Karamba3D v1.3.3
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English 英文
  • Welcome to Karamba3D
  • 1: Introduction
    • 1.1: Installation
    • 1.2: Licenses
      • 1.2.1: Cloud Licenses
      • 1.2.2: Network Licenses
        • 1.2.2.1: Network license (archived)
      • 1.2.3: Temporary Licenses
      • 1.2.4: Standalone Licenses
  • 2: Getting Started
    • 2: Getting Started
      • 2.1: Karamba3D Entities
      • 2.2: Setting up a Structural Analysis
        • 2.2.1: Define the Model Elements
        • 2.2.2: View the Model
        • 2.2.3: Add Supports
        • 2.2.4: Define Loads
        • 2.2.5: Choose an Algorithm
        • 2.2.6: Provide Cross Sections
        • 2.2.7: Specify Materials
        • 2.2.8: Retrieve Results
      • 2.3: Physical Units
      • 2.4: Quick Component Reference
  • 3: In Depth Component Reference
    • 3.1: Model
      • 3.1.1: Assemble Model
      • 3.1.2: Disassemble Model
      • 3.1.3: Modify Model
      • 3.1.4: Connected Parts
      • 3.1.5: Activate Element
      • 3.1.6: Line to Beam
      • 3.1.7: Connectivity to Beam
      • 3.1.8: Index to Beam
      • 3.1.9: Mesh to Shell
      • 3.1.10: Modify Element
      • 3.1.11: Point-Mass
      • 3.1.12: Disassemble Element
      • 3.1.13: Make Beam-Set 🔷
      • 3.1.14: Orientate Element
      • 3.1.15: Select Element
      • 3.1.16: Support
    • 3.2: Load
      • 3.2.1: Loads
      • 3.2.2: Disassemble Mesh Load
      • 3.2.3: Prescribed displacements
    • 3.3: Cross Section
      • 3.3.1: Beam Cross Sections
      • 3.3.2: Shell Cross Sections
      • 3.3.3: Spring Cross Sections
      • 3.3.4: Disassemble Cross Section 🔷
      • 3.3.5: Beam-Joint Agent 🔷
      • 3.3.6: Beam-Joints 🔷
      • 3.3.7: Eccentricity on Beam and Cross Section 🔷
      • 3.3.8: Modify Cross Section 🔷
      • 3.3.9: Cross Section Range Selector
      • 3.3.10: Cross Section Selector
      • 3.3.11: Cross Section Matcher
      • 3.3.12: Generate Cross Section Table
      • 3.3.13: Read Cross Section Table from File
    • 3.4: Material
      • 3.4.1: Material Properties
      • 3.4.2: Material Selection
      • 3.4.3: Read Material Table from File
      • 3.4.4: Disassemble Material 🔷
    • 3.5: Algorithms
      • 3.5.1: Analyze
      • 3.5.2: AnalyzeThII 🔷
      • 3.5.3: Analyze Nonlinear WIP
      • 3.5.4: Large Deformation Analysis
      • 3.5.5: Buckling Modes 🔷
      • 3.5.6: Eigen Modes
      • 3.5.7: Natural Vibrations
      • 3.5.8: Optimize Cross Section 🔷
      • 3.5.9: BESO for Beams
      • 3.5.10: BESO for Shells
      • 3.5.11: Optimize Reinforcement 🔷
      • 3.5.12: Tension/Compression Eliminator 🔷
    • 3.6: Results
      • 3.6.1: ModelView
      • 3.6.2: Deformation-Energy
      • 3.6.3: Nodal Displacements
      • 3.6.4: Principal Strains Approximation
      • 3.6.5: Reaction Forces 🔷
      • 3.6.6: Utilization of Elements 🔷
      • 3.6.7: BeamView
      • 3.6.8: Beam Displacements 🔷
      • 3.6.9: Beam Forces
      • 3.6.10: Resultant Section Forces
      • 3.6.11: ShellView
      • 3.6.12: Line Results on Shells
      • 3.6.13: Result Vectors on Shells
      • 3.6.14: Shell Forces
    • 3.7: Export 🔷
      • 3.7.1: Export Model to DStV 🔷
    • 3.8 Utilities
      • 3.8.1: Mesh Breps
      • 3.8.2: Closest Points
      • 3.8.3: Closest Points Multi-dimensional
      • 3.8.4: Cull Curves
      • 3.8.5: Detect Collisions
      • 3.8.6: Get Cells from Lines
      • 3.8.7: Line-Line Intersection
      • 3.8.8: Principal States Transformation 🔷
      • 3.8.9: Remove Duplicate Lines
      • 3.8.10: Remove Duplicate Points
      • 3.8.11: Simplify Model
      • 3.8.12: Element Felting 🔷
      • 3.8.13: Mapper 🔷
      • 3.8.14: Interpolate Shape 🔷
      • 3.8.15: Connecting Beams with Stitches 🔷
      • 3.8.16: User Iso-Lines and Stream-Lines
  • Troubleshooting
    • 4.1: Miscellaneous Questions and Problems
      • 4.1.1: Installation Issues
      • 4.1.2: Purchases
      • 4.1.3: Licensing
      • 4.1.4: Runtime Errors
      • 4.1.5: Definitions and Components
      • 4.1.6: Default Program Settings
    • 4.2: Support
  • Appendix
    • A.1: Release Notes
      • Work in Progress Versions
      • Version 1.3.3
      • Version 1.3.2 build 190919
      • Version 1.3.2 build 190731
      • Version 1.3.2 build 190709
      • Version 1.3.2
    • A.2: Background information
      • A.2.1: Basic Properties of Materials
      • A.2.2: Additional Information on Loads
      • A.2.3: Tips for Designing Statically Feasible Structures
      • A.2.4: Hints on Reducing Computation Time
      • A.2.5: Natural Vibrations, Eigen Modes and Buckling
      • A.2.6: Approach Used for Cross Section Optimization
    • A.3: Bibliography
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  1. 3: In Depth Component Reference
  2. 3.5: Algorithms

