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چكيده انگليسي :

Development of a Finite Element Code Based on ALE Technique Ahmad Zamanian a zamaniankhorasgani@me iut ac ir Date of Submission 2012 06 28 Department of Mechanical Engineering Isfahan University of Technology Isfahan 84156 83111 Iran Degree M Sc Language FarsiSupervisor Dr Mohammad Reza Forouzan forouzan@cc iut ac irAbstract Many engineering problems involve large material deformation large boundary motion andcontinuous changes in boundary conditions The Arbitrary Lagrangian Eulerian ALE formulation hasemerged in recent years as a technique that can alleviate many of the shortcomings of the traditionalLagrangian and Eulerian formulations in handling these types of problems Using the ALE formulation thecomputational grid need not adhere to the material Lagrangian nor be fixed in space Eulerian but can bemoved arbitrarily Two distinct techniques are being used to implement the ALE formulation namely theoperator split approach and the fully coupled approach A survey of the ALE literature shows that themajority of ALE implementations for quasi static and dynamic analyses are based on the computationallyconvenient operator split technique In addition all previous dynamic ALE formulations are based onexplicit time integration where no linearization is needed This thesis presents a fully coupled implicit ALE formulation for the simulation of quasi static largedeformation and metal forming problems ALE virtual work equations are derived from the basic principlesof continuum mechanics A method for the treatment of convective terms that sidesteps the computation ofthe spatial gradients of stresses is used in the derivation The ALE virtual work equations are discretizedusing isoparametric finite elements Full expression for the resulting ALE finite element matrices andvectors are given A new relation that relates grid displacements with material displacements is introduced A 2D finite element program ALEFE based on the presented formulation is developed and tested The program may reduce to an updated Lagrangian or Eulerian methods as special cases The output dataformat is designed to be compatible with general graphic simulation and data processing commercialsoftwares so that contour x y and deformed mesh plots may be easily created from the output data ofALEFE The transfinite mapping method is used as the mesh motion scheme for internal nodes A newtreatment for mesh motion on material boundaries is introduced and implemented Implicit time integrationschemes are implemented in the code Different numerical algorithms for the integration of the rate typeconstitutive equation are investigated and coupled with the return mapping algorithm to provide plasticincremental consistency Jaumann and Truesdell rates are taken as the objective stress rates in theconstitutive equation Several quasi static large deformation applications are solved using the developed code Practicalsimulation cases include flat punch forging and sheet metal extrusion process ALE results are in goodagreement with Lagrangian results obtained by ABAQUS commercial FE software ALE is shown toprevent mesh distortion and eliminate the need for special contact treatments for problems with frictionlesscontact Keywords ALE Large Deformation Problem Finite Element Mesh Motion

زمانيان، احمد

توسعه يك كد المان محدود بر اساس تكنيك لاگرانژي-اويلري اختياري

ALE , مسايل با جابه جايي هاي بزرگ , اجزائء محدود