김경종
250 lines
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Markdown
250 lines
15 KiB
Markdown
<!-- source-page: 1271 -->
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• Materials: Brittle cracking and shear failure models are also not supported. Rayleigh mass proportional damping is not supported.
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• Elements: The Eulerian formulation is implemented only for EC3D8R and EC3D8RT elements.
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• Element import: Eulerian elements are not available for import.
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• Double-sided contact: Penetration of Eulerian material through the contact interface can occur in some cases involving Eulerian material contacting Lagrangian shell or membrane elements. This type of contact introduces complexity because the sign of the outward normal direction must be determined on the fly as material approaches the Lagrangian element; contact with either side of the element is potentially allowable. You should simplify the contact problem wherever possible by using Lagrangian solid elements instead of shell or membrane elements, since the outward normal direction at solid element faces is unique. For example, if a model involves Eulerian material flowing around a rigid Lagrangian obstacle, mesh the obstacle with solid elements rather than shell elements.
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• Contact penetration: In some cases Eulerian material may penetrate through the Lagrangian contact surface near corners. This penetration should be limited to an area equal to the local Eulerian element size. Penetration can be minimized by refining the Eulerian mesh or adding a fillet to the Lagrangian mesh with radius equal to the local Eulerian element size.
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• Contact types: Eulerian-Lagrangian contact does not support Lagrangian beam elements, Lagrangian pipe elements, Lagrangian truss elements, or analytical rigid surfaces.
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• Contact import: Import of the Eulerian-Lagrangian contact states is not supported.
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• Thermal contact: Gap radiation and gap conductance as a function of clearance are not supported.
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• Contact output: Contact variables are output only for the Lagrangian side of Eulerian-Lagrangian interfaces.
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• Surface loads: You cannot use the Eulerian material surface type for general surface loading. However, distributed loads such as pressure can be applied to surfaces defined on Eulerian element faces.
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• Mass scaling: You cannot apply mass scaling to Eulerian elements.
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• Heat transfer: Use coupled temperature-displacement EC3D8RT Eulerian elements to model a fully coupled thermal-stress analysis. Adiabatic conditions are assumed in Eulerian materials when EC3D8R elements are used.
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• Output: Total strain (LE) is not available for Eulerian elements in field or history output, but it can be accessed via the utility routine VGETVRM.
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• Subcycling: You cannot include Eulerian elements in subcycling zones.
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# Input file template
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The following example illustrates a coupled Eulerian-Lagrangian analysis of a Lagrangian boat floating on Eulerian water. A conforming mesh is assumed, so Eulerian material initialization is achieved by whole element filling. Material-specific interactions between the Lagragian body and the Eulerian materials are implemented: a contact interaction is defined between the boat and water, but contact
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<!-- source-page: 1272 -->
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between the boat and air is ignored. Output is requested for Eulerian volume fractions, Eulerian element-averaged stress, and material stress.
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```txt
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*HEADING
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...
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*ELEMENT, TYPE=C3D8R, ELSET=BOAT_ELSET
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element definitions for Lagrangian boat
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*ELEMENT, TYPE=EC3D8R, ELSET=ALL_EULERIAN
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element definitions for whole Eulerian mesh
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*ELSET, NAME=AIR_ELSET
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data lines giving Eulerian elements that are initially filled with air
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*ELSET, NAME=WATER_ELSET
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data lines giving Eulerian elements that are initially filled with water
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**
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*MATERIAL, NAME=AIR
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material definition for air
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*MATERIAL, NAME=WATER
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material definition for water
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**
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*EULERIAN SECTION, ELSET=ALL_EULERIAN
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AIR
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WATER
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**
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*INITIAL CONDITIONS, TYPE=VOLUME FRACTION
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AIR_ELSET, AIR, 1.0
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WATER_ELSET, WATER, 1.0
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*INITIAL CONDITIONS, TYPE=STRESS, GEOSTATIC
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data lines to define water pressure due to gravity
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**
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*SURFACE, NAME=WATER_SURFACE, TYPE=EULERIAN MATERIAL
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WATER
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*SURFACE, NAME=BOAT_SURFACE
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BOAT_ELSET
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**
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*STEP
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*DYNAMIC, EXPLICIT
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*DLOAD
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data lines to define gravity load
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**
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*CONTACT
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*CONTACT INCLUSIONS
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BOAT_SURFACE, WATER_SURFACE
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**
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```
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<!-- source-page: 1273 -->
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\*OUTPUT, FIELD \*ELEMENT OUTPUT EVF, SVAVG, PEEQVAVG \*END STEP
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# Additional references
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• Benson, D. J., “Computational Methods in Lagrangian and Eulerian Hydrocodes,” Computer Methods in Applied Mechanics and Engineering, vol. 99, pp. 235–394, 1992.
