김경종
268 lines
6.1 KiB
Markdown
268 lines
6.1 KiB
Markdown
<!-- source-page: 231 -->
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# Three-dimensional solid continuum elements
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<details>
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<summary>text_image</summary>
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4 ×3 4×
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×1 2×
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1 2
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</details>
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CIN3D8
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<details>
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<summary>text_image</summary>
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4
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×3
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7
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4×
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3
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8
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×1
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1
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5
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2×
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6
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2
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</details>
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CIN3D12R
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<details>
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<summary>text_image</summary>
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4
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×3
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7
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4×
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3
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8
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×1
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1
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5
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2×
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6
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2
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</details>
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CIN3D18R
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This shows the scheme in the layer closest to the 1–2–3–4 face. The integration points in the second layer are numbered consecutively.
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<!-- source-page: 232 -->
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<!-- source-page: 233 -->
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# 28.4 Warping elements
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• “Warping elements,” Section 28.4.1
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• “Warping element library,” Section 28.4.2
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<!-- source-page: 234 -->
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<!-- source-page: 235 -->
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# 28.4.1 WARPING ELEMENTS
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Product: Abaqus/Standard
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# References
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• “Meshed beam cross-sections,” Section 10.6.1
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• \*SOLID SECTION
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# Overview
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Warping elements:
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• are used to model an arbitrarily shaped beam cross-section profile for use with Timoshenko beams;
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• are used in conjunction with the beam section generation procedure described in “Meshed beam cross-sections,” Section 10.6.1; and
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• model linear elastic behavior only.
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# Typical applications
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Warping elements are special-purpose elements that are used to discretize a two-dimensional model of a beam cross-section. This two-dimensional cross-section model is used in Abaqus/Standard to calculate the out-of-plane component of the warping function, as well as relevant sectional stiffness and mass properties that are required in a subsequent beam analysis in either Abaqus/Standard or Abaqus/Explicit. Applications include any structure whose overall behavior is beam-like, yet the cross-section is nonstandard or includes multiple materials. Examples include the cross-section of a ship for performing whipping analysis, a beam model of an airfoil-shaped rotor blade or wing, a laminated I-beam, etc.
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# Choosing an appropriate element
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To mesh an arbitrarily shaped solid beam cross-section Abaqus/Standard offers two elements: a 3-node linear triangle, WARP2D3, and a 4-node bilinear quadrilateral, WARP2D4. Adjacent elements in the cross-sectional mesh must share common nodes; mesh refinement using multi-point constraints is not allowed.
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# Naming convention
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Warping elements are named as follows:
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<!-- source-page: 236 -->
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<details>
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<summary>flowchart</summary>
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```mermaid
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graph TD
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A["WARP"] --> B["2D"]
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B --> C["3"]
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C --> D["number of nodes"]
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B --> E["two-dimensional"]
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B --> F["warping elements"]
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```
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</details>
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For example, WARP2D4 is 4-node warping element in two dimensions.
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# Defining the element’s section properties
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You use a solid section definition to define the section properties. You must associate these properties with a region of your model. No additional data are necessary.
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Input File Usage: \*SOLID SECTION, ELSET=name
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where the ELSET parameter refers to a set of warping elements.
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# Assigning a material definition to a set of warping elements
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You must associate a linear elastic material definition with each warping element section definition. Optionally, you can associate a material orientation definition with the section (see “Orientations,” Section 2.2.5).
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Only isotropic linear elasticity (“Defining isotropic elasticity” in “Linear elastic behavior,” Section 22.2.1) or orthotropic linear elasticity for warping elements (“Defining orthotropic elasticity for warping elements” in “Linear elastic behavior,” Section 22.2.1) are valid material models for warping elements.
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Input File Usage: \*SOLID SECTION, ELSET=name, MATERIAL=name, ORIENTATION=name
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<!-- source-page: 237 -->
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# 28.4.2 WARPING ELEMENT LIBRARY
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Product: Abaqus/Standard
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# References
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• “Meshed beam cross-sections,” Section 10.6.1
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• \*SOLID SECTION
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# Overview
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This section provides a reference to the warping elements available in Abaqus/Standard.
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# Element types
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WARP2D3 3-node linear two-dimensional warping element WARP2D4 4-node bilinear two-dimensional warping element
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Active degree of freedom
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3, representing the out-of-plane warping function
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Additional solution variables
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None.
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# Nodal coordinates required
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X, Y
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# Element property definition
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Input File Usage: \*SOLID SECTION
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# Element-based loading
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There is no loading for these element types.
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# Element output
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No output is available for these element types. The two-dimensional warping elements are used to calculate the out-of-plane warping function for beams using a meshed cross-section. This warping function can be viewed in the Visualization module of Abaqus/CAE. The derivatives of the warping function are used to calculate the shear strain and stress at the integration points of the elements due to torsion.
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<!-- source-page: 238 -->
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# Node ordering on elements
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<details>
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<summary>text_image</summary>
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Y
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X
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</details>
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<details>
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<summary>text_image</summary>
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1
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2
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3
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</details>
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3 - node element
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<details>
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<summary>text_image</summary>
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1
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2
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3
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4
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</details>
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4 - node element
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# Numbering of integration points for output
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<details>
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<summary>text_image</summary>
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3
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× 1
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1
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2
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</details>
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3 - node element
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<details>
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<summary>text_image</summary>
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4
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×3
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4×
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×1
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2×
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1
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2
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3
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</details>
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4 - node element
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<!-- source-page: 239 -->
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# 29. Structural Elements
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Membrane elements 29.1
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Truss elements 29.2
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Beam elements 29.3
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Frame elements 29.4
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Elbow elements 29.5
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Shell elements 29.6
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<!-- source-page: 240 -->
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