Abstract
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.
Highlights
Computational solid modeling is an incredibly valuable tool for todays engineers [1,2,3,4,5,6], thankfully due to the powerful computers available at low costs
Finite element analysis (FEA) is just one of many meshed solid modeling techniques used in countless industries to study mechanical stresses in numerous different components today
The last step in this effort is to join the Lagrangian specification solid modeling efforts with smoothed particle hydrodynamics; this was demonstrated with a 2-D pressure vessel
Summary
Computational solid modeling is an incredibly valuable tool for todays engineers [1,2,3,4,5,6], thankfully due to the powerful computers available at low costs. The vast majority of numerical methods in engineering, including finite element, are meshed, analyzing stresses and mass flows in a fixed region of space This approach to solving continuum mechanics is considered the Eulerian specification. One of the main disadvantages of this method is that the entire domain needs to be modeled, and if there are large voids and empty spaces, there is a waste in computational effort as empty domains are studied repeatedly at each time step Another approach to avoid this wasted computational effort is to use meshless numerical methods, studying the stresses and forces in the Lagrangian specification [10,11,12,13]. With an accurate model consisting of particles of liquids and solids interacting, an engineer could investigate eventual material failures and crack propagation in real time for highly dynamic fluid flow within a moving solid boundary
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