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1. Structural Analysis Overview
1.1. Structural Analysis Types
1.1.1. Selecting Elements
1.1.2. Selecting Material Models
1.2. Damping
1.2.1. Alpha and Beta Damping (Rayleigh Damping)
1.2.2. Material-Dependent Alpha and Beta Damping (Rayleigh Damping)
1.2.3. Damping Ratio
1.2.4. Constant Structural Damping Coefficient
1.2.5. Mode-Dependent Damping Ratio
1.2.6. Viscoelastic Material Damping
1.2.7. Element Damping
1.3. Solution Method
2. Structural Static Analysis
2.1. Linear vs. Nonlinear Static Analyses
2.2. Performing a Static Analysis
2.2.1. Build the Model
2.2.2. Set Solution Controls
2.2.3. Set Additional Solution Options
2.2.4. Apply the Loads
2.2.5. Solve the Analysis
2.2.6. Review the Results
2.3. Example: Static Analysis (GUI Method)
2.3.1. Problem Description
2.3.2. Problem Specifications
2.3.3. Problem Sketch
2.4. Example: Static Analysis (Command Method)
2.5. Where to Find Other Examples
3. Modal Analysis
3.1. Uses for Modal Analysis
3.2. Understanding the Modal Analysis Process
3.3. Building the Model for a Modal Analysis
3.4. Applying Loads and Obtaining the Solution
3.4.1. Enter the Solution Processor
3.4.2. Define Analysis Type and Options
3.4.3. Apply Loads
3.4.4. Specify Load Step Options
3.4.5. Solve
3.4.6. Participation Factor Table Output
3.4.7. Modal Mass and Kinetic Energy Output
3.4.8. Exit the Solution Processor
3.5. Reviewing the Results
3.5.1. Points to Remember
3.5.2. Reviewing Results Data
3.5.3. Option: Listing All Frequencies
3.5.4. Option: Display Deformed Shape
3.5.5. Option: Line Element Results
3.5.6. Option: Contour Displays
3.5.7. Option: Tabular Listings
3.5.8. Other Capabilities
3.6. Applying Prestress Effects in a Modal Analysis
3.6.1. Performing a Prestressed Modal Analysis from a Linear Base Analysis
3.6.2. Performing a Prestressed Modal Analysis from a Large-Deflection Base Analysis
3.7. Modal Analysis Examples
3.7.1. An Example Modal Analysis (GUI Method)
3.7.2. An Example Modal Analysis (Command or Batch Method)
3.7.3. Brake-Squeal (Prestressed Modal) Analysis
3.7.4. Reuse of Jobname.modesym in the QRDAMP Eigensolver
3.7.5. Calculate the Complex Mode Contribution Coefficients (CMCC)
3.7.6. Where to Find Other Modal Analysis Examples
3.8. Comparing Mode-Extraction Methods
3.8.1. Block Lanczos Method
3.8.2. PCG Lanczos Method
3.8.3. Supernode (SNODE) Method
3.8.4. Subspace Method
3.8.5. Unsymmetric Method
3.8.6. Damped Method
3.8.7. QR Damped Method
3.9. Modal Analysis Tools for Subsequent Mode-Superposition Analysis
3.9.1. Using the Residual Vector or the Residual Response Method to Improve Accuracy
3.9.2. Reusing Eigenmodes
3.9.3. Generating and Using Multiple Loads in Mode-Superposition Analyses
3.9.4. Restarting a Modal Analysis
3.9.5. Enforced Motion Method for Mode-Superposition Transient and Harmonic Analyses
3.9.6. Using Mode Selection
3.9.7. Node-based Mode File Scoping for Mode-Superposition Analysis
4. Harmonic Analysis
4.1. Uses for Harmonic Analysis
4.2. Commands Used in a Harmonic Analysis
4.3. Overview of Harmonic Analysis Solution Methods
4.3.1. Full Harmonic Analysis Method
4.3.2. Frequency-Sweep Harmonic Analysis via the Variational Technology Method
4.3.3. Frequency-Sweep Harmonic Analysis via the Krylov Method
