Functions and Analysis

1702 Submissions

[2] viXra:1702.0119 [pdf] submitted on 2017-02-09 07:58:42

Lagrangian Solid Modeling

Authors: Matthew Marko
Comments: 114 pages including supplementary code

The author demonstrates a stable Lagrangian solid modeling method, tracking the interactions of solid mass particles, rather than using a meshed grid. This numerical method avoids the problem of tensile instability often seen with Smooth Particle Applied Mechanics by having the solid particles apply stresses expected with Hooke's law, as opposed to using a smoothing function for neighboring solid particles. This method has been tested successfully with a bar in tension, compression, and shear, as well as a disk compressed into a flat plate, and the numerical model consistently matched the analytical Hooke's law as well as Hertz contact theory for all examples. The solid modeling numerical method was then built into a 2-D model of a pressure vessel, which was tested with liquid water particles under pressure and simulated with Smoothed Particle Hydrodynamics. This simulation was stable, and demonstrated the feasibility of Lagrangian specification modeling for Fluid Solid Interactions.
Category: Functions and Analysis

[1] viXra:1702.0039 [pdf] submitted on 2017-02-03 03:27:16

Proof to Euler's Formula

Authors: Carl-Gustav Hedenby
Comments: 1 Page. -

The author proves Euler's formula for the imaginary exponential without reverting to series expansions.
Category: Functions and Analysis