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• Benson, D. J., “Contact in a Multi-Material Eulerian Finite Element Formulation,” Computer Methods in Applied Mechanics and Engineering, vol. 193, pp. 4277–4298, 2004.
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• Peery, J. S., and D. E. Carroll, “Multi-Material ALE methods in Unstructured Grids,” Computer Methods in Applied Mechanics and Engineering, vol. 187, pp. 591–619, 2000.
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<!-- source-page: 1274 -->
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<!-- source-page: 1275 -->
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# 14.1.2 DEFINING EULERIAN BOUNDARIES
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Products: Abaqus/Explicit Abaqus/CAE
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# References
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• “Eulerian analysis,” Section 14.1.1
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• “Eulerian elements,” Section 32.14.1
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• \*EULERIAN BOUNDARY
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• “Defining an Eulerian boundary condition,” Section 16.10.21 of the Abaqus/CAE User’s Guide
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# Overview
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In an Eulerian analysis you can define independent inflow and outflow conditions at an Eulerian boundary. An Eulerian boundary condition:
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• can be used to control the flow of material into the Eulerian domain;
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• can be used to define a pressure field at the boundary of an Eulerian domain;
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• can be used to apply a nonreflecting boundary condition at the truncated artificial boundary to simulate an infinite domain; and
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• is associated with a surface defined on the Eulerian mesh boundary where inflow or outflow occurs.
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# Defining the Eulerian boundary
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Eulerian boundaries must be defined at surfaces on the Eulerian mesh boundary. You cannot define multiple Eulerian boundaries at the same surface.
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Input File Usage: \*EULERIAN BOUNDARY surface name
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Abaqus/CAE Usage: Load module: Create Boundary Condition: Category: Other, Types for Selected Step: Eulerian boundary: select region
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# Defining the inflow condition
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You can use the inflow condition to control the flow of material into the Eulerian domain.
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# Free inflow
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If no Eulerian boundary is defined, material can flow into the Eulerian domain freely; and the material content and the state of each inflow material are equal to that which presently exists within the element. If an Eulerian boundary is defined, free inflow is the default inflow condition.
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Input File Usage: \*EULERIAN BOUNDARY, INFLOW=FREE
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Abaqus/CAE Usage: Eulerian boundary condition editor: Flow type: Inflow, Inflow: Free
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<!-- source-page: 1276 -->
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# No inflow
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You can specify an Eulerian boundary where no inflow can occur—no material or void can flow into the Eulerian domain through the specified boundary. The normal component of the velocity is set to zero if the velocity is directed inward at the boundary, while the tangential component of the velocity remains unchanged.
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Input File Usage: \*EULERIAN BOUNDARY, INFLOW=NONE
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Abaqus/CAE Usage: Eulerian boundary condition editor: Flow type: Inflow, Inflow: None
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# Void inflow
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You can also specify a boundary through which inflow can occur but the influx volume contains only void. Due to the inflow of void, an Eulerian domain that is initially completely full of material might become partially full during the analysis.
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Input File Usage: \*EULERIAN BOUNDARY, INFLOW=VOID
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Abaqus/CAE Usage: Eulerian boundary condition editor: Flow type: Inflow, Inflow: Void
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# Defining the outflow condition
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The outflow condition can be used to simulate an unbounded domain by reducing reflection at the outflow boundary or to prescribe a pressure field at the boundary.
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# Free outflow
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If no Eulerian boundary condition is specified, material can flow out of the Eulerian domain freely; and the material content and the state of each outflow material are equal to that which presently exists within the element. If an Eulerian boundary condition is defined, free outflow is the default behavior if the void inflow condition is specified at the same surface.
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Input File Usage: \*EULERIAN BOUNDARY, OUTFLOW=FREE
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Abaqus/CAE Usage: Eulerian boundary condition editor: Flow type: Outflow, Outflow: Free
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# Nonreflecting outflow
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A nonreflecting outflow condition can be used in boundary value problems defined in unbounded domains or problems in which the region of interest is small in size compared to the surrounding medium. Like the infinite element formulation described in “Using solid medium infinite elements in dynamic analyses” in “Infinite elements,” Section 28.3.1, the nonreflecting outflow condition introduces additional normal and shear tractions on the domain boundary that are proportional to the normal and shear components of the velocity of the boundary. These boundary damping constants are chosen to minimize the reflection of dilatational and shear wave energy back into the finite element mesh. This condition does not provide perfect transmission of energy out of the mesh except in the case of plane body waves impinging orthogonally on the boundary in an isotropic medium. However, it usually provides acceptable modeling for most practical cases. An exception is the case when significant material transport occurs through the boundary, in which case this condition is not suitable to be used.