3.5.6: Eigen Modes

Previous3.5.5: Buckling Modes 🔷Next3.5.7: Natural Vibrations

Last updated 4 years ago

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Karamba3D’s “EigenMode”-component allows to calculate eigenmodes and corresponding eigenvalues of structures (see fig. 3.5.6.1).

The input parameters are a model, the index of the first eigenmode to be computed and the number of desired eigenmodes. The model which comes out on the right side lists the computed eigenmodes as result-cases. Thus they can be superimposed using the “ModelView”-component for form-finding or structural optimization. All loads which were defined on the input model get discarded. The determination of eigenshapes can take some time in case of large structures or many modes to be calculated. Grasshopper has no “Cancel”-button. Therefore you should save your model before activating the component.

The number of different eigenmodes in a structure equals the number of degrees of freedom. In case of beams there are six degrees of freedom per node, with only trusses attached, a node possesses three degrees of freedom. Fig. 3.5.6.2 shows the first nine eigenmodes of a triangular beam mesh that is fixed at its lower corners. In the upper left corner of fig. 3.5.6.2 one sees the undeformed shape. The higher the index of an eigenmode the more folds it exhibits.

The eigenvalues represent a measure for the resistance of a structure against being deformed to the corresponding eigenform. Values of zero or nearly zero signal rigid body modes. In case that the “Analyze”- or “AnalyzeThII”-components complain about a kinematic structure the eigenforms can be used to detect those kinematic modes.

Again the displacements of the eigenmodes get scaled such that the largest displacement-component corresponds to 1.

Fig. 3.5.6.1: Left: 14th eigen-mode with strain display enabled. Right: EigenMode-component in action
Fig. 3.5.6.2: Undeformed geometry (upper left corner) and the first nine eigen-modes of the structure