4.3.4. Mode-Superposition Harmonic Analysis Method
4.3.5. Restrictions for All Harmonic Analysis Methods
4.4. Full Harmonic Analysis
4.4.1. Building the Model
4.4.2. Applying Loads and Obtaining the Solution
4.4.3. Reviewing the Results
4.4.4. Examples: Full Harmonic Analysis
4.5. Frequency-Sweep Harmonic Analysis via the Variational Technology method
4.5.1. Using the Frequency-Sweep Method with Frequency-Dependent Material Properties
4.5.2. Example: Frequency-Sweep Harmonic Analysis of a Cantilever Beam
4.6. Frequency-Sweep Harmonic Analysis via the Krylov Method
4.6.1. Modeling and Loading Considerations
4.6.2. Krylov Method Implemented using Mechanical APDL Commands
4.6.3. Krylov Method Implemented via Macros
4.7. Mode-Superposition Harmonic Analysis
4.7.1. Obtaining the Modal Solution
4.7.2. Obtaining the Mode-Superposition Harmonic Solution
4.7.3. Expanding the Mode-Superposition Solution
4.7.4. Reviewing the Results of the Expanded Solution
4.7.5. Example: Mode-Superposition Harmonic Analysis
4.8. Applying Prestress Effects in a Harmonic Analysis
4.8.1. Prestressed Harmonic Analysis
4.8.2. Prestressed Full-Harmonic Analysis Using the PSTRES Command (Legacy Procedure)
5. Transient Dynamic Analysis
5.1. Preparing for a Transient Dynamic Analysis
5.2. Two Solution Methods for Transient Analysis
5.2.1. Full Method for Transient Analysis
5.2.2. Mode-Superposition Method for Transient Analysis
5.3. Performing a Full Transient Dynamic Analysis
5.3.1. Build the Model
5.3.2. Establish Initial Conditions
5.3.3. Set Solution Controls
5.3.4. Apply the Loads
5.3.5. Save the Load Configuration for the Current Load Step
5.3.6. Repeat Steps 3-6 for Each Load Step
5.3.7. Save a Backup Copy of the Database
5.3.8. Start the Transient Solution
5.3.9. Exit the Solution Processor
5.3.10. Review the Results
5.3.11. Example: Full Transient Dynamic Analysis
5.4. Performing a Mode-Superposition Transient Dynamic Analysis
5.4.1. Build the Model
5.4.2. Obtain the Modal Solution
5.4.3. Obtain the Mode-Superposition Transient Solution
5.4.4. Expand the Mode-Superposition Solution
5.4.5. Review the Results of the Expanded Solution
5.4.6. Example: Mode-Superposition Transient Dynamic Analysis
5.5. Performing a Prestressed Transient Dynamic Analysis
5.5.1. Prestressed Full Transient Dynamic Analysis
5.5.2. Prestressed Mode-Superposition Transient Dynamic Analysis
5.6. Transient Dynamic Analysis Options
5.6.1. Guidelines for Integration Time Step
5.6.2. Automatic Time Stepping
5.6.3. Transient Dynamic Analysis Settings Based on Application
5.7. Where to Find Other Examples
6. Spectrum Analysis
6.1. Understanding Spectrum Analysis
6.1.1. Response Spectrum
6.1.2. Dynamic Design Analysis Method (DDAM)
6.1.3. Power Spectral Density
6.1.4. Deterministic vs. Probabilistic Analyses
6.1.5. Calculating Elemental Results for Large Models
6.2. Performing a Single-Point Response Spectrum (SPRS) Analysis
6.2.1. Step 1: Build the Model
6.2.2. Step 2: Obtain the Modal Solution
6.2.3. Step 3: Obtain the Spectrum Solution
6.2.4. Step 4: Review the Results
6.2.5. Running Multiple Spectrum Analyses
6.3. Example: Spectrum Analysis (GUI Method)
6.3.1. Problem Description
6.3.2. Problem Specifications
6.3.3. Problem Sketch
6.3.4. Procedure
6.4. Example: Spectrum Analysis (Command or Batch Method)
