Karamba3D v2
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English 英文
  • Welcome to Karamba3D
  • New in Karamba3D 2.2.0
  • See Scripting Guide
  • See Manual 1.3.3
  • 1: Introduction
    • 1.1 Installation
    • 1.2 Licenses
      • 1.2.1 Cloud Licenses
      • 1.2.2 Network Licenses
      • 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
    • 3.0 Settings
      • 3.0.1 Settings
      • 3.0.2 License
    • 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: Dispatch Elements
      • 3.1.16: Select Elements
      • 3.1.17: Support
    • 3.2: Load
      • 3.2.1: General Loads
      • 3.2.2: Beam Loads
      • 3.2.3: Disassemble Mesh Load
      • 3.2.4: 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: Eccentricity on Beam and Cross Section 🔷
      • 3.3.6: Modify Cross Section 🔷
      • 3.3.7: Cross Section Range Selector
      • 3.3.8: Cross Section Selector
      • 3.3.9: Cross Section Matcher
      • 3.3.10: Generate Cross Section Table
      • 3.3.11: Read Cross Section Table from File
    • 3.4: Joint
      • 3.4.1: Beam-Joints 🔷
      • 3.4.2: Beam-Joint Agent 🔷
      • 3.4.3: Line-Joint
    • 3.5: Material
      • 3.5.1: Material Properties
      • 3.5.2: Material Selection
      • 3.5.3: Read Material Table from File
      • 3.5.4: Disassemble Material 🔷
    • 3.6: Algorithms
      • 3.6.1: Analyze
      • 3.6.2: AnalyzeThII 🔷
      • 3.6.3: Analyze Nonlinear WIP
      • 3.6.4: Large Deformation Analysis
      • 3.6.5: Buckling Modes 🔷
      • 3.6.6: Eigen Modes
      • 3.6.7: Natural Vibrations
      • 3.6.8: Optimize Cross Section 🔷
      • 3.6.9: BESO for Beams
      • 3.6.10: BESO for Shells
      • 3.6.11: Optimize Reinforcement 🔷
      • 3.6.12: Tension/Compression Eliminator 🔷
    • 3.7: Results
      • 3.7.1: ModelView
      • 3.7.2: Deformation-Energy
      • 3.7.3: Element Query
      • 3.7.4: Nodal Displacements
      • 3.7.5: Principal Strains Approximation
      • 3.7.6: Reaction Forces 🔷
      • 3.7.7: Utilization of Elements 🔷
        • Examples
      • 3.7.8: BeamView
      • 3.7.9: Beam Displacements 🔷
      • 3.7.10: Beam Forces
      • 3.7.11: Node Forces
      • 3.7.12: ShellView
      • 3.7.13: Line Results on Shells
      • 3.7.14: Result Vectors on Shells
      • 3.7.15: Shell Forces
      • 3.7.16 Results at Shell Sections
    • 3.8: Export 🔷
      • 3.8.1: Export Model to DStV 🔷
      • 3.8.2 Json / Bson Export and Import
    • 3.9 Utilities
      • 3.9.1: Mesh Breps
      • 3.9.2: Closest Points
      • 3.9.3: Closest Points Multi-dimensional
      • 3.9.4: Cull Curves
      • 3.9.5: Detect Collisions
      • 3.9.6: Get Cells from Lines
      • 3.9.7: Line-Line Intersection
      • 3.9.8: Principal States Transformation 🔷
      • 3.9.9: Remove Duplicate Lines
      • 3.9.10: Remove Duplicate Points
      • 3.9.11: Simplify Model
      • 3.9.12: Element Felting 🔷
      • 3.9.13: Mapper 🔷
      • 3.9.14: Interpolate Shape 🔷
      • 3.9.15: Connecting Beams with Stitches 🔷
      • 3.9.16: User Iso-Lines and Stream-Lines
      • 3.9.17: Cross Section Properties
    • 3.10 Parametric UI
      • 3.10.1: View-Components
      • 3.10.2: Rendered View
  • Troubleshooting
    • 4.1: Miscellaneous Questions and Problems
      • 4.1.0: FAQ
      • 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 2.2.0 WIP
      • 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: Workflow Examples
    • A.4: Bibliography
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  1. 3: In Depth Component Reference
  2. 3.7: Results

3.7.2: Deformation-Energy

Previous3.7.1: ModelViewNext3.7.3: Element Query

Last updated 3 years ago

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In mechanics, energy is equal to force times displacement parallel to its direction. Think of a rubber band: If you stretch it, you do work on it. This work gets stored inside the rubber and can be transformed into other kinds of energy. You may for example launch a small toy airplane with it: Then the elastic energy in the rubber gets transformed into kinetic energy. When stretching an elastic material the force to be applied at the beginning is zero and then grows proportionally to the stiffness and the increase of length of the material. The mechanical work is equal to the area beneath the curve that results from drawing the magnitude of the applied force over its corresponding displacement. In case of linear elastic materials this gives a rectangular triangle with the final displacement forming one leg and the final force being its other leg. From this one sees, that for equal final forces the elastic energy stored in a material decreases with decreasing displacements which corresponds to increasing stiffness.

Via the input “Elems|Ids” one can supply identifiers od elements of those parts for which the deformation energy shall be calculated. An empty list means that all elements are considered. The “LCase”-input lets one select the load-case for which results shall be retrieved. The structure of the data trees returned from the “D-Energy”-component (see fig. 3.7.2.1) contains one branch per element. A list of axial deformation energy and bending energy for each element is displayed. In case of shells the branches contain the in-plane or bending energy of each face of the shell.

36KB
Shell_BendingEnergy.gh
40KB
Shell_DeformationEnergy.gh
Fig. 3.7.2.1: Simply supported beam under axial and transversal point-load