Basic Concepts and Definitions

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The topics in this section describe several key concepts within Patran geometry. It will be helpful to you to understand these concepts before you start building a geometry model.

Patran utilizes the concept of parametric space for simpler and more efficient internal computations. In parametric space, a curve is defined in terms of only one parametric axis, x1. A surface is defined in terms of two axes, x1 and x2. And a solid is defined in terms of the x1, x2, and x3 parametric axes. Every object has a size of exactly one on each parametric axis for which it is defined. Therefore, coordinates along these axes always range in value between 0 and 1.

You can use parametric space as a powerful modeling concept. Many Patran application forms and PCL functions allow you to specify parametric values rather than global XYZ values. For example, you can subdivide a highly curved surface along its parametric one-third point without having to make complex measurements in real space.

Note: Patran application forms refer to parametric coordinate values as C1, C2, and C3, rather than x1, x2, and x3.

For each curve, surface, or solid that you construct in Patran, the software derives a unique mapping function (F) that can translate between the object’s set of parametric coordinates and its more standard three-dimensional XYZ coordinates, as shown in the Patran viewport. The following illustration compares how a surface would look in parametric space with a realistic rendering in the viewport’s three-dimensional XYZ space.

Connectivity is the location and orientation of the parametric axes. The parametric axes x1, x2, and x3 have a unique orientation and location on each curve, surface, and solid. For example, the following two surfaces are identical, but their connectivity is different.

For a curve, there are two possible connectivity definitions. For a four-sided surface, there are a total of eight possible connectivity definitions. For a triparametric solid with six faces, there are a total of 24 possible connectivity definitions in Patran, three orientations at each of the eight vertices.

This section provides a detailed look at the characteristics of the geometric entities that you may select as building blocks.

• Surface: supported types include bi-parametric, general trimmed, simply trimmed, composite trimmed, and ordinary composite trimmed.

The following additional entities serve as frames of reference for geometry construction, rather than building blocks:

In Patran, all points are non-parameterized, dimensionless coordinate locations in three-dimensional XYZ space. You may use points by themselves to create point elements such as masses, and to construct higher-level geometric entities.

A curve has one parametric dimension in space. You can subdivide a curve into 1-D elements such as truss or beam elements, and you can use them in geometric construction. A curve has one parametric variable, ξ1, used to describe the location of any given point, P, along a curve, as shown below.

Patran supports simple and general surfaces.

In terms of parameterization, simple surfaces are two-dimensional point sets in three-dimensional global XYZ space. Any given point, P, on a surface can be located by the coordinates ξ1 and ξ2, as shown.

Each trimmed surface has an invisible associated parent surface that defines its parameterization and curvature.

There are several types of general surfaces: trimmed surfaces may be either planar (stays in a two-dimensional plane) or 3D; composite surfaces merge a collection of surfaces into one entity defined within a specific boundary.

Patran supports simple tri-parametric solids and general boundary representation solids.

Most solids created with the Geometry application are tri-parametric. In terms of parameterization, each solid is a three-dimensional point set in global XYZ space. For any given point in the solid, P can be located by the three coordinates, ξ1, ξ2, and ξ3, whose values range between 0 and 1 inside the solid.

• General Boundary Representation (B-rep) solids are formed from an arbitrary number of surfaces that define a completely closed volume. B-rep solids can include interior voids or holes.

Vectors and planes serve as useful entities for constructing geometry models.

• Vectors define an origin and an endpoint, for use in modeling operations such as translating geometry, or constructing geometry between two points. You may create vectors in Patran using numerous Create/Vector options.

• Planes are particularly useful in symmetric operations, such as creating a mirror image of geometry components. Patran provides numerous Create/Plane options.

Coordinate systems define a coordinate frame of reference used in modeling operations. Patran automatically defines a global rectangular (Cartesian) coordinate system in every database. The system origin, 0, is indicated by a white plus sign in the viewport. The global axes in the lower left of the viewport indicate the current orientation of the global coordinate system.

In addition to the default global coordinate system, you may create your own local coordinate systems. For example, if you need to create a cylinder perpendicular to a curved surface, creating a cylindrical coordinate system that is orthogonal (perpendicular) to the surface can make this task much easier.

The Geometry option Create/Coord allows you to create three types of local coordinate systems:

Coordinate frame angles for the cylindrical and spherical coordinate frames (that is, θ and Φ) are always expressed in degrees.

Later, when creating a finite element model, coordinate systems help establish the principal directions in which your analysis results are displayed. Alternate coordinate systems are very simple to use in Patran, and they are closely integrated with Patran's geometric modeling operations. Nearly all of those options involving coordinate data support the ability to enter a coordinate system to interpret the input values
you supply.

Topological entities determine adjacency between geometric entities, and identify subcomponents of higher-order entities. While each geometric entity has a separate number, (such as Curve 1 or Surface 2), Patran assigns numbers to topological entities that are relative to adjacent higher order objects. For example, the input Surface 4.2 in a form databox denotes Edge number 2 of Surface 4.

Each curve, surface, and solid in Patran has a set of defined topological entities, as follows:

Topological congruency is a prerequisite for creating a valid finite element mesh for your analysis model. It ensures that all regions of the model’s geometry are made into one connected entity during the meshing process so that the model yields meaningful analysis results. If the finite element model is not topologically congruent, "cracks" result, invalidating the analysis results.

Vertex	Defines the topological endpoint of a curve, or a corner of a surface or a solid. A vertex is a subcomponent of a curve. (Every point references a vertex, but a vertex does not have to reference a point.)
Edge	Defines the topologic curve on a surface or a solid. An edge is a subcomponent of a surface or solid.
Face	Defines the topologic surface of a solid. A face is a subcomponent of a solid.

To be topologically congruent, adjacent regions of geometry in your model must share matching boundaries and vertices. In addition, the geometric components must form a closed surface or solid region, and there must be no overlap between adjacent regions. The Geometry application provides several methods for verifying congruency and correcting incongruencies. For more information, see Ensuring Topological Congruency.