1. PAT328, Section 3, March 2001MAR120, Lecture 4, March 2001MAR120, Lecture 1, March 2001S2-1MAR120, Section 2, December 2001 SECTION 2 OVERVIEW OF MSC.MARC AND MSC.PATRAN ~ PART 2

2. PAT328, Section 3, March 2001MAR120, Lecture 4, March 2001MAR120, Lecture 1, March 2001S2-2MAR120, Section 2, December 2001 TABLE OF CONTENTS SectionPage 2.0 Overview of MSC.Marc and MSC.Patran ~ Part 2 MSC.Marc Nonlinear Analysis Background………………………………………………………………………2-3 The Pulley Ensemble Example…………………………………………………………………………………….2-7 Continuous Product Enhancements For Both MSC.Patran And MSC.Marc…………………………………2-8 Continuous Product Enhancements For Both MSC.Patran And MSC.Marc…………………………………2-9 Summary Of MSC.Marc Nonlinear Analysis Capabilities………………………………………………………2-10 MSC.Marc General Solution Features……………………………………………………………………………2-16 General Solution Features…………………………………………………………………………………………2-17 Material Models In MSC.Marc……………………………………………………………………………………..2-18 Nonlinear Material Models…………………………………………………………………………………………2-19 Element Library: 0-D & 1-D………………………………………………………………………………………..2-23 Element Library: 2-D………………………………………………………………………………………………..2-24 Element Library: 3-D………………………………………………………………………………………………..2-25 Element Library Categories………………………………………………………………………………………..2-26 Element Library: Connecting………………………………………………………………………………………2-27 Element Library Examples…………………………………………………………………………………………2-28 Relevance Of Choice Of Elements A 2-DOF, 1-element Example: Hanging Bar…………………………..2-29 The FEM Math For The Hanging Bar Example………………………………………………………………….2-30 Results For The Hanging Bar Example………………………………………………………..………………..2-31 Nonlinear FEA And Iterative Solution…………………………………………………………………………….2-32 The Newton Raphson Method…………………………………………………………………………………….2-33 The Modified Newton Raphson Method………………………………………………………………………….2-34 MSC.Patran Support Selecting Methods ………………………………………………………………………..2-35 Direct Versus Iterative ……………………………………………………………………………………………..2-36 Iterative Method An Comparison To Direct Solver ……………………………………………………………..2-37 Tolerances Controlling The Solution Cycles …………………………………………………………………….2-38 Convergence Testing Of Solution Procedures ………………………………………………………………….2-39 Cost Of Nonlinear Analysis ………………………………………………………………………………………..2-40 Cost Of Linear Versus Nonlinear Analysis ………………………………………………………………………2-41 Follower Forces …………………………………………………………………………………………………….2-42 Updated Lagrange …………………………………………………………………………………………………2-43 Load Incrementation Control ……………………………………………………………………………………..2-44 Nonlinearity Results From Contact, Geometric And/or Material Response. ………………………………..2-45 MSC.Marc Contnuously Improved…………………………………………….. ………………………………..2-46

3. PAT328, Section 3, March 2001MAR120, Lecture 4, March 2001MAR120, Lecture 1, March 2001S2-3MAR120, Section 2, December 2001 Many types of nonlinearity such as contact, material, large deflections and large strains can be combined in one model. Example: Metal (Rolling) Forming MSC.MARC NONLINEAR ANALYSIS BACKGROUND

4. PAT328, Section 3, March 2001MAR120, Lecture 4, March 2001MAR120, Lecture 1, March 2001S2-4MAR120, Section 2, December 2001 Virtual Physical MSC.Marc was the first commercially available FEA code for nonlinear analysis, and has been accepted as a robust, mature, advanced nonlinear analysis solver for many years MSC.MARC NONLINEAR ANALYSIS BACKGROUND(CONT.) Example Application: Rubber Boot Actual Physical Test MSC.Marc Virtual Test

5. PAT328, Section 3, March 2001MAR120, Lecture 4, March 2001MAR120, Lecture 1, March 2001S2-5MAR120, Section 2, December 2001 Common look and feel for many analysis codes, strong CAD geometry integration, and powerful meshing and model manipulation through MSC.Patran MSC.MARC NONLINEAR ANALYSIS BACKGROUND(CONT.)

