김경종
192 lines
15 KiB
Markdown
192 lines
15 KiB
Markdown
<!-- source-page: 1061 -->
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# 11.7.1 SELECTIVE SUBCYCLING
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# Product: Abaqus/Explicit
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# References
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• “Explicit dynamic analysis,” Section 6.3.3
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• “Fully coupled thermal-stress analysis,” Section 6.5.3
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• \*SUBCYCLING
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# Overview
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Selective subcycling:
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• allows different time increments to be used for different groups of elements;
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• reduces run time for an analysis when a small region of elements in the model controls the stable time increment; and
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• is invoked by defining the subcycling zones.
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# Introduction
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The selective subcycling method in Abaqus/Explicit is based on domain decomposition. In this method subcycling zones are defined that remain unchanged during the analysis. The domain-level parallelization method (“Parallel execution in Abaqus/Explicit,” Section 3.5.3) is invoked automatically when subcycling zones are defined. Each subcycling zone, as well as the non-subcycling zone, is independently decomposed into the user-specified number of parallel domains. The “master” domains are defined as the parallel domains that are derived from the non-subcycling zone and are integrated with the largest stable time increment. The remaining parallel domains derived from the subcycling zones are integrated using smaller time increments, or “subcycles.”
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The subcycle time increment sizes are chosen as integer divisors of the time increment used in the master parallel domains. Therefore, all parallel domains exactly reach the same time points as the master parallel domains. During subcycling, nodes that lie on the interface with the non-subcycling zone require special treatment. The velocity at the interface nodes is taken from the non-subcycling zone and is constant during subcycles. This produces an interface node displacement field that varies linearly during the subcycles.
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# Defining subcycling zones
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Subcycling zones are defined by element sets. You can include all element types in these sets except Eulerian element types EC3D8R and EC3D8RT. However, all parallel domains must have at least one deformable element to provide the stable time increment. Abaqus/Explicit issues an error message if there is no deformable element in a parallel domain. You can define an arbitrary number of subcycling zones. However, some modeling features cannot be split between subcycling zones. Abaqus/Explicit
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<!-- source-page: 1062 -->
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automatically merges subcycling zones that contain features that cannot be split. Subcycling zones are merged together when:
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• the zones overlap;
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• the zones share the same nodes;
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• a node is in one subcycling zone, but its adjacent nodes are in a different subcycling zone;
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• subcycling zones are involved in the same constraint equation, connector, or rigid body; or
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• general contact is specified in the analysis.
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When subcycling zones are merged, the smallest stable time increment among the merged zones is used. The constraint, connector, or rigid body is always assigned to the subcycling zone if any one of its nodes is involved in that subcycling zone. Since the domain-level parallelization method is used, all restrictions on parallel domain decomposition apply to subcycling zones. These restrictions prevent certain features from being split across master parallel domains, as well as parallel domains that contain the subcycling zones (See “Parallel execution in Abaqus/Explicit,” Section 3.5.3). Analytical rigid surfaces cannot be included in the general contact domain when a subcycling zone is defined.
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Efficient selective subcycling requires proper choice of subcycling zones. For each subcycling zone, the time increment size should be small compared to the non-subcycling zone, producing a large number of subcycles. The number of subcycles is the ratio of the stable time increment size in the non-subcycling zone to the stable time increment sizes in the subcycling zones. In addition to a large number of subcycles, the number of elements in a subcycling zone should generally be small compared to the total number of elements in the model for optimal performance benefit. If a majority of elements in the model are in subcycling zones, there will not be much performance benefit.
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Input File Usage: Use the following option to define a subcycling zone: \*SUBCYCLING, ELSET=element\_set\_name
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# Accuracy of results
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The subcycling algorithm used in Abaqus/Explicit provides sufficient accuracy for most complex dynamic models. However, because of the relatively large time increment size used in the non-subcycling zone and the interpolation used on zone interface nodes, subcycling solutions can introduce a truncation error, which may slightly alter results compared with traditional solutions. This error should not affect the overall dynamic behavior of the model. Special attention should be given to the interface between the subcycling zone and non-subcycling zone when general contact (see “Defining general contact interactions in Abaqus/Explicit,” Section 36.4.1) is involved. It is not necessary to define a pair of surfaces that have the potential for contacting each other within the same zone. However, to minimize truncation errors, it is highly recommended that a single surface that has the potential for contacting others not be split across the zones.