6.4.1. Single-Point Response Spectrum Analysis on a Beam Structure
6.4.2. Single-Point Response Spectrum Analysis on a Piping Structure with Excitation Along X, Y, and Z Directions
6.4.3. Single-Point Response Spectrum Analysis on a Piping Structure with Excitation along X, Y, and Z Directions Separately by Reusing the Existing Mode File
6.4.4. Single-Point Response Spectrum Analysis on a Piping Structure with Excitation Along X, Y, and Z Directions, missing mass effect, Elcalc = YES and SpecCum = NO on SPOPT command
6.4.5. Single-Point Response Spectrum Analysis on a Piping Structure with Excitation Along X, Y, and Z Directions, missing mass effect, Elcalc = YES and SpecCum = YES on SPOPT command: method 1
6.4.6. Single-Point Response Spectrum Analysis on a Piping Structure with Excitation Along X, Y, and Z Directions, missing mass effect, Elcalc = YES on SPOPT command: method 2
6.4.7. Single-Point Response Spectrum Analysis of a Cylindrical Tank Filled with Water Excitation Along X Direction Using Rock Spectrum
6.5. Where to Find Other Examples
6.6. Performing a Random Vibration (PSD) Analysis
6.6.1. Obtain the PSD Solution
6.6.2. Combine the Modes
6.6.3. Review the Results
6.6.4. Example: Random Vibration (PSD) Analysis
6.7. Performing a DDAM Spectrum Analysis
6.7.1. Step 3: Obtain the Spectrum Solution
6.7.2. Step 4: Review the Results
6.7.3. Example: DDAM Spectrum Analysis
6.8. Performing a Multi-Point Response Spectrum (MPRS) Analysis
6.8.1. Step 3: Obtain the Spectrum Solution
6.8.2. Step 5: Combine the Modes
6.8.3. Step 6: Review the Results
6.8.4. Example: Multi-Point Response Spectrum (MPRS) Analysis
7. Buckling Analysis
7.1. Types of Buckling Analyses
7.1.1. Nonlinear Buckling Analysis
7.1.2. Eigenvalue Buckling Analysis
7.2. Performing a Nonlinear Buckling Analysis
7.2.1. Applying Load Increments
7.2.2. Automatic Time Stepping
7.2.3. Unconverged Solution
7.2.4. Hints and Tips for Performing a Nonlinear Buckling Analysis
7.3. Performing a Post-Buckling Analysis
7.4. Eigenvalue Buckling Analysis Process
7.4.1. Step 1. Build the Model
7.4.2. Step 2. Obtain the Static Solution
7.4.3. Step 3. Obtain the Eigenvalue Buckling Solution
7.4.4. Step 4. Review the Results
7.5. Example: Eigenvalue Buckling Analysis (GUI Method)
7.5.1. Problem Description
7.5.2. Problem Specifications
7.5.3. Problem Sketch
7.6. Example: Eigenvalue Buckling Analysis (Command Method)
7.7. Where to Find Other Examples
8. Nonlinear Structural Analysis
8.1. Forward Solving vs. Inverse Solving
8.2. Causes of Nonlinear Behavior
8.2.1. Changing Status (Including Contact)
8.2.2. Geometric Nonlinearities
8.2.3. Material Nonlinearities
8.3. Understanding Nonlinear Analyses
8.3.1. Conservative vs. Nonconservative Behavior; Path Dependency
8.3.2. Substeps
8.3.3. Load Direction in a Large-Deflection Analysis
8.3.4. Rotations in a Large-Deflection Analysis
8.3.5. Nonlinear Transient Analyses
8.4. Using Geometric Nonlinearities
8.4.1. Stress-Strain
8.4.2. Stress Stiffening
8.5. Modeling Material Nonlinearities
8.5.1. Nonlinear Materials
8.6. Performing a Nonlinear Static Analysis
8.6.1. Building the Model
8.6.2. Setting Solution Controls
8.6.3. Setting Additional Solution Options
8.6.4. Applying Loads
8.6.5. Solving the Analysis
8.6.6. Reviewing the Results
