/FeSi2/Si composites produced via reactive infiltration

Remaining silicon in SiC-based materials produced via reactive infiltration limits their use in high-temperature applications due to the poor mechanical properties of silicon: low fracture toughness, extreme fragility and creep phenomena above 1000 °C. In this paper SiC–FeSi2 composites are fabricated by reactive infiltration of Si–Fe alloys into porous Cf/C preforms. The resulting materials are SiC/FeSi2 composites, in which remaining silicon is reduced by formation of FeSi2. For the richest Fe alloys (35 wt% Fe) a nominal residual silicon content below 1% has been observed. However this, the relatively poor mechanical properties (bending strength) measured for those resulting materials can be explained by the thermal mismatch of FeSi2 and SiC, which weakens the interface and does even generate new porosity, associated with a debonding phenomenon between the two phases.

Influence of drill speed and feed rate on bone damage

Implant failures and postoperative complications are often associated to the bone drilling. Estimation and control of drilling parameters are critical to prevent mechanical damage to the bone tissues. For better performance of the drilling procedures, it is essential to understand the mechanical behaviour of bones that leads to their failures and consequently to improve the cutting conditions. This paper investigates the effect of drill speed and feed-rate on mechanical damage during drilling of solid rigid foam materials, with similar mechanical properties to the human bone. Experimental tests were conducted on biomechanical blocks instrumented with strain gauges to assess the drill speed and feed-rate influence. A three-dimensional dynamic finite element model to predict the bone stresses, as a function of drilling conditions, drill geometry and bone model, was developed. These simulations incorporate the dynamic characteristics involved in the drilling process. The element removal scheme is taken into account and allows advanced simulations of tool penetration and material removal. Experimental and numerical results show that generated stresses in the material tend to increase with tool penetration. Higher drill speed leads to an increase of von-Mises stresses and strains in the solid rigid foams. However, when the feed-rate is higher, the stresses and strains are lower. The numerical normal stresses and strains are found to be in good agreement with experimental results. The models could be an accurate analysis tool to simulate the stresses distribution in the bone during the drilling process.

Refinement of finite element analysis of automobile structures under crash loading. Volume I. Summary final report.

National Highway Traffic Safety Administration, Washington, D.C.

A finite element scheme for shock capturing /

At head of title: "In-house Laboratory Independent Research Program."

Finite element modeling of motor vehicles. Protocol for developing INGRID data input desks for DYNA3D computer code. Final report.

Federal Highway Administration, Office of Safety and Traffic Operations Research Development, McLean, Va.

Refinement of finite element analysis of automobile structures under crash loading. Volume II. Final technical report.

National Highway Traffic Safety Administration, Washington, D.C.

Validation and application of the WRECKER nonlinear finite element program in analyzing vehicle side structures. Vol. I - summary report. Final report.

National Highway Traffic Safety Administration, Washington, D.C.

Validation and application of the WRECKER nonlinear finite element program in analyzing vehicle side structures. Vol. II - technical report. Final report.

National Highway Traffic Safety Administration, Washington, D.C.

Rapid solution of finite element equations on locally refined grids by multi-level methods /

"UILU-ENG 80 1712."

An efficient iterative procedure for use with the finite element method,

Vita.

Analysis of underground openings in rock by finite element methods : final report /

"This research was supported by the Advanced Research Projects Agency of the Department of Defense and was monitored by the Bureau of Mines ..."

Finite-difference model to simulate the areal flow of salt water and fresh water separated by an interface /

"April 1980."

Stresses in reinforced nozzle-cylinder attachments under external moment loadings analyzed by the finite-element method : a parameter study /

"ORNL/NUREG-52."