INTRODUCTION Chapter 1

Training Manual March 15, 2001 Inventory # Chapter Objectives In this chapter, students will be introduced to explicit dynamics and the ANSYS/LS-DYNA program. 1. Describe the background of ANSYS/LS-DYNA 2. Discuss applications of the ANSYS/LS-DYNA program 3. Compare Implicit and Explicit Solution Techniques 4. Define critical time step size in an explicit analysis 5. Overview of the organization of files in ANSYS/LS-DYNA

Training Manual March 15, 2001 Inventory # About this Seminar Requirements for taking this course: 1. Knowledge of ANSYS modeling and meshing procedures 2. Experience solving nonlinear problems in ANSYS 3. Some knowledge of nonlinear transient phenomena Expected outcomes of this course: 1. The ability to distinguish what problems should be analyzed explicitly and implicitly. 2. A complete working knowledge of the steps required for performing an analysis in ANSYS/LS-DYNA. 3. Practical experience on how to efficiently obtain and analyze results in an explicit dynamic analysis.

Training Manual March 15, 2001 Inventory # What is ANSYS/LS-DYNA? General purpose explicit dynamic finite element program Used to solve highly nonlinear transient dynamic problems –Efficient for a wide range of contact types –Advanced material modeling capabilities –Robust for very large deformation analyses Seamless interface of the ANSYS and LS-DYNA programs –Full integration of the LS-DYNA solver into ANSYS –All pre and post-processing performed using standard ANSYS conventions –GUI has look and feel of general ANSYS –Supports capability of implicit - explicit sequential solutions

Training Manual March 15, 2001 Inventory # Benefits of ANSYS/LS-DYNA Excellent combination of explicit and implicit solution technology ANSYS Pre and Post Processing: –All explicit dynamic specific commands begin with EDxx prefix –Customized ANSYS GUI for efficient execution of explicit problems –Supports all ANSYS Solid Modeling and Boolean Operations –Allows direct geometry import from IGES, Pro/E, ACIS, Parasolid, etc. –Supports all ANSYS automatic meshing features –APDL and design optimization can be used –Supports all general postprocessing features and animation macros –Specialized time-history postprocessing LS-DYNA Solver –Fastest explicit solver in marketplace –More features than any other explicit code –Full version of LS-DYNA (with airbags, seatbelts, explosives, etc.) –Full versions of LS-TAURUS and LS-POST postprocessors

Training Manual March 15, 2001 Inventory # Applications of ANSYS/LS-DYNA Crashworthiness Analysis –ANSYS/LS-DYNA: Full Car Crash Car Component Analyses Crash in ALL Vehicle Industries –Car –Truck –Bus –Train –Ship –Aircraft

Training Manual March 15, 2001 Inventory # (continued) Applications of ANSYS/LS-DYNA Manufacturing Process Simulation Deep drawing Hydro forming Superplastic forming Rolling Extrusion Stamping Machining Drilling Almost all forming processes have been simulated with LS- DYNA

Training Manual March 15, 2001 Inventory # Pipe whip (ANSYS News 3/93): Impact of a pipe with a rotational velocity of 50 rad/sec CPU time (SGI Octane R12000) < 20 seconds (continued) Applications of ANSYS/LS-DYNA Contact/Impact –Drop test –Pendulum impact test –Jet engine fan containment A wide range of contact types are possible

Training Manual March 15, 2001 Inventory # Stress wave propagation solid elements. CPU time 2 sec (SGI Octane R12000) F(t) (continued) Applications of ANSYS/LS-DYNA Nonlinear buckling Snap-through buckling Sonic wave propagation Failure analysis

Training Manual March 15, 2001 Inventory # PUNCH DIE BLANK STATIC‘QUASI’ STATIC DYNAMIC Structural Problems Metal Forming Impact Problems  F = 0  F  0  F = ma IMPLICIT METHOD EXPLICIT METHOD Comparison of Implicit and Explicit Methods

Training Manual March 15, 2001 Inventory # Comparison of Implicit and Explicit Methods Implicit Time Integration: Inertia effects ([C] and [M]) are typically not included Average acceleration - displacements evaluated at time t+  t: Linear Problems: –Unconditionally stable when [K] is linear –Large time steps can be taken Nonlinear problems: –Solution obtained using a series of linear approximations (Newton- Raphson) –Requires inversion of nonlinear stiffness matrix [K] –Small iterative time steps are required to achieve convergence –Convergence is not guaranteed for highly nonlinear problems