8.6.7. Terminating and Restarting a Running Job
8.7. Nonlinear Static Analysis with Inverse Solving
8.7.1. Inverse-Solving Applications
8.7.2. Building the Model in an Inverse-Solving Analysis
8.7.3. Applying Loads in an Inverse-Solving Analysis
8.7.4. Obtaining the Solution in an Inverse-Solving Analysis
8.7.5. Using the Solutions from an Inverse-Solving Analysis
8.7.6. Reviewing Inverse-Solving Analysis Results
8.7.7. Restarting an Inverse-Solving Analysis and Linear Perturbation
8.7.8. Inverse-Solving Limitations
8.8. Performing a Nonlinear Transient Analysis
8.8.1. Build the Model
8.8.2. Apply Loads and Obtain the Solution
8.8.3. Review the Results
8.8.4. Example: Nonlinear Transient Analysis
8.9. Restarts
8.10. Using Nonlinear Elements
8.10.1. Element Birth and Death
8.11. Unstable Structures
8.11.1. Using Nonlinear Stabilization
8.11.2. Using the Arc-Length Method
8.11.3. Nonlinear Stabilization vs. the Arc-Length Method
8.12. Guidelines for Nonlinear Analysis
8.12.1. Setting Up a Nonlinear Analysis
8.12.2. Overcoming Convergence Problems
8.13. Monitoring Result Section Data During Solution
8.13.1. Result Section Overview
8.13.2. Anchor Point and Local Coordinate System
8.13.3. Generating the Result Section
8.13.4. Outputting Section Results
8.13.5. Result Section Limitations
8.13.6. Example: Result Section in a Bolt Thread Model
8.14. Example: Nonlinear Analysis
8.14.1. Where to Find Other Examples
9. Linear Perturbation Analysis
9.1. Understanding Linear Perturbation
9.2. General Procedure for Linear Perturbation Analysis
9.2.1. Process Flow for a Linear Perturbation Analysis
9.2.2. The Base (Prior) Analysis
9.2.3. First Phase of the Linear Perturbation Analysis
9.2.4. Second Phase of the Linear Perturbation Analysis
9.2.5. Stress Calculations in a Linear Perturbation Analysis
9.2.6. Reviewing Results of a Linear Perturbation Analysis
9.2.7. Downstream Analysis Following the Linear Perturbation Analysis
9.3. Considerations for Load Generation and Controls
9.3.1. Generating and Controlling Mechanical Loads
9.3.2. Generating and Controlling Non-mechanical Loads
9.4. Considerations for Perturbed Stiffness Matrix Generation
9.5. Considerations for Rotating Structures
9.5.1. Stationary Reference Frame
9.5.2. Rotating Reference Frame
9.6. Example Inputs for Linear Perturbation Analysis
9.7. Where to Find Other Examples
10. Gasket Joints Simulation
10.1. Performing a Gasket Joint Analysis
10.2. Finite Element Formulation
10.2.1. Element Topologies
10.2.2. Thickness Direction
10.3. Interface Elements
10.3.1. Element Selection
10.3.2. Applications
10.4. Material Definition
10.4.1. Material Characteristics
10.4.2. Input Format
10.4.3. Temperature Dependencies
10.4.4. Plotting Gasket Data
10.5. Meshing Interface Elements
10.6. Solution Procedure and Result Output
10.6.1. Typical Gasket Solution Output Listing
10.7. Reviewing the Results
10.7.1. Reviewing Results in POST1
10.7.2. Reviewing Results in POST26
10.8. Example: Element Verification Analysis
11. Composites
11.1. Modeling Composites
11.1.1. Selecting the Composite Element Type
11.1.2. Defining the Layered Configuration
11.1.3. Specifying Failure Criteria for Composites
11.1.4. Composite Modeling and Postprocessing Tips
12. Beam and Pipe Cross Sections
12.1. Overview of Cross Sections