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<!-- source-page: 1277 -->
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Input File Usage: \*EULERIAN BOUNDARY, OUTFLOW=NONREFLECTING
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Abaqus/CAE Usage: Eulerian boundary condition editor: Flow type: Outflow, Outflow: Nonreflecting
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# Equilibrium outflow
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Equilibrium outflow is another outflow condition that can effectively reduce spurious reflection at artificial outflow boundaries in unbounded domains. It is assumed that the stress is zero-order continuous across the element faces on the boundary. Traction is applied to these element faces to balance the nodal forces created by the stress in the boundary elements. This condition is usually applied at the outflow boundary where the pressure distribution is unknown.
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Input File Usage: \*EULERIAN BOUNDARY, OUTFLOW=NONUNIFORM PRESSURE
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Abaqus/CAE Usage: Eulerian boundary condition editor: Flow type: Outflow, Outflow: Equilibrium
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# Zero-pressure outflow
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It is common in flow problems to specify a zero pressure at the outlet of the flow. Since the normal traction on the boundary contains the contribution from both the pressure and the shear stress, the natural boundary condition, also known as the “do-nothing condition,” is not sufficient to provide such a condition if the shear behavior of the flow is also considered. The zero pressure outflow condition applies a traction that counteracts the shear contribution and, thus, generates a uniformly distributed pressure field on the boundary. You can apply a distributed surface load (see “Surface tractions and pressure loads” in “Distributed loads,” Section 34.4.3) on the same boundary to specify a nonzero pressure. This is the default outflow condition if the inflow condition is not specified.
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Input File Usage: \*EULERIAN BOUNDARY, OUTFLOW=ZERO PRESSURE
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Abaqus/CAE Usage: Eulerian boundary condition editor: Flow type: Outflow, Outflow: Zero pressure
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# Using Eulerian boundaries in restart analyses
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You can define a new Eulerian boundary in a restart analysis, but you cannot specify a void inflow condition at this boundary. In addition, you cannot change the inflow condition at an existing Eulerian boundary to the void inflow condition in a restart analysis.
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<!-- source-page: 1278 -->
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<!-- source-page: 1279 -->
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# 14.1.3 EULERIAN MESH MOTION
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Products: Abaqus/Explicit Abaqus/CAE
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# References
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• “Eulerian surface definition,” Section 2.3.5
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• “Eulerian analysis,” Section 14.1.1
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• \*EULERIAN MESH MOTION
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• \*EULERIAN SECTION
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• \*SURFACE
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• “Defining an Eulerian mesh motion boundary condition,” Section 16.10.22 of the Abaqus/CAE User’s Guide, in the HTML version of this guide
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# Overview
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In a traditional Eulerian analysis, material flows through an Eulerian mesh that is fixed in space. Since it is stationary, the Eulerian mesh must be large enough to enclose the entire trajectory of interest. In some simulations, such as a tumbling liquid-filled bottle, this trajectory can be long, requiring a large Eulerian mesh whose elements are mostly empty. The Eulerian mesh motion feature allows the Eulerian mesh to move in space, following, expanding, and contracting to enclose a target object. This can greatly reduce mesh size and, hence, simulation cost. Mesh motion can also simplify modeling by ensuring that the entire trajectory of interest, which may be unpredictable, is indeed covered by the Eulerian mesh.
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# Activating mesh motion
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You can independently activate mesh motion for each Eulerian section in a model. The motion applies to all of the elements in the section.
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Input File Usage: \*EULERIAN MESH MOTION, ELSET=name
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Abaqus/CAE Usage: Load module: BC→Create, Category: Other, Types for Selected Step: Eulerian mesh motion: select an Eulerian part instance
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# Computing mesh motion
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The motion of the Eulerian mesh is computed using an internally constructed bounding box that encloses the entire Eulerian section. The bounding box has six degrees of freedom: translation of the box center and scaling of each of the three box dimensions.
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The bounding box is constructed in a local coordinate system. Its six degrees of freedom are also defined in this local system. The local coordinate directions remain fixed in space during the simulation. If no local coordinate system is specified, the local system coincides with the global system.
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Input File Usage: \*EULERIAN MESH MOTION, ORIENTATION= name
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<!-- source-page: 1280 -->
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Abaqus/CAE Usage: Load module: Eulerian mesh motion editor: Bounding Box Csys: Edit or Create
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# Defining the target object
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You use a surface to define the target object that the Eulerian mesh will follow. By default, the Eulerian mesh bounding box (and, hence, the Eulerian mesh) moves to enclose the surface at all times, subject to any constraints specified on the mesh motion. If the surface type is Lagrangian, the Eulerian mesh bounding box moves to enclose the surface nodes (see Figure 14.1.3–1). If the surface type is Eulerian, the Eulerian mesh bounding box moves to enclose the Eulerian material named in the surface definition (see Figure 14.1.3–2).
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Figure 14.1.3–1 Mesh motion, where the target object is the Lagrangian bottle.
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Figure 14.1.3–2 Mesh motion, where the target object is the Eulerian liquid.
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The Eulerian mesh may not fully enclose the target object due to:
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• constraints on the bounding box motion;
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