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# Output and mass scaling
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Output (see “Output,” Section 4.1.1) and mass scaling (see “Mass scaling,” Section 11.6.1) are always performed at the same time points reached by all parallel domains.
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<!-- source-page: 1063 -->
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Input file template
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```txt
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*HEADING
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...
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*ELSET, ELSET=ZONE1
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...
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*SUBCYCLING, ELSET=ZONE1
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**************************
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*STEP
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*DYNAMIC, EXPLICIT
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Data line to specify the time period of the step
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...
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*END STEP
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```
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<!-- source-page: 1064 -->
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<!-- source-page: 1065 -->
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# 11.8 Steady-state detection
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• “Steady-state detection,” Section 11.8.1
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<!-- source-page: 1066 -->
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<!-- source-page: 1067 -->
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# 11.8.1 STEADY-STATE DETECTION
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# Product: Abaqus/Explicit
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# References
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• “Output,” Section 4.1.1
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• \*STEADY STATE DETECTION
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• \*STEADY STATE CRITERIA
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# Overview
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Steady-state detection:
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• can be used to detect the time in a quasi-static uni-directional Abaqus/Explicit simulation when a steady-state condition has been reached and then terminate the simulation;
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• can be used to output quantities that are useful in tracking the progress of a uni-directional Abaqus/Explicit simulation; and
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• is available only for three-dimensional analysis.
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# Introduction
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Many types of uni-directional processes are used to transform preformed shapes into forms more suitable for further processing. The most common examples are rolling, wire drawing, and extrusion processes. Since the processes are usually carried out at low speeds, explicit dynamic procedures such as those in Abaqus/Explicit are often used to model the processes as quasi-static. The analyses usually consist of a workpiece that is formed into a desired shape by any number of rollers or other forming surfaces along a primary direction. The forming surfaces are usually modeled as rigid bodies. For rolling simulations the rigid body reference node is usually defined at the center of the roller. The mesh of the workpiece is often extruded and may be constructed of multiple layers of material. As the workpiece progresses through the forming surfaces, the shape eventually reaches a constant state. The position where the workpiece exits the final forming surface is referred to as the exit plane and is usually aligned with the rigid body reference node of the final forming surface. As soon as this constant shape is reached, the analysis is considered to have reached steady state. The force and torque on the final forming surfaces at this steady-state condition have also reached constant values or oscillate about constant values. A significant computational savings can be achieved by detecting the steady-state condition and halting the analysis either immediately or as soon as the steady-state cross-section progresses beyond the exit plane to a position referred to as the cutting plane.
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# Mesh requirements
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The workpiece mesh is required to meet certain conditions for use with the steady-state detection capability. First, the mesh must be topologically regular in the primary direction. In other words, the
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mesh should consist of multiple planes of elements with each plane being similar to its adjacent leading and trailing planes in that it contains the same number of elements and the same element topology in the cross-section. Furthermore, each element in a plane is connected to elements in leading and trailing planes that reference the same material and section properties. Therefore, meshes with multiple materials and section properties are permitted, but any row of elements in the primary direction must be of the same type and must reference the same material and section properties (see Figure 11.8.1–1).
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<details>
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<summary>text_image</summary>
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2
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3 1
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rolling direction
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exit plane
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cutting plane
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material 1
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material 2
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</details>
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Figure 11.8.1–1 Acceptable multiple-material extruded mesh for a rolling analysis.
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# Steady-state detection criteria sampling
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To determine if steady state has been reached, steady-state detection “norms” are calculated, which represent an averaged value of a variable of interest over the cross-section of the workpiece as material passes through a given position along the primary direction. This position is referred to as the exit plane and usually coincides with the position of the last rigid forming tool (e.g., roller) that the workpiece passes through. The normal of the exit plane is by definition coincident with the primary direction. The time intervals at which the norms are sampled vary depending on whether the rolling analysis is modeled in an Eulerian or Lagrangian manner.
