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Bending operations are essential for many real-world applications. The bending functionality in
ACIS is easily incorporated in applications and is easily applied to any
ACIS entity.
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Entity bending bends a solid model around a given axis. In any bending operation, some material is stretched while other material is compressed, but the topology of the model is maintained.
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ACIS uses the concept of a neutral plane for bending. The neutral plane is defined by a neutral root, a bending axis, and a bending direction (Figure 1-5), and defines the location along which the material is neither stretched nor compressed during bending. A neutral plane is the location where the materiel is not stretched or compressed during bending. The material above the neutral plane (e.g., along the bending direction) is compressed and the material below the neutral plane is stretched. The location of a neutral plane varies with the type of material to be bent.
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The bending axis, denoted by
ba, and the bending direction, denoted by
bd, define the vector normal of the bending plane,
ba x bd. The bending axis and bending direction should be perpendicular to each other. The cross product of these two vectors also defines the positive and negative sides of the entity to be bent.
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Figure 1-5. Entity (Fixed-end) Bending
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neutral_root
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a position that, in conjunction with the bending axis and the bending direction, defines the location of neutral plane.
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bending_axis
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a vector that defines the rotational axis of bending action.
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bending_direction
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an auxiliary
SPAvector used to define a bending plane.
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bend_radius
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a real number that specifies the radius from the center of the bend to the neutral plane.
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bend_angle
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the angle in degrees that specifies the amount to bend.
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bend_width
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the width of the bend region. The
bend_radius,
bend_angle, and
bend_width are used to determine the region to be bent. Because only two parameters are independent,
bend_width can be optional. Assigning zero or negative values to any of the three parameters implies that the parameter value is to be ignored. It is always desirable to use just two parameters among these three. However, if only the
bend_radius is given, the entire entity is bent. These parameters are related by:
bend_width=bend_radius*bend_angle
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Both the
api_entity_blend function and the
entity:bend Scheme extensions have a center bend flag and a means of further specifying the bend region. The center bend flag is used to control the final orientation of the bend entity. When set, material on both sides of the bending plane is equally bent by half of the
bend_angle. When not set, the negative side remains fixed (called "fixed end bending"), and only the positive side is bent by
bend_angle. To handle cases in which the bend region consists of a number of disjoint regions, not all of which are to be bent, the bend region can be further specified through an array of positions. These positions must lie on a face used as part of bending, or within the bent material itself.
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To fully support localized bending, the entity bending functions recognize the connectivity between portions of the entity to be bent. Based on the connectivity, portions are either bent or transformed to maintain integrity of the entity. Hence the bending operation performs intelligently, and models the real-world bending process more closely than would otherwise be the case.
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The ability to automatically recognize connectivity eliminates the requirement that an end-user application specify a complete list of bend positions. This ability not only guarantees that a valid entity is produced but also is essential for feature-based applications. Such applications can effortlessly reproduce a bending operation after performing entity modifications that may change the connectivity of the bending portions.
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Bending operations generally involve complicated material deformations. The nature of material deformation is well captured in the bending function. Also, deformed faces are converted to analytic faces to enhance performance. For example, planes are bent into cylinders; cylinders are bent into tori, etc. This capability is critical for modeling complicated piping models with enhanced performance and reduced data complexity.
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