6. PAT328, Section 3, March 2001MAR120, Lecture 4, March 2001MAR120, Lecture 1, March 2001S2-6MAR120, Section 2, December 2001 Truly “general purpose” FEA capability. MSC.Marc is fully modular. All capabilities can be mixed and used together. MSC.Patran incorporates the most commonly used features of the MSC.Marc analysis code to produce an integrated interface: MSC.MARC NONLINEAR ANALYSIS BACKGROUND(CONT.) Code specific translator. Analysis model set-up and submission of Marc jobs supported through MSC.Patran Customer support provided for setting up analyses for all Marc procedures. Pulley ensemble MSC.Marc example can be setup, launched, and post- processed entirely from MSC.Patran

7. PAT328, Section 3, March 2001MAR120, Lecture 4, March 2001MAR120, Lecture 1, March 2001S2-7MAR120, Section 2, December 2001 Rotational motion (twist) is prescribed on a rigid drive pulley. This twist is transferred to another rigid pulley driven by an elastic belt. The rotational velocity of the driven pulley is unknown and depends upon the stiffness of the torsional spring and friction. This new feature shows how to transfer rotation (twist) from one rigid body to another. Prior to this feature, both pulleys would have required prescribed velocities, and this simulation would not have been possible since the angular velocity of the driven pulley is initially unknown. In the past, rigid bodies were only displacement (velocity or position) controlled, and motion of one rigid body could not have affected the motion of another. Torque Controlled Dies with Twist Transfer THE PULLEY ENSEMBLE EXAMPLE

8. PAT328, Section 3, March 2001MAR120, Lecture 4, March 2001MAR120, Lecture 1, March 2001S2-8MAR120, Section 2, December 2001 MSC.Patran general modeling and PCL customization capabilities, along with direct text input, help support advanced capabilities (such as fracture mechanics, acoustics and multi-physics analysis) that aren’t directly supported through the GUI. Case in point: SPF Super Plastic Forming CONTINUOUS PRODUCT ENHANCEMENTS FOR BOTH MSC.PATRAN AND MSC.MARC.

9. PAT328, Section 3, March 2001MAR120, Lecture 4, March 2001MAR120, Lecture 1, March 2001S2-9MAR120, Section 2, December 2001 Examples of recent MSC.Marc (version 2000) enhancements: increased robustness, new rubber models and element technology, improvements in rigid-plastic flow and structural-acoustic analyses, general contact post-processing including area, force and stress calculation between deformable bodies (surface-to-surface) and Data Transfer from Axisymmetric to 3-D Analysis. Example Data Transfer from Axisymmetric to 3-D Analysis CONTINUOUS PRODUCT ENHANCEMENTS FOR BOTH MSC.PATRAN AND MSC.MARC

10. PAT328, Section 3, March 2001MAR120, Lecture 4, March 2001MAR120, Lecture 1, March 2001S2-10MAR120, Section 2, December 2001 Nonlinear Transient Analysis Nonlinear Static Analysis Sources of Nonlinearity:  Geometric Nonlinearity  Material Nonlinearity  Contact Nonlinearity Example of Material nonlinearity: Rubber (Hyperelastic Material) SUMMARY OF MSC.MARC NONLINEAR ANALYSIS CAPABILITIES

11. PAT328, Section 3, March 2001MAR120, Lecture 4, March 2001MAR120, Lecture 1, March 2001S2-11MAR120, Section 2, December 2001 Chapter 6 in Volume E has many examples on this kind of analysis. The one illustrated here is # 6.2. Notice calculated frequencies are quite close to the theoretical values. Natural Frequencies/ Normal Modes  Lanczos or Inverse Power Sweep Methods  Shift provided: allows modes of free (unrestrained) structure to be obtained  Initial stress/displacement effects may be included. ANALYSIS SOLUTIONS

12. PAT328, Section 3, March 2001MAR120, Lecture 4, March 2001MAR120, Lecture 1, March 2001S2-12MAR120, Section 2, December 2001 Time Based Dynamics  Linear and Nonlinear solutions are provided  Direct or Modal Integration of dynamic response  Automatic impact solution (velocity and acceleration jumps) due to contact bodies including rigid structures Example: Dynamic Collapse of a Cylinder ANALYSIS SOLUTIONS (CONT.)

