김경종
21 KiB
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local directions 1 α = 45° y z x 2 1 3 4
Figure 2.2.4–4 Skew rebar defined relative to default local coordinate directions.
Input File Usage:
Use the following option to define skew rebars relative to the default projected local coordinate system in three-dimensional shell elements:
*REBAR, ELEMENT=SHELL, MATERIAL=mat, GEOMETRY=SKEW
Use the following option to define skew rebars relative to the default projected local coordinate system in general membrane elements:
*REBAR, ELEMENT=MEMBRANE, MATERIAL=mat, GEOMETRY=SKEW
Defining skew rebars relative to a user-defined local coordinate system
To define skew rebars relative to a user-defined local coordinate system, you specify the elements that contain the rebars; the cross-sectional area, A, of each rebar; the rebar spacing in the plane, s; the position of the rebars in the thickness direction (for shell elements only), measured from the midsurface of the shell (positive in the direction of the positive normal to the shell); and the angle, , in degrees, between the user-defined 1-direction and the rebars. See “Orientations,” Section 2.2.5, for a description of how the local coordinate system is calculated from the user-defined directions for definition of rebar in shells and membranes. A positive angle defines a rotation from local direction 1 to local direction 2 around the user-defined normal direction. For example, in a shell the following data would result in the skew rebar definition shown in Figure 2.2.4–5: A=0.01; s=0.1; distance of rebar from the shell midsurface=0.0; =30.; and the rebar definition refers to a local rectangular orientation defined to have its X-axis go through the point (−0.7071, 0.7071, 0.0), its X–Y plane include the point (−0.7071, −0.7071, 0.0), and an additional rotation of 0.0 degrees about the 3-direction.
Input File Usage:
Use the following option to define skew rebars relative to a user-defined local coordinate system in three-dimensional shell elements:
*REBAR, ELEMENT=SHELL, MATERIAL=mat, GEOMETRY=SKEW, ORIENTATION=name
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OR₁ α = 30° 4 2 3 1 1 2 y z x OR₂
OR = user-defined local directions 1, 2 = default local directions
Figure 2.2.4–5 Skew rebar defined relative to user-defined local coordinate directions.
Use the following option to define skew rebars relative to a user-defined local coordinate system in general membrane elements:
*REBAR, ELEMENT=MEMBRANE, MATERIAL=mat, GEOMETRY=SKEW, ORIENTATION=name
Defining rebars in axisymmetric shell and membrane elements
Rebars in an axisymmetric membrane must lie in the membrane reference surface, whereas rebars in an axisymmetric shell can lie in the shell reference surface or can be offset from the midsurface. Rebars in axisymmetric shells and membranes can be defined to have any orientation with respect to the r–z plane. See Figure 2.2.4–6 for an example of circumferential rebars and Figure 2.2.4–7 for an example of radial rebars in axisymmetric shells.
You specify the cross-sectional area, A, of each rebar; the rebar spacing, s; for shell elements the position of the rebars in the shell thickness direction, measured from the midsurface of the shell (positive in the direction of the positive normal to the shell); the angular orientation with respect to the r–z plane, , measured in degrees; and the radial position at which the rebar spacing is measured. The angular orientation is measured positive about the positive normal to the shell or membrane element. If the shell’s thickness is defined by nodal thicknesses (“Nodal thicknesses,” Section 2.1.3), the distance from the midsurface will be scaled by the ratio of the thickness defined by the nodal thickness to the thickness defined by the section definition. If the shell’s thickness is defined with a distribution (“Distribution definition,” Section 2.8.1) the distance from the midsurface will be scaled by the ratio of the element thickness defined by the distribution to the default thickness.
If an orientation angle other than 0 or 90° is specified for rebar in an axisymmetric shell or membrane without twist, Abaqus assumes that the rebars are balanced (i.e., half the rebar lie at the specified angle and the other half at an angle of ) and internal calculations are handled accordingly.
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z 10 circumferential rebar (90° orientation) middle surface of shell spacing of rebar n position in shell thickness direction 20 r C
Figure 2.2.4–6 Example of circumferential rebars in axisymmetric shell elements.
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middle surface of shell position in shell thickness direction z radial position where rebar spacing is given rebar spacing radial rebar (orientation angle 0°) r
Figure 2.2.4–7 Example of radial rebars in axisymmetric shell elements.
