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Theory & Application of SPH & SPG Methods


  • Jingx­i­ao Xu, Ph.D.
  • You­cai Wu, Ph.D.


  • $350
  • $175 for students

What's Included

  • One day of in­struc­tion
  • Class notes

Theory & Application of SPH & SPG Methods


This course overviews the fun­da­men­tal the­o­ret­i­cal back­ground of the Smoothed Par­ti­cle Hy­dro­dy­nam­ics (SPH) for­mu­la­tion. It al­so cov­ers the avail­able for­mu­la­tions, im­ple­men­ta­tions, and lat­est de­vel­op­ments of the SPH method cou­pled with the La­grangian for­mu­la­tion in LS-DY­NA® and teach­es you how to use these SPH op­tions. De­tailed de­scrip­tions of the da­ta re­quired to run LS-DY­NA analy­ses are giv­en. Ex­am­ples are used to il­lus­trate the con­cepts cov­ered. To ad­dress some nu­mer­i­cal is­sues of SPH in low-speed ma­te­r­i­al fail­ure analy­sis of solids and struc­tures, a nov­el par­ti­cle method Smoothed Par­ti­cle Galerkin (SPG) is in­tro­duced with the­o­ret­i­cal back­ground, fea­tures, key­words and ap­pli­ca­tions.


  1. In­tro­duc­tion of SPH
    1. His­to­ry of the method
    2. Smooth­ing func­tion (ker­nel)
    3. Vari­able smooth­ing length
    4. Dif­fer­ent SPH For­mu­la­tions
  2. SPH dis­cretiza­tion
    1. SPH Dis­cretiza­tion of Con­tin­u­um/­Bal­ance Equa­tions
    2. To­tal and up­dat­ed La­grangian
  3. SPH ther­mal for­mu­la­tions
    1. Ther­mo­me­chan­i­cal cou­pling op­tions be­tween SPH and solids
  4. SPH ten­sion in­sta­bil­i­ty
    1. La­grangian and Euler­ian ker­nel func­tions
    2. Renor­mal­iza­tion and con­sis­ten­cy
  5. Gen­er­al fea­tures and ap­pli­ca­tions of SPH (solids and flu­ids)
    1. Key­words
    2. Use of SPH
  6. In­ter­ac­tions
    1. Bound­ary con­di­tions
    2. Con­tacts
    3. SPH/­La­grangian cou­pling
    4. Ther­mal op­tions
    5. Cou­pling be­tween SPH parts
    6. Cou­pling be­tween SPH and oth­er par­ti­cle meth­ods (such as DEM, SPG, and peri­dy­nam­ics)
  7. Pre- and post-pro­cess­ing us­ing LS-Pre­Post®
    1. Cre­ation of SPH mod­els
    2. Vi­su­al­iza­tion of SPH par­ti­cles
  8. De­tailed ex­am­ple of SPH
    1. Con­trol cards
    2. Ma­te­ri­als
    3. Sec­tions
    4. Parts
    5. Out­puts
  9. In­tro­duc­tion of SPG
    1. Ker­nel types
    2. Sta­bi­lized DNI
    3. Key­words
    4. Bond-based fail­ure mech­a­nism
  10. SPG ap­pli­ca­tions
    1. Im­pact and pen­e­tra­tion
    2. Wa­ter­jet im­pact