13. PAT328, Section 3, March 2001MAR120, Lecture 4, March 2001MAR120, Lecture 1, March 2001S2-13MAR120, Section 2, December 2001 Spectrum Response of a Space Frame (Problem 6.6) A typical displacement spectral density function is entered. The program computes the root mean square of the displacement (RMS), velocity, and acceleration. Frequency based Dynamics  Features: Raleigh, Composite or Direct modal damping are available Base Motion excitation available  Frequency Response (Steady State Dynamics) Harmonic response for the steady state response of a sinusoidal excitation  Modal Linear Transient Dynamics Modal superposition for loads known as a function of time  Response Spectrum Analysis (Steady State Dynamics for base excitation including seismic events) Provides an estimate of the peak response when a structure is subjected to a dynamic base excitation ANALYSIS SOLUTIONS (CONT.)

14. PAT328, Section 3, March 2001MAR120, Lecture 4, March 2001MAR120, Lecture 1, March 2001S2-14MAR120, Section 2, December 2001 Creep of Concrete Beam Under Point Loads (Problem 7.11) Frequency based Dynamics (cont.)  Random Vibration Analysis - such as response of an airplane due to turbulence (current release requires input via user-subroutine) Predicts the response of a system subjected to a random continuous excitation. This excitation is expressed in a statistical sense using a power spectral density function Creep and Viscoelastic analysis  Integration of material rate equations by either explicit or implicit methods  Time domain  Frequency-dependent complex elastic modulus ANALYSIS SOLUTIONS (CONT.)

15. PAT328, Section 3, March 2001MAR120, Lecture 4, March 2001MAR120, Lecture 1, March 2001S2-15MAR120, Section 2, December 2001 Nonlinear Heat Conduction of a Channel (Problem 5.8) Heat Transfer analysis  Steady State or Transient  Conductivity and radiation across interfaces can be modeled  Results may easily be used as prescribed loads in a stress analysis for the same or a different mesh ANALYSIS SOLUTIONS (CONT.)

16. PAT328, Section 3, March 2001MAR120, Lecture 4, March 2001MAR120, Lecture 1, March 2001S2-16MAR120, Section 2, December 2001 Load, P Displacement 1.0 AB Proportional loading with unstable response. No fixed problem size limits, domain decomposition avail. for parallel solution MSC.Marc 2001 introduced advanced automated procedures for load step, convergence control, and equilibrium/stability control in nonlinear analysis Reliable Newton-Raphson algorithm Arc length control for static collapse problems MSC.MARC GENERAL SOLUTION FEATURES

17. PAT328, Section 3, March 2001MAR120, Lecture 4, March 2001MAR120, Lecture 1, March 2001S2-17MAR120, Section 2, December 2001 Energies Output Plot Demonstrating Energy Balance No fixed problem size limits, domain decomposition available for parallel solution MSC.Marc 2001 release has automated procedures for load step, convergence control, and equilibrium/stability control in nonlinear analysis Reliable Newton-Raphson algorithm Arc length control for static collapse problems MSC.Marc 2001computes Energy Output and Energy Balance GENERAL SOLUTION FEATURES

18. PAT328, Section 3, March 2001MAR120, Lecture 4, March 2001MAR120, Lecture 1, March 2001S2-18MAR120, Section 2, December 2001 All material models can be temperature dependent This is supported by MSC.Patran Isotropic 2- and 3-D Orthotropic 2- and 3-D Anisotropic Laminated and 3D Composites MATERIAL MODELS IN MSC.MARC

19. PAT328, Section 3, March 2001MAR120, Lecture 4, March 2001MAR120, Lecture 1, March 2001S2-19MAR120, Section 2, December 2001 Time-Independent Inelastic Behavior Perfectly Plastic and Rigid Plastic Elastic Plastic with Hardening or Softening  Isotropic  Kinematic  Combined and others Plastic - Hardening Laws: Plastic - Yielding: With a dependence of the yield stress on strain rate  von Mises and Drucker- Prager  Linear and Parabolic Mohr- Coulomb  Various Oak Ridge National Laboratory models and others NONLINEAR MATERIAL MODELS

20. PAT328, Section 3, March 2001MAR120, Lecture 4, March 2001MAR120, Lecture 1, March 2001S2-20MAR120, Section 2, December 2001 Hyperelastic - Including Graphical Experimental Data Fitting in MSC.Marc Mentat or in MSC.Patran Marc 2002  Large strain for elastic materials (e.g. rubber) using Neo-Hookean, Mooney- Rivlin, Ogden, Gent, Arruda-Boyce, Jamus-Green-Simpson models  Large strain, elastic analysis of compressible foams NONLINEAR MATERIAL MODELS (CONT.)