See “Rebar modeling in two dimensions,” Section 3.7.1 of the Abaqus Theory Guide, for details. If the symmetric model generation capability (“Symmetric model generation,” Section 10.4.1) is used to create a three-dimensional model from an axisymmetric shell or membrane model, only balanced rebars will be translated appropriately. The definition of balanced rebars in the axisymmetric model will result in balanced rebars in the three-dimensional model; such a translation with unbalanced rebars is
not available. Unbalanced rebars in generalized axisymmetric membranes with twist will be translated properly.
If the radial position for the rebar spacing is given, the total cross-sectional area of rebar will remain constant as the radial position changes; this behavior corresponds to the number of rebar in the circumferential direction remaining constant and implies that the thickness of the smeared layer of rebar decreases and that the spacing of the rebars increases as r increases (see Figure 2.2.4–7). If the radial position for the rebar spacing is omitted (or is set to zero), Abaqus assumes that the spacing of the rebar remains constant; the thickness of the corresponding smeared layer is held fixed such that t = A / s .
Input File Usage:
Use the following option to define rebars in an axisymmetric shell element:
* { \mathrm { R E B A R } } , { \mathrm { E L E M E N T } } { = } { \mathrm { A X I S H E L L } } , \ { \mathrm { M A T E R I A L } } { = } m a t
Use the following option to define rebars in an axisymmetric membrane element:
\scriptstyle * { \mathrm { R E B A R } } , { \mathrm { E L E M E N T } } = { \mathrm { A X I M E M B R A N E } } , { \mathrm { M A T E R I A L } } = m a t
Defining rebars in continuum elements
Two- or three-dimensional continuum (solid) elements can contain rebars; rebars cannot be defined in triangular, prism, tetrahedral, or infinite elements. If triangular or wedge-shaped elements are needed, collapsed quadrilateral or brick elements can be used. Be careful when collapsing elements that contain rebar. It is important to check that the location and orientation of the rebar are correct.
Rebars are defined as single bars or in layers. In the latter case the layer is a surface in each element; you provide the rebar orientation in the surface.
Defining layers of rebars in planar and axisymmetric continuum elements
By default, the rebars form a layer that lies in a surface that is at right angles to the plane of the model. You define the line where this rebar surface intersects the plane of the model, as described below.
The orientation of the rebars within the rebar surface is defined by giving an angle, in degrees, between the line of intersection in the plane of the model and the rebars. This angle is measured in physical three-dimensional space, not in isoparametric space. See “Rebar modeling in two dimensions,” Section 3.7.1 of the Abaqus Theory Guide, for details. The positive direction along the line of intersection is from the lower to the higher numbered element edge that is intersected, and a positive angle indicates rebars oriented down into the plane of the model (where the plane is parallel to the z-axis in plane strain analysis or the -axis for axisymmetric analysis), as shown in Figure 2.2.4–8.
If an orientation angle other than 0 or 90° is specified for rebar in an axisymmetric element without twist, it is assumed that the rebar in the element are balanced (i.e., half the rebar lie at the specified angle and the other half at the angle ).
Defining isoparametric rebars
For isoparametric rebars the intersection of the rebar layer with the plane of the model will lie along the mapping of a constant isoparametric line in the element. You specify the elements that contain the rebars; the cross-sectional area, A, of each rebar; the rebar spacing, s; the rebar orientation, (as described
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Orientation angle Rebar 1 4 Positive direction from lower to higher numbered edge. edge 4 rebar spacing y edge 1 x z z r edge 3 edge 2 edge 3 θ
Figure 2.2.4–8 Orientation of rebars in plane and axisymmetric solid elements.
above); the fractional distance from the edge, f (the ratio of the distance between the edge and the rebar to the distance across the element); and the edge number from which the rebars are defined. In addition, for axisymmetric elements you specify the radial position at which the rebar spacing is measured.
If the radial position for the rebar spacing is given for rebar in axisymmetric elements, the total cross-sectional area of rebar will remain constant as the radial position changes; this behavior corresponds to the number of rebar remaining constant as r increases; that is, the thickness of the smeared layer of rebar decreases as r increases. If the radial position for the rebar spacing is omitted (or is set to zero), Abaqus assumes that the spacing of the rebar remains constant; the thickness of the corresponding smeared layer is held fixed such that t = A / s .
Figure 2.2.4–9 shows an example of isoparametric rebar. In the isoparametric mapping of the element, the line of rebars is parallel to one of the edges of the element. In this figure the line for rebar layer A can be defined using edges 1 or 3 and rebar layer B can be defined by edges 2 or 4. The fractional distance from edge 1 for rebar layer A is the ratio f _ { 1 } = L _ { A 2 } / L _ { 2 } = L _ { A 4 } / L _ { 4 } ; ; alternatively, layer A can be defined from edge 3, so that f _ { 3 } = 1 . - L _ { A 2 } / L _ { 2 } = 1 . - L _ { A 4 } / L _ { 4 } .