12.2. Commands Used for Cross Sections
12.2.1. Defining a Section and Associating a Section ID Number
12.2.2. Defining Cross Section Geometry and Setting the Section Attribute Pointer
12.2.3. Meshing a Line Model with BEAM188 or BEAM189 Elements
12.3. Creating Cross Sections
12.3.1. Using the Beam Tool to Create Common Cross Sections
12.3.2. Creating Custom Cross Sections with a User-Defined Mesh
12.3.3. Creating Custom Cross Sections with Mesh Refinement and Multiple Materials
12.3.4. Defining Composite Cross Sections
12.3.5. Defining a Tapered Beam or Pipe
12.3.6. Defining a Noncircular Pipe
12.4. Using Nonlinear General Beam Sections
12.4.1. Defining a Nonlinear General Beam Section
12.4.2. Considerations for Using Nonlinear General Beam Sections
12.5. Using Preintegrated Composite Beam Sections
12.5.1. Defining a Composite Beam Section
12.5.2. Considerations for Using Composite Beam Sections
12.5.3. Example: Composite Beam Section Input
12.6. Managing Cross Section and User Mesh Libraries
12.7. Cross Section Analysis Examples
12.7.1. Example: Lateral Torsional Buckling Analysis
12.7.2. Example: Problem with Cantilever Beams
13. Shell Analysis and Cross Sections
13.1. Understanding Cross Sections
13.2. Creating a Shell Cross Section
13.2.1. Defining a Section and Associating a Section ID Number
13.2.2. Defining Layer Data
13.2.3. Overriding Program Calculated Section Properties
13.2.4. Specifying a Shell Thickness Variation (Tapered Shells)
13.2.5. Setting the Section Attribute Pointer
13.2.6. Associating an Area with a Section
13.2.7. Using the Shell Tool to Create Sections
13.2.8. Managing Cross-Section Libraries
13.3. Creating a Preintegrated General Shell Section
13.3.1. Defining the Preintegrated Shell Section
13.3.2. Considerations for Using Preintegrated Shell Sections
14. Reinforcing and Direct Element Embedding
14.1. Reinforcing Workflow
14.1.1. Reinforcing Assumptions
14.1.2. Modeling Options for Reinforcing
14.1.3. Defining Reinforcing Sections and Elements
14.1.4. Updating Reinforcing Elements
14.1.5. Applying an Initial State to Reinforcing Elements
14.1.6. Reinforcing Simulation and Postprocessing
14.2. Direct-Embedding Workflow
14.2.1. Assumptions About Direct Embedding
14.2.2. Defining Direct Embedding of Line Elements
14.2.3. Defining Direct Embedding of Shell Elements
14.2.4. Element Size Recommendations
14.2.5. Limitations
14.2.6. Direct-Embedding Simulation and Postprocessing
14.3. Comparing Reinforcing and Direct-Embedding Workflows
14.3.1. Typical Usages for Reinforcing vs. Direct Embedding
15. Modeling Hydrostatic Fluids
15.1. Hydrostatic Fluid Element Features
15.2. Defining Hydrostatic Fluid Elements
15.3. Material Definitions and Loading
15.3.1. Fluid Materials
15.3.2. Loads and Boundary Conditions
15.4. Example Model Using Hydrostatic Fluid Elements
15.5. Results Output
A. Example: Analyses with Multiple Imposed Rotations
A.1. Problem Description
A.2. Example: Imposed Rotations
A.2.1. Sequentially Applied Rotations
A.2.2. Simultaneously Applied Rotations
B. Example: Energy Calculations in Transient and Harmonic Analyses
B.1. Problem Description
B.2. Analysis Assumptions and Modeling Considerations
B.3. Input Listings
B.3.1. Harmonic Analysis
B.3.2. Transient Analysis
B.3.3. Results Comparison