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Advanced FE & Meshfree Methods for Manufacturing & Failure


  • C.T. Wu, Ph.D.
  • Bo Ren, Ph.D.


  • $650
  • $325 for students

What's Included

  • Two days of in­struc­tion
  • Class notes

Advanced FE & Meshfree Methods for Manufacturing & Failure


  • Equiv­a­lent knowl­edge to an in­tro­duc­to­ry class on LS-DY­NA®
  • Fun­da­men­tal FEM the­o­ry


Com­pu­ta­tion­al meth­ods have been used ex­ten­sive­ly in in­dus­try to of­fer a cost-ef­fec­tive ap­proach for eval­u­a­tion and op­ti­miza­tion of prod­uct de­sign and man­u­fac­tur­ing. Among evolv­ing com­pu­ta­tion­al meth­ods, mesh­free and nov­el fi­nite el­e­ment meth­ods have emerged as a new class of nu­mer­i­cal meth­ods and are play­ing an in­creas­ing­ly sig­nif­i­cant role in ad­dress­ing many chal­leng­ing com­pu­ta­tion­al is­sues, such as mesh dis­tor­tion, se­vere de­for­ma­tion, em­bed­ded and im­mersed struc­tures, bridg­ing and cross-scale in­ter­ac­tions, ma­te­r­i­al fail­ure, mod­el­ling of ar­bi­trary and mul­ti­ple crack prop­a­ga­tion, mod­el­ling frac­ture in com­pos­ites, con­cretes and oth­er men-made ma­te­ri­als, and free sur­face flow.

This class in­tro­duces sev­er­al in­no­v­a­tive mesh­free and fi­nite el­e­ment meth­ods that go be­yond the clas­si­cal the­o­ries and in­cor­po­rate more pro­found phys­i­cal mech­a­nisms in deal­ing with those com­pu­ta­tion­al chal­lenges in which con­ven­tion­al meth­ods are in­ef­fec­tive or dif­fi­cult to han­dle. The meth­ods em­pha­sized in this class are Smoothed Par­ti­cle Galerkin (SPG), Flu­id Par­ti­cle Galerkin (FPG), Peri­dy­nam­ics, adap­tive El­e­ment-Free Galerkin (EFG), and Ex­tend­ed Fi­nite El­e­ment method (XFEM). Rep­re­sen­ta­tive ex­am­ples will be pre­sent­ed with each method.


  1. SPG method
    1. Method han­dles:
      1. Large de­for­ma­tion and fail­ure in duc­tile ma­te­ri­als
      2. Em­bed­ded struc­tures
      3. Form ma­te­ri­als
    2. Rep­re­sen­ta­tive ap­pli­ca­tions
      1. Join­ing process and post-fail­ure analy­ses
      2. Met­al cut­ting/­grind­ing/­ma­chin­ing
      3. Im­pact/­pen­e­tra­tion
      4. Two-scale analy­sis
  2. FPG method
    1. Overview:
      1. A se­mi-im­plic­it in­com­press­ible flu­id solver to ef­fi­cient­ly deal with free sur­face flow with strong sur­face ten­sion
    2. Rep­re­sen­ta­tive ap­pli­ca­tions:
      1. Re­flow in sol­der­ing
      2. Slosh­ing
  3. Peri­dy­nam­ics method
    1. For mod­el­ling in-plane and de­lam­i­na­tion frac­ture in car­bon fiber re­in­forced poly­mers (CFRPs)
  4. XFEM
    1. For mod­el­ling crack prop­a­ga­tion in sheet met­al
  5. Oth­er ad­vance nu­mer­i­cal meth­ods