Input File Usage:
Use the following option to define layers of isoparametric rebars in planar and axisymmetric continuum elements:
*REBAR, ELEMENT=CONTINUUM, MATERIAL=mat, GEOMETRY=ISOPARAMETRIC
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Edge Corner nodes 1 1-2 2 2-3 3 3-4 4 4-1 rebar layer B, defined with edge 2 or 4 L₄ L₄ rebar layer A, defined with edge 1 and f = L₄/₂ = L₄/₂ L₄ L₄ actual element y x L₂ rebar layer A rebar layer B Isoparametric mapping of element with rebar
Figure 2.2.4–9 Isoparametric rebar layer definition in solid elements.
Defining skew rebars
For skew rebars the intersection of the rebar layer with the plane of the model can intersect any two edges of an element. You specify the elements that contain the rebars; the cross-sectional area, A, of each rebar; the rebar spacing, s; and the rebar orientation, (as described above). In addition, for axisymmetric elements you specify the radial position at which the rebar spacing is measured. You also specify the fractional distance along the element edge, from the first node of the edge (as listed in Figure 2.2.4–10) to where the rebar layer intersects the edge, for all edges. Only the two values corresponding to the two edges that the rebar intersects can be nonzero.
Figure 2.2.4–10 shows an example of skew rebar. In the isoparametric mapping of the element, the line of rebars intersects two of the element edges. The intersection points are located by defining a fractional distance along each intersected edge. In this figure rebar layer A is defined by the ratio f _ { 1 } = L _ { A 1 } / L _ { 1 } along edge 1 and the ratio f _ { 2 } = L _ { A 2 } / L _ { 2 } along edge 2. Rebar layer B is defined by the ratio f _ { 3 } = L _ { B 3 } / L _ { 3 } along edge 3 and the ratio f _ { 4 } = L _ { B 4 } / L _ { 4 } along edge 4.
Defining skew rebars in continuum elements can increase the run time for an Abaqus/Explicit analysis significantly. The element’s stable time increment will, in most cases, be determined by the stable time increment of the rebar, which is proportional to the rebar length. The rebar length is determined by factors including the rebar surface position in the element, the rebar spacing, the rebar area, and the rebar orientation within the rebar surface. If a skew rebar in a continuum element is defined
| Edge | Corner nodes |
| 1 | 1-2 |
| 2 | 2-3 |
| 3 | 3-4 |
| 4 | 4-1 |
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rebar layer B defined with f₁ = 0, f₂ = 0, f₃ = L_B3 / L_3 and f₄ = L_B4 / L_4 rebar layer A defined with f₁ = L_A1 / L_1, f₂ = L_A2 / L_2, f₃ = 0 and f₄ = 0 rebar layer B 4 L_B3 L_B4 L_A1 L_A2 L_1 Actual element y x Isoparametric mapping of element with rebar
Figure 2.2.4–10 Skew rebar layer definition in solid elements.
such that it intersects two adjacent element edges, the resulting rebar length could be considerably less than the average element edge length, thus resulting in a very small element stable time increment.
Input File Usage: Use the following option to define layers of skew rebars in planar and axisymmetric continuum elements:
*REBAR, ELEMENT=CONTINUUM, MATERIAL=mat, GEOMETRY=SKEW
Defining single rebars in two-dimensional axisymmetric and generalized plane strain continuum elements
You can define single rebars in axisymmetric and generalized plane strain continuum elements. In this case the rebar is assumed to be at right angles with the plane of the model—in the thickness direction for generalized plane strain elements or the hoop direction for axisymmetric elements.
The intersection of the rebar with the plane of the model is defined by the fractional distances along edges 1 and 2 of the intersections of constant isoparametric lines that pass through the rebar location (see Figure 2.2.4–11). The fractional distances are measured from the first edge node listed in Figure 2.2.4–11.
| Edge | Corner nodes |
| 1 | 1-2 |
| 2 | 2-3 |
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single rebar defined with f₁ = l₁ / L₁ and f₂ = l₂ / L₂ 1 l₁ L₁ 2 3 4 L₂ l₂ y x Actual element Isoparametric mapping of element with rebar
Figure 2.2.4–11 Single rebar in a solid element.
You specify the elements that contain the rebars; the cross-sectional area, A, of each rebar; and the fractional distances locating the rebar’s position in the element, f _ { 1 } and f _ { 2 } .
Input File Usage: Use the following option to define single rebars in axisymmetric and generalized plane strain continuum elements:
* { \mathrm { R E B A R } } , { \mathrm { E L E M E N T } } { = } { \mathrm { C O N T I N U U M } } , { \mathrm { M A T E R I A L } } { = } m a t , { \mathrm { S I N G L E } }
Defining layers of rebars in three-dimensional continuum elements
By default, the rebars in three-dimensional continuum elements are defined as layers lying in surfaces. The surfaces are most easily defined with respect to the isoparametric mapped cube of the element. Therefore, you must consider how the rebar will be defined before generating the mesh; if the rebar surfaces are not taken into account in designing the mesh, the rebar definition can be very inefficient.
In the isoparametric mapped cube the rebar surface always has two edges (opposite to one another) that are parallel to an isoparametric direction. The isoparametric directions are defined in Figure 2.2.4–12. You specify this isoparametric direction (1, 2, or 3).
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actual element isoparametric mapping
Isoparametric direction: 1 (parallel to the 1-2 edge of the element and intersecting face 1-4-8-5)
| Edge | Corner nodes |
| 1 | 1-4 |
| 2 | 4-8 |
| 3 | 8-5 |
| 4 | 5-1 |
Isoparametric direction: 2 (parallel to the 1-4 edge of the element and intersecting face 1-5-6-2)
| Edge | Corner nodes |
| 1 | 1-5 |
| 2 | 5-6 |
| 3 | 6-2 |
| 4 | 2-1 |
Isoparametric direction: 3 (parallel to the 1-5 edge of the element and intersecting face 1-2-3-4)
| Edge | Corner nodes |
| 1 | 1-2 |
| 2 | 2-3 |
| 3 | 3-4 |
| 4 | 4-1 |
Figure 2.2.4–12 Isoparametric direction and edge definitions for three-dimensional elements.
A particular face of the element, which is perpendicular to this isoparametric direction in the isoparametric mapped cube, is used to define the position of the other two edges of the surface; the faces are defined in Figure 2.2.4–12, where the edges of the faces are also defined.
If isoparametric rebars are defined, the two edges of the rebar surface that are not parallel to the user-specified isoparametric direction will be parallel to one of the other two isoparametric directions; in the isoparametric-mapped cube one isoparametric coordinate is constant on the rebar surface. Figure 2.2.4–13 illustrates this concept with an element containing two layers of isoparametric rebars. The position of each surface is given by the fractional distance f from an edge of the face defined in Figure 2.2.4–12 for the isoparametric direction chosen; you must specify the edge from which the fractional distance is measured.
If skew rebars are defined, the two edges of the rebar surface, which are not parallel to the userspecified isoparametric direction, are generally not parallel to one of the other isoparametric directions. The positions of these two edges of the rebar surface are specified by the intersection of the rebar surface with edges of the intersecting face, defined in Figure 2.2.4–12, for the isoparametric direction chosen; the intersections are given by the fractional distance f along each edge of the face. (Note that the fractional distance is along the edge for skew rebars; for isoparametric rebars the fractional distances are measured from an edge.) The fractional distance along an edge is measured from the first node of the edge. All four fractional distances must be given, but only two can be nonzero.
The orientation angle, , of the rebars within the rebar layer is defined in the isoparametric-mapped cube; it is measured in degrees and is the angle between the line of intersection of the rebar surface with the face for the isoparametric direction chosen and the rebar. The positive direction of the line of intersection is from the lower numbered edge to the higher numbered edge; the positive direction for the rebars points into the elements. An example is shown in Figure 2.2.4–14. The orientation angle is defined in the rebar layer in the isoparametric-mapped cube; therefore, the definition is the same for isoparametric and skew rebar.
If the rebar layer is not flat in physical space, the orientation angle at each integration point may be different. Since it is possible to define only one orientation angle per element, an average value orientation angle for the element must be used; for reasonable meshes this approximation should not affect the results significantly.
Defining isoparametric rebars
You specify the elements that contain the rebars; the cross-sectional area, A, of each rebar; the rebar spacing, s; the rebar orientation, (as described above); the fractional distance, f, from the edge; the number of the edge from which the fractional distance is measured; and the isoparametric direction of the rebar surface.
Input File Usage:
Use the following option to define layers of isoparametric rebars in three-dimensional continuum elements:
*REBAR, ELEMENT=CONTINUUM, MATERIAL=mat, GEOMETRY=ISOPARAMETRIC