Training Manual March 15, 2001 Inventory # Comparison of Implicit and Explicit Methods Explicit Time Integration Central difference method used - accelerations evaluated at time t: where{F t ext } is the applied external and body force vector, {F t int } is the internal force vector which is given by: F hg is the hourglass resistance force (see ELEMENTS Chapter) and F cont is the contact force. The velocities and displacements are then evaluated: where  t t+  t/2 =.5(  t t +  t t+  t ) and  t t-  t/2 =.5(  t t -  t t+  t )

Training Manual March 15, 2001 Inventory # Explicit Time Integration (continued): The geometry is updated by adding the displacement increments to the initial geometry {x o }: Comparison of Implicit and Explicit Methods Nonlinear problems: –Lumped mass matrix required for simple inversion –Equations become uncoupled and can be solved for directly (explicitly) –No inversion of stiffness matrix is required. All nonlinearities (including contact) are included in the internal force vector. –Major computational expense is in calculating the internal forces. –No convergence checks are needed –Very small time steps are required to maintain stability limit

Training Manual March 15, 2001 Inventory # Stability Limit Implicit Time Integration For linear problems, the time step can be arbitrarily large (always stable) For nonlinear problems, time step size may become small due to convergence difficulties Explicit Time Integration Only stable if time step size is smaller than critical time step size Where  max = largest natural circular frequency Due to this very small time step size, explicit is useful only for very short transients

Training Manual March 15, 2001 Inventory # Critical time step size of a rod –Natural frequency: Critical time step: –Courant-Friedrichs-Levy-criterion –Δt is the time needed of the wave to propagate through the rod of length l Note: The critical time step size for explicit time integration depends on element length and material properties (sonic speed). with(wave propagation velocity) Critical Time Step Size

Training Manual March 15, 2001 Inventory # ANSYS/LS-DYNA checks all elements when calculating the required time step. For stability reasons a scale factor of 0.9 (default) is used to decrease the time step: The characteristic length l and the wave propagation velocity c are dependent on element type: L1L1 L4L4 L3L3 L2L2 A Shell elements: Beam elements: ANSYS/LS-DYNA Time Step Size

Training Manual March 15, 2001 Inventory # File Organization ANSYS /SOLU or LS-DYNA solver task reads jobname.K ANSYS /PREP7 INT preprocessing writes jobname.K (standard LS-DYNA input) ANSYS Results jobname.rst Binary Result File EDRST,FREQ ANSYS/POST26 EDREAD,... LS-TAURUS LS-POST phs3 LS-TAURUS, LS-POST, ASCII GLSTAT, MATSUM, … ASCII Result Files EDOUT,File ANSYS/POST1 ANSYS Results jobname.his Time History Data EDHIST,Comp and EDHTIME,FREQ LS-TAURUS & LS- POST phs1 LS-TAURUS & LS-POST binary d3plot Binary Result Files similar to jobname.rst LS-TAURUS & LS- POST phs2 LS-TAURUS and LS-POST binary d3thdt Binary Result Files similar to jobname.his ANSYS/POST26

Training Manual March 15, 2001 Inventory # (continued) File Organization Description of ANSYS Files Generated During an ANSYS/LS-DYNA run: Jobname.k LS-DYNA input stream that is automatically generated upon execution of the ANSYS SOLVE command. Contains all geometry, load, and material data that exists in the ANSYS database The file is 100% compatible with LS-DYNA version 950e File can also be manually generated using the EDWRITE command: Solution: Write Jobname.k Jobname.rst Explicit dynamics results file that is nearly identical to standard ANSYS.rst Primarily used to review results in the general ANSYS postprocessor (POST1) Contains results at a relatively small number of time steps (e.g., )

Training Manual March 15, 2001 Inventory # (continued) File Organization Description of ANSYS Files Generated During an ANSYS/LS-DYNA run: Jobname.his Explicit dynamics time history results files used in POST26 Contains results for a subset of nodes and/or elements of the model Typically will contain results at significantly more time steps than Jobname.rst Time history ASCII files Specialized files containing additional information about the explicit analysis User must specify which files are written before solution ASCII files include: GLSTAT:Global energies MATSUM:Material energies SPCFORC:Nodal constraint reaction forces RCFORC:Resultant contact interface forces RBDOUT:Rigid body data NODOUT:Nodal data ELOUT:Element data etc....

Training Manual March 15, 2001 Inventory # (continued) File Organization Since the LS-TAURUS and LS-POST postprocessors automatically come with ANSYS/LS-DYNA, the following two DYNA results files are easily generated during an explicit dynamic analysis: D3PLOT –LS-TAURUS and LS-POST binary results file –Similar to ANSYS Jobname.rst D3DHDT –LS-TAURUS and LS-POST time-history results file –Similar to ANSYS Jobname.his