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. 3.6: Results

3.6.4: Principal Strains Approximation

Previous3.6.3: Nodal DisplacementsNext3.6.5: Reaction Forces 🔷

Last updated 4 years ago

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Karamba3D includes shell elements from which principal stress lines can be retrieved (see section . In case of single layer grid shells made up of beams the "Approximate Principal Strains"-component can be used to determine the approximate principal strain directions of such structures (see fig. 3.6.5.1). It works on arbitrary sets of deformed points.

The calculation of principal strains is based on the assumption of a continua. When applied to nodes connected with linear elements the result can thus only result in a qualitative picture -- therefore the term "Approximate".

The "Approximate Principal Strains"-component expects as input a reference model (input-plug "Model") and the same model in a deformed configuration (input-plug "def.Model"). The deformed model can be the output of a "ModelView"-component. Hand over a list of points to the input-plug "Point" where principal strain directions shall be computed. For each point in this list the following two steps are applied: First those three nodes of the reference model that do not lie on a line and have minimum distance to the given point are determined. Second the strains in the sides of the thus found triangle determine the principal strain directions -- plane stress is assumed. The conversion of first (output-plug "VT1") and second principal strains (output-plug "VT2") to vectors occurs in such a way that they align with the average displacement of the triangle that defines the corresponding strain-state. The size of the vectors emanating from "VT1" and "VT2" can be scaled by providing a factor in the input-plug "Scale".

The principal strains are tangents to the principal stress lines of a structure. Use e.g. Daniel Hambleton's "SPM Vector Components" (see ) to retrieve these lines from the strain-vector-field.

http://www.grasshopper3d.com/group/spmvectorcomponents
3.6.12)
Fig. 3.6.5.1: Approximation of principal strains in a grid of beams.