21. PAT328, Section 3, March 2001MAR120, Lecture 4, March 2001MAR120, Lecture 1, March 2001S2-21MAR120, Section 2, December 2001 Creep  Behavior for materials where, for a constant stress state, strain increases with time  Relaxation where stress decreases with time at constant deformation NONLINEAR MATERIAL MODELS (CONT.)

22. PAT328, Section 3, March 2001MAR120, Lecture 4, March 2001MAR120, Lecture 1, March 2001S2-22MAR120, Section 2, December 2001 Gurson Failure Model for Ductile Metals Other Material Formulations  Viscoelastic Behavior for elastic materials that relax and dissipate energy under transient loadings  Damping Using Mass or Stiffness Matrix, or Numerical Multipliers - can be used together NONLINEAR MATERIAL MODELS (CONT.) Failure  Hill, Hoffman, Tsai-Wu, Maximum Stress or Strain, Gurson Viscoelastic Uniaxial Test

23. PAT328, Section 3, March 2001MAR120, Lecture 4, March 2001MAR120, Lecture 1, March 2001S2-23MAR120, Section 2, December 2001 MSC.MARC supports an extensive Element library that can be used to simulate a variety of “real world” structure 0-D Elements 1-D Elements 0-D Elements  Point mass and inertia elements  Grounded springs and dashpots 1-D Elements Axial and torsional dashpot elements  Axial and torsional springs  2 and 3 node axial truss elements  2 and 3 node planar beam  2 node beam in 3-D space  2 and 3 node thin-walled beam  2 and 3 node axisymmetric shell elements  2 and 3 node axial heat transfer elements  Initial stress or length input cable  2 node gap elements ELEMENT LIBRARY: 0-D & 1-D

24. PAT328, Section 3, March 2001MAR120, Lecture 4, March 2001MAR120, Lecture 1, March 2001S2-24MAR120, Section 2, December 2001 2-D elements  3, 4, 6 and 8 node thin shell elements  3, 4, 6 and 8 node (general) thick shells  3, 4, 6 and 8 node elements for plane stress, plane and generalized plan  strain and axisymmetric analysis  3, 4 and 8 node membrane elements  4 node shear panel  3, 4, 6 and 8 node 2-D planar and axisymmetric heat transfer elements  2 and 3 node axisymmetric shell heat transfer elements  3, 4 and 8 node general shell heat transfer elements  Note that Herrmann formulation elements have an additional internal node for linear elements for a compressibility degree of freedom. For quadratic elements an additional compressibility DOF is added to each corner nodes. This is done in MSC.Marc –not in the GUI. ELEMENT LIBRARY: 2-D

25. PAT328, Section 3, March 2001MAR120, Lecture 4, March 2001MAR120, Lecture 1, March 2001S2-25MAR120, Section 2, December 2001 3-D elements  4, 6, 8, 10, 15, 20 node 3D elements  4, 6, 8, 10, 15 and 20 node 3-D heat transfer elements. ELEMENT LIBRARY: 3-D

26. PAT328, Section 3, March 2001MAR120, Lecture 4, March 2001MAR120, Lecture 1, March 2001S2-26MAR120, Section 2, December 2001 Element types fall into three basic categories:  Continuum Elements are: bricks, plane stress, plane strain, generalized plane strain, and axisymmetric.  Shell Elements are: beams, plates, shells, trusses, and shells of revolution.  Special Elements are: gaps, pipe bend, shear panel, semi-infinite, incompressible, and reduced integration. ELEMENT LIBRARY CATEGORIES

27. PAT328, Section 3, March 2001MAR120, Lecture 4, March 2001MAR120, Lecture 1, March 2001S2-27MAR120, Section 2, December 2001 Generalized multi-point constraint equations  Explicit  Rigid (fixed and rigid link)  Mechanism joint definition (ex. pinned, full moment, sliding surface, cyclic symmetric)  Mesh transition constraint definitions (linear or quadratic, surface-surface  volume-volume)  Solid to shell interfaces Mixing different element types is easy if the number of degrees of freedom is the same for all types. Otherwise constraints must be used to insure proper compatibility. ELEMENT LIBRARY: CONNECTING

28. PAT328, Section 3, March 2001MAR120, Lecture 4, March 2001MAR120, Lecture 1, March 2001S2-28MAR120, Section 2, December 2001 Where on MSC.Patran? ELEMENT LIBRARY EXAMPLES

29. PAT328, Section 3, March 2001MAR120, Lecture 4, March 2001MAR120, Lecture 1, March 2001S2-29MAR120, Section 2, December 2001 The problem to solve is a bar subjected to its own self weight. The bar is hang from a support, we want to know the deformations and the stresses. Let’s start with a one element solution. Let’s choose a specific element type and use the typical six steps of FEM (Finite Element Method) to solve the simple problem of the illustration. Choosing the shape function in step 1 determines the type of element to be used. For simplicity, a bar element is chosen. RELEVANCE OF CHOICE OF ELEMENTS A 2-DOF, 1-ELEMENT EXAMPLE: HANGING BAR

30. PAT328, Section 3, March 2001MAR120, Lecture 4, March 2001MAR120, Lecture 1, March 2001S2-30MAR120, Section 2, December 2001 THE FEM MATH FOR THE HANGING BAR EXAMPLE Step 2: The strain and stress: B D (Elasticity) Step 3: The element matrices: Step 4: Assemble system of equations: Step 5: Solve system of equations: exact u2 (!) Reaction Step 6: Recover stresses: constant over the element (!) Step 1: The shape function: two linear functions

31. PAT328, Section 3, March 2001MAR120, Lecture 4, March 2001MAR120, Lecture 1, March 2001S2-31MAR120, Section 2, December 2001 Bar subject to own weight Axial position Displacement Stress 1 element 2 elements 3 elements Axial position The FEM approximation to the stress is a piece-wise constant representation to a line, and the displacement approximation is a piece-wise linear representation to a parabola. If a parabolic shape function would have been selected, the finite element solution would have agree exactly with the theoretical solution. Knowing the element type is very important. RESULTS FOR THE HANGING BAR EXAMPLE

32. PAT328, Section 3, March 2001MAR120, Lecture 4, March 2001MAR120, Lecture 1, March 2001S2-32MAR120, Section 2, December 2001 For the solution step, we must solve the equations: For the linear case, Gauss elimination is applied directly. However, for nonlinear equations both the stiffness and external forces may be functions of the nodal displacements, To solve such a nonlinear set of equations the default method in MSC.Marc includes the Newton-Raphson method. This is an iterative method. Given a general nonlinear equation, and a known point, we calculate a correction, as follows: with NONLINEAR FEA AND ITERATIVE SOLUTION

33. PAT328, Section 3, March 2001MAR120, Lecture 4, March 2001MAR120, Lecture 1, March 2001S2-33MAR120, Section 2, December 2001 Assembly and decomposition of stiffness matrix during every iteration or recycle Good convergence Expensive for large systems THE NEWTON RAPHSON METHOD

34. PAT328, Section 3, March 2001MAR120, Lecture 4, March 2001MAR120, Lecture 1, March 2001S2-34MAR120, Section 2, December 2001 Assembly and decomposition of stiffness matrix only at start of increment Slow convergence behavior Respective for mildly nonlinear problems without material nonlinearities THE MODIFIED NEWTON RAPHSON METHOD

35. PAT328, Section 3, March 2001MAR120, Lecture 4, March 2001MAR120, Lecture 1, March 2001S2-35MAR120, Section 2, December 2001 Where on MSC.Patran? MSC.PATRAN SUPPORT SELECTING METHODS

36. PAT328, Section 3, March 2001MAR120, Lecture 4, March 2001MAR120, Lecture 1, March 2001S2-36MAR120, Section 2, December 2001 Each iteration of say, the Newton-Raphson Method requires solving the system of equations; this can be done with a Direct Solver or with an Iterative Solver. Where on MSC.Patran? DIRECT VERSUS ITERATIVE

37. PAT328, Section 3, March 2001MAR120, Lecture 4, March 2001MAR120, Lecture 1, March 2001S2-37MAR120, Section 2, December 2001 Example: f(x) = sqrt(x) -1 = 0. An iterative solver requires more iterations to achieve solution Each cycle in an iterative method take less time to compute that the time needed for a cycle in a direct methods. ITERATIVE METHOD AN COMPARISON TO DIRECT SOLVER

38. PAT328, Section 3, March 2001MAR120, Lecture 4, March 2001MAR120, Lecture 1, March 2001S2-38MAR120, Section 2, December 2001 TOLERANCES CONTROLING THE SOLUTION CYCLES Termination of iterative procedure when convergence ratio is less than Tolerance. (default ). Types include: Residual checking, possible in one cycle: Relative: and/or Absolute: and/or Displacement checking, not possible in one cycle: Relative: and/or Absolute: and/or (Convergence ratio)

39. PAT328, Section 3, March 2001MAR120, Lecture 4, March 2001MAR120, Lecture 1, March 2001S2-39MAR120, Section 2, December 2001 CONVERGENCE TESTING OF SOLUTION PROCEDURES

40. PAT328, Section 3, March 2001MAR120, Lecture 4, March 2001MAR120, Lecture 1, March 2001S2-40MAR120, Section 2, December 2001 Notice the CPU costs of each of the steps from a typical run. The last recycle took 80% of the total time in Assembly and Recovery, with the remainder in the Solver. Furthermore, this increment took 12 recycles for a total time of 2500 seconds. A linear analysis would only take 372 seconds! Assembly and Recovery times have to do with performing the integrations shown in Step 3. Reducing the amount of integration points will greatly improve performance to the possible cost of lesser quality. 11 increments … COST OF NONLINEAR ANALYSIS

41. PAT328, Section 3, March 2001MAR120, Lecture 4, March 2001MAR120, Lecture 1, March 2001S2-41MAR120, Section 2, December 2001 Linear and Nonlinear FEA differ greatly in the amount of time spent on each of the three solution steps. In linear FEA, step 5, Solve Equations dominates (or has in the past dominated) the overall cpu time. In nonlinear FEA the costs of each step are more equal. With recent advances in solver technology, the time spent in assembly and recovery now exceed that spent in the solver. Figures below are but an example; numbers vary widely depending on the problem and the methods selected. COST OF LINEAR VERSUS NONLINEAR ANALYSIS 35 30 35 100 15 70 100

42. PAT328, Section 3, March 2001MAR120, Lecture 4, March 2001MAR120, Lecture 1, March 2001S2-42MAR120, Section 2, December 2001 Distributed loads are taken into account by means of equivalent nodal loads; changes in direction and area can be taken into account using the MSC.Marc parameter option FOLLOW FOR Where on MSC.Patran? The pressure stays normal to the deformed shape thus changes direction, in turn also producing a change in the reaction forces and moments. FOLLOWER FORCES

43. PAT328, Section 3, March 2001MAR120, Lecture 4, March 2001MAR120, Lecture 1, March 2001S2-43MAR120, Section 2, December 2001 Updated Lagrange is especially useful for beam and shell structures with large rotations and for large strain plasticity problems; activated using the UPDATE parameter option UPDATED LAGRANGE

44. PAT328, Section 3, March 2001MAR120, Lecture 4, March 2001MAR120, Lecture 1, March 2001S2-44MAR120, Section 2, December 2001 Constant load incrementation Variable load incrementation (equilibrium) Variable load incrementation (arc length) LOAD INCREMENTATION CONTROL

45. PAT328, Section 3, March 2001MAR120, Lecture 4, March 2001MAR120, Lecture 1, March 2001S2-45MAR120, Section 2, December 2001 Using MSC.MARC all nonlinearities can appear together in any analysis NONLINEARITY RESULTS FROM CONTACT, GEOMETRIC AND/OR MATERIAL RESPONSE.

46. PAT328, Section 3, March 2001MAR120, Lecture 4, March 2001MAR120, Lecture 1, March 2001S2-46MAR120, Section 2, December 2001 MSC.MARC CONTINUOSLY IMPROVED