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# Sampling in a Lagrangian analysis
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In a Lagrangian-based analysis (which may include adaptive meshing employed on a Lagrangian domain) the steady-state norms are calculated as the trailing control node of each plane of elements passes the exit plane. Figure 11.8.1–2 illustrates the control node definitions.
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<!-- source-page: 1069 -->
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<details>
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<summary>text_image</summary>
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first steady-state
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rolling plane
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trailing control
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node of the first plane
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leading control
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node of the first plane
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</details>
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Figure 11.8.1–2 Control node positioning.
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The time period of norm sampling is, therefore, based on the frequency at which the planes of elements cross the exit plane. For output purposes the values of the norms are assumed to remain constant between the times at which successive control nodes pass the exit plane.
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# Sampling in an Eulerian analysis
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An Eulerian analysis employs a control volume approach in which material is drawn from an inflow Eulerian boundary and is pushed or pulled out through an outflow boundary. Adaptive mesh domains are defined on the workpiece, and sliding boundary regions are defined to model contact between the workpiece and forming tools such as rollers. See “ALE adaptive meshing: overview,” Section 12.2.1, for details of adaptive meshing techniques. The mesh remains relatively stationary while the material moves through the exit plane. The time period between sampling is, therefore, based on the progress of the material moving through the exit plane. To determine a time period in a manner consistent with the Lagrangian case, the sampling period is determined by dividing the characteristic element length of the workpiece by the speed of the material flow. This period is roughly the time it takes for material to pass through an element of typical size.
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# Steady-state detection norm definitions
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An individual norm is considered to have achieved steady state if its relative change in value over three consecutive planes does not exceed a tolerance. You can provide the norm tolerances when you define
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<!-- source-page: 1070 -->
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the steady-state criteria, or default values of tolerances can be chosen by Abaqus/Explicit. The norms can be output by requesting their identifiers listed in the definitions below.
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# Equivalent plastic strain norm
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The plastic strain norm of a plane of elements is defined by summing the product of the equivalent plastic strain and the element volume of each element on the plane, then dividing by the total volume of the elements on the plane. This norm provides a weighted average of the equivalent plastic strain for the plane. The identifier for the equivalent plastic strain norm is SSPEEQ.
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# Spread norm
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The spread norm of a plane of elements is computed as the largest of the area moments of inertia of the cross-section of the plane. In determining the spread norm, the cross-section of the plane of elements is determined by projecting the element faces whose normals originally coincided with the primary direction onto the exit plane. The area moments of inertia are then determined about the centroid of the section in the directions of the original principal axes of the cross-section. The identifier for the spread norm is SSSPRD.
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# Force norm
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The force norm is computed by averaging the magnitude of the force at the rigid body reference node of a forming tool, such as the exit roller, over the time period between sampling points. You provide the rigid body reference node and force direction. The identifier for the force norm is SSFORC.
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# Torque norm
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The torque norm is computed by averaging the magnitude of the torque at the rigid body reference node of a forming tool, such as the exit roller, over the time period between sampling points. You provide the rigid body reference node and torque direction. The identifier for the torque norm is SSTORQ.
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# Requesting steady-state detection during an analysis
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You must define the criteria that are used to determine if steady state has been reached. Abaqus/Explicit will halt the analysis based on the achievement of steady state.
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# Steady-state detection
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A steady-state detection definition is used to define the elements in the workpiece, the primary direction of the workpiece, the cutting position, and the type of sampling used. The primary direction is defined by specifying the direction cosines with respect to the global Cartesian coordinate system. The cutting position is defined by specifying the global coordinates of a point lying in the cutting plane. The normal to the cutting plane is assumed to coincide with the primary direction. Once steady state has been detected, the analysis is terminated when the plane of the workpiece that was first detected to have reached steady state has progressed to the cutting plane. You can choose the sampling